Develop Simplified Methodology to Determine Heat Transfer ... · flooring system based on the particular installation method. The flooring system tests investigated the use of insulation

ASHRAE Research Project 1036

Develop Simplified Methodology to Determine Heat Transfer Design

Impacts Associated with Common Installation Alternatives for Radiant

Conduit

FINAL REPORT

Kirby S. Chapman

And

Jacque D. Shultz

National Gas Machinery Laboratory Kansas State University

245 Levee Drive Manhattan, KS 66502

June 22, 2002

NGML Final Report: RP-1036 Radiant Conduit…

ii

ABSTRACT

This goal of this research project was to develop a thorough understanding of surface heat-transfer rates emitted from a selection of radiant heating panels, and to develop a simplified method of calculating heat transfer rates from these systems. Working with the Project Monitoring Subcommittee, the research team designed a radiant panel test chamber and identified a series of test scenarios that focused on the most common floor panel systems. The test data was used to determine the heat transfer rate from the flooring system based on the particular installation method. The flooring system tests investigated the use of insulation at various depths, the use of heat transfer plates, and, in the case of concrete slab installations, the depth of the radiant conduit beneath the surface of the concrete slab. The systems were tested at to determined “ramp-up” times and then at steady state conditions.

The test chamber was developed to provide the experimental data for the hydronic systems, although the results are neutral to the radiant conduit, i.e., hydronic or electric cabling systems. A computer data-acquisition system recorded floor and wall surface temperatures, chamber interior dry-bulb air temperatures, and the measured values from heat flux sensors specifically designed and built for this application. The data collection system was rigorously calibrated using known energy sources in the sub-floor space of the test chamber. This calibration procedure ensured that the data collected with the heat flux sensors was a true and a true and accurate representation of the heat flux delivered by the particular radiant panel system. After completing the experimental data collection, the heat transfer rate from the floor panel system was calculated.

While the original goal of this project was to develop a general formulation of heat transfer rates from a large variety of radiant conduit systems, the PMS and research team realized that this original goal was too aggressive for the limited resources available for this project. Instead, the PMS and research team focused on understanding the heat transfer rate from the most common systems. In all cases, the research team attempted to present the heat transfer rate in terms of the input power so that the results would apply equally to electrical and hydronic radiant systems . This defines the system as a radiant panel independent of the input conditions, and focuses on the required loads as the primary requirements.

The results from this project provide a predictive method of calculating the heat transfer rate from the most common radiant heating systems. The time required for each system to reach steady-state conditions is also presented in this report, by comparing all systems and showing how the construction of the system impacts the time required to reach steady state conditions.


iii

TABLE OF CONTENTS

ABSTRACT ................................................................................................................................................................II TABLE OF CONTENTS ......................................................................................................................................... III DEFINITIONS ........................................................................................................................................................... IV INTRODUCTION.........................................................................................................................................................1 LITERATURE REVIEW .............................................................................................................................................5 TEST SETUP ............................................................................................................................................................11

Experimental: ..............................................................................................................................................11 Numerical:....................................................................................................................................................12

EXPERIMENTAL SETUP .....................................................................................................................................12 Pre-Panel Equipment .................................................................................................................................13 Panel Equipment ........................................................................................................................................14 Loading Equipment ....................................................................................................................................16 Instrumentation ...........................................................................................................................................16

TESTING METHODS...............................................................................................................................................20 CALIBRATION ....................................................................................................................................................20 TESTING PROCEDURE ......................................................................................................................................23 NUMERICAL METHODS .....................................................................................................................................23

RESULTS AND ANALYSIS....................................................................................................................................24 DATA REDUCTION.............................................................................................................................................24 ANALYSIS ..........................................................................................................................................................24

Heat flux .......................................................................................................................................................25 Thermal Delivery with Heat Transfer Plates ...........................................................................................25 Ramp-up time to steady-state...................................................................................................................27 Numerical Results ......................................................................................................................................29

CONCLUSION ..........................................................................................................................................................32 FUTURE WORK .......................................................................................................................................................34 ACKNOWLEDGEMENTS .......................................................................................................................................35 REFERENCES ..........................................................................................................................................................36 APPENDIX A.............................................................................................................................................................38 APPENDIX B.............................................................................................................................................................39


iv

DEFINITIONS

BTUH (BTU/hr) - British Thermal Units per Hour

A measure of thermal energy as input or output from a thermal system

Characteristic length - Ratio of a solids volume to surface area

Electrical Heating Panel - Radiant system utilizing electrical resistance to generate an internal heat created from an applied voltage

Heat Flux (BTU/hr·ft²) - Heat transfer rate per unit area

Heat Flux Sensor - Thermocouple stack separated by a given distance applied to a surface for measuring heat transfer through the surface by measuring the temperature difference between the thermocouples.

Hydronic System - Radiant system utilizing a temperature controlled liquid passing through a series of tubes for means of energy transfer for heating and/or cooling

Mean Radiant Temperature (MRT) -

Defined as “uniform surface temperature of a radiantly black enclosure in which an occupant would exchange the same amount of radiant heat as in the actual non-uniform space”. (ASHRAE, 1981)

Nusselt number - Dimensionless measure of the convection heat transfer occurring at a surface

Radiant Heat - Energy transferred by radiating energy

Radiant Panel - Panel of electric or hydronic system for radiating energy

Radiant System - Thermal system with more than 50% energy transferred radiantly

Temperature Gradient - Temperature change according to position vector of a given system according to the systems heat transfer exchange rates


v

Thermal Comfort - “The condition of mind that expresses satisfaction with the thermal environment.” (ASHRAE, 1992)

Thermal Comfort Signature (TCS)-

A contour slice representing the localized thermal comfort produced by the combination of room structure and the radiant heating and/or cooling panels (Watson and Chapman, 2002)

Thermocouple - Device for measuring temperature in which a pair of wires of dissimilar metals (as copper and iron) are joined and the free ends of the wires are connected to an instrument measuring difference potential of the metals


1

INTRODUCTION

The objective of this project as listed in the work statement is:

Relevant and accurate data pertaining to the effects of internal radiant panel heat transfer or acceptance characteristics will assist design engineers in predicting actual panel output required for thermal comfort, energy performance, and conformance with related laboratory, government, or code safety standards or requirements. The objective of this research project is the development of simplified heat transfer design information associated with the common installation alternatives for radiant conduit to enable the designer to select and design such installations.

The objective of this research project is to develop an improved understanding of how heat energy transfers from a radiant conduit system to the built environment. This improved understanding will provide the necessary information for designers and installers to predict surface heat-transfer rates from radiant conduits by knowing the internal characteristics of a radiant heater. This project presents a simplified tool for calculating the heat transfer rate as a function of the various heater construction materials and design parameters. These construction materials and design parameters encompass the water temperature and flow rate of a hydronic heating system, the thermal conductivity of a radiant heating panel, and the material properties and thickness of a hydronically heated floor. The Project Monitoring Subcommittee worked with the research team to identify up to five separate configurations that would represent the most common configurations encountered by designers and installers. The power to each panel system was a hydronic heating system, and included configurations with and without insulation below the tubes, and with and without extruded aluminum heat transfer plates. The numerical study analyzes a hydronic/electric cable embedded in four separates cases: surfaces with convective heat transfer coefficients of 5 W/m2-K and 10 W/m2-K; radiant conduit ½ inch and ¾ inch below the concrete surface.

The target audiences for this work are heating, ventilation, and air-conditioning (HVAC) engineers and radiant panel installers responsible for optimizing thermal comfort delivery in the built environment. One other research project was sponsored by ASHRAE under the auspices of TC 6.5 (Pedersen, 1997). This project, RP-876, was completed at the University of Illinois and investigated the impact of surface characteristics on radiant heat transfer from radiant panels. The results from this investigation showed that the only significant parameter is the insulating value of the material that covers the panel. The investigation conclusively found that the radiative properties of the covering insignificantly influenced the heat transfer from the panel.

The definition of radiant heating systems is a thermal system with more than 50% energy transferred radiantly. Radiant heating systems provide an efficient means of delivering thermal comfort to a specific location in an occupied space without requiring


2

thermal conditioning of the area. As opposed to heating systems that control room air temperature, these systems efficiently provide thermal comfort by focusing thermal energy directly on occupants. Thermal comfort is defined as “The condition of mind that expresses satisfaction with the thermal environment” (ASHRAE, 1992). The relationship between the heat transfer rate emitting from a panel surface and the construction and operating characteristics, defining the radiant heating panel are important design parameters that are often misunderstood.

The work completed under this research project at Kansas State University, as well as other projects over the last 10 years, focused on understanding and designing radiant heating and cooling systems for thermal comfort. The thermal comfort design methodology relies on the rate of heat transfer from the face of a radiant panel, as illustrated in the hydronically-heated floor in Figure 1. The heat transfer to or from the room depends on the internal characteristics of the radiant heating panel, as shown in the figure, as well as a variety of other parameters (Jones and Chapman, 1994 [RP-657]), (Chapman and DeGreef, 1998 [RP-907]). In turn, the creation of a thermally comfortable environment is affected not only by the operating characteristics of the heating panel and construction materials, but also by the room geometry and the conditions that determine the temperatures of the other surfaces in the room.

A hydronic system utilizes water for the means of transferring heat to the specified environment. The water temperature and flow rate determine the amount of heat transferred by the hydronic system to the built environment. This project focuses on answering the question of how the panel construction materials influence the amount of heat that is available for transfer from the panel surface per square foot of surface area to the room. This heat transfer rate is critical in relation to calculating the level of thermal comfort created in the room, and the heating system size and radiant panel surface-area requirements to establish the appropriate thermal comfort environment.

The method described herein solves this problem by establishing the functional relationship that includes the internal hydronic heater characteristics and the power supplied to the heater. The functional relationship must include a wide range of building materials and operating conditions to be a valuable model. The following equation represents this relationship:

( ), , , , ,d s h sys air sQ f k L P T Nuε=! ! (1)

where:

dQ! = radiation heat transfer linearization coefficient

sysP! = heating panel energy consumption

εs = heater surface emissivity


kh = the

L = cha

Tair = roo

Nus = the

The linkage relatinASHRAE ResearchTemperature (MRT1994). This projecSpace Heating andmethod for design thermal comfort. TBuilding Comfort Athermal comfort anOrdinates Radiatioradiative heat transprovide an accurat

The BCAP methodASHRAE RP-907, Combined Radiantand DeGreef, 1997and Cooling. This attempt at definingin-space convectiv

The work completeidentifying significa

Figure 1. Sche mode

Heat transfer to room

InletL k

Hydronically heated floor

matic of a hydronically heated floor with the appropriateling parameters.

3

rmal conductivity of the tubing

racteristic length of the heater shown in Figure 1

m air temperature

Nusselt number

g radiant heating and the occupied space has been explored in Project RP-657, Simplified Method to Factor Mean Radiant ) into Building and HVAC System Design (Jones and Chapman, t was completed in 1994 under the auspices of TC 6.5, Radiant Cooling. This effort provided a concise, universal, and accurate and application of radiant heating systems to optimize occupant he outcome of this project was a design methodology known as the nalysis Program (BCAP). BCAP is a computer program that includes d inclusive energy balance calculations utilizing the Discrete-n Solver (DORS) as the core computational engine. In addition to fer, BCAP incorporates the effect of convective in-space heating to

e and complete simulation of combined heating systems.

ology has since been extensively validated and expanded in Design Factor Development to Obtain Thermal Comfort with and Convective In-Space Heating and Cooling Systems (Chapman ) and completed under the auspices of TC 6.4, In-Space Heating project validated the BCAP methodology and developed a first the functional relationship provided in equation (1) for a radiative or e heating system.

d in this project continues along the lines of the previous work by nt parameters that couple the radiant panel system to the built


4

environment. This coupling will provide information that can be included in simulation programs such as BCAP and EnergyPlus, to determine accurately the impact of the radiant panel on occupant thermal comfort.


5

LITERATURE REVIEW

The literature review was completed through an extensive literature search at the Kansas State University library. The resources include computer searches of international archives as well as numerous engineering indices. Personal interviews, industry literature and site visits complimented the information obtained in the open literature. However, the exhaustive literature search of radiant systems offered only limited scientific publications that related to the specific heat transfer rate from various floor radiant systems. There are many radiant heating systems available, which largely encompass the same basic properties. The following literature review provides a compilation of the literature available in the public domain that focuses on determining the specific heat transfer rates from radiant heaters of different types.

Radiant heating and cooling systems maintain thermal comfort in buildings, offices, and homes. These systems have the ability to provide indoor thermal comfort with lower energy requirements than conventional ventilated heating and cooling systems. Radiant systems are divided into the three categories as listed in Table 1.

Table 1. Categories for Radiant Systems (ASHRAE, 1999)

Category Operating Temperature Range

Low Temperature Range Heating: 80°F - 200°F Cooling: 50°F - 70°F

Med Temperature Range 700°F – 1100°F

High Temperature Range 1200°F – 2000°F

One of the first studies of radiant systems developed a computerized technique to relate surface heater temperature to the space heating requirements under the sponsorship of ASHRAE RP-394 (Howell, 1988). This study focused on obtaining relevant data of radiant systems for heating and cooling to calculate loads, and to size and position equipment. The computer model performed calculations of four types of radiant systems; ceiling panel heating and cooling, heated floor panels, U-tube infrared and modular infrared. The model results showed that the air infiltration rate had a significant effect on the difference between actual heat loss and the ASHRAE standard heat loss. Evidence showed the ASHRAE design heat loss procedure would over predict the radiant unit size by up to 16%. The study also showed that additional work was needed to predict surface convection coefficients, room air-temperature stratification, surface emissivity, radiant system dynamics, and the design procedures for heated floor systems.


6

An electrical radiant panel was the focus of “An Analytical Model for the Design of In-Slab Electric Heating Panels” by Kilkis and Ritter (1998). This paper showed that by utilizing basic principles and an accurate control volume, it was possible to model radiant heating systems. This study modeled equations for either ceiling or floor heating with radiant panels in an enclosed space, and incorporated allowances for the exposed surfaces of room walls.

They found that the heat output of radiant panels depends on the temperature of the unheated surfaces, the temperature of the interior air of occupied spaces, the surface emissivity, and the space size for convection. The total output of a radiant panel is the sum of the radiant energy and the convection energy of the system, which can be expressed in terms of the panel surface temperature.

They state that the mean water temperature is especially important for heating systems that utilize geothermal or solar heating sources for supply water. In such cases, the balance between installation cost and operating performance requires accurate calculations from the prediction model. Maintaining turbulent flow and allowing for adequate pressure drop in the system circuits for a fixed heat load requires educated design consideration from panel designers.

The study “Computer-Aided Design of Radiant Subfloor Heating Systems”, by Kilkis and Sapci (1995), incorporated a mathematical model in a computer program to analyze hydronic subfloor heating systems. The algorithm is capable of solving for the mean water temperature of hydronic systems. The analysis requires knowledge of the construction materials, tube spacing, heat load, and room characteristics.

For a horizontally heated floor with a surface temperature of pt , the required heat output flux equation for the panel is:

5 2.627 1.251( ) (1 2.257 10 ) 2.67 ( )u r D p p aq F C t AUST h F t t−= − + − × × − (2)

where:

rF = radiation heat transfer linearization coefficient

DC = surface radiation coefficient

h = elevation relative to sea level

at = indoor air temperature

1F = convective heat transfer coefficient

AUST = area-averaged temperature of uncontrolled surfaces


7

This model is an important design tool for evaluating system performance before the installation in order to optimize the hydronic circuit designs for the construction materials, space consideration, and available energy sources. This also allows designers to manipulate different design considerations for adequately predicting system performance.

“Practical Applications of Radiant Heating and Cooling to Maintain Comfort Conditions” by Simmonds (1996) shows that utilizing the predicted mean vote (PMV) as the design criteria clearly requires heating and cooling with radiant systems to control the mean radiant temperature adequately. Given the space requirements for ‘ducting’ with radiant systems provides a great amount of architectural freedom. However, weak points in the thermal design come from the configuration of perimeter walls and the glazing of internal and external walls.

Accurate accounting of the summer and winter heating and cooling loads is required for a given building design to plan the appropriate circuits and equipment sizes for the system. The solar interaction with the built environment can upset the thermal balance by adding to the heat load of the system, thereby requiring modifications to the mean radiant temperature (MRT) to account for the effects of solar radiation. The heat delivered by occupants and effects of spatial arrangement contribute to the total thermal balance of the building energy system as well.

This study followed three installed radiant systems in completely different dynamic environments: office space, multifunctional space, and retail store. It shows that radiant systems can properly condition a space, if the application and prediction model incorporate dynamic loads in the system evaluation procedures. Many simulation programs convert radiant loads to convective heat loads in order to simplify the calculation method, which does not adequately account for the MRT for radiant systems. The low energy requirements and low swing in MRT with radiant heating and cooling systems permit maintaining the PMV for the built environment more closely than possible with convective heating and cooling systems, keeping the thermal comfort closer to optimal conditions.

“Numerical Study of Thermostat Setpoint Profiles for Floor Radiant Heating and the Effect of Thermal Mass” by Athienitis and Tingyao (1997) tested different thermal mass thicknesses, control schemes, and different setpoint schemes. A problem exists with thermal lag times of high thermal mass systems, which may allow overheating or under-heating. There is a benefit of shifting the thermal energy required to increase or decrease radiant panel temperatures to lower-cost off-peak times. This requires an appropriate control strategy to maintain desired thermal conditions, and incorporate the energy timing to maximize cost savings and thermal comfort.

They show that one existing problem with heating/cooling late at night is not accounting for solar radiation when the morning hours arrive. Therefore, a control scheme should incorporate the maximum heating device output and the thermal mass thickness for better predicting required energy loads to achieve thermal comfort. An economical


8

solution for maintaining thermal comfort is incorporating a simple proportional controller with an anticipator. This should include a reset controller with room temperature feedback as part of the prediction method. The use of a simple thermostat setpoint contributes to energy savings, but leads to slow response on cold days, requiring auxiliary heating to maintain thermal comfort. A predictive control scheme can anticipate solar gains in thermal mass by keeping a lower nighttime setpoint for the upcoming solar gain in the morning.

Using a nonlinear finite difference network model allowed the study of optimal setpoint profiles for floor heating with a proportional controller. Comparing three control methods, constant setpoint, square-wave setpoint, and half-sinusoid setpoint, showed that a half-sinusoid setpoint control scheme allows for minimal room temperature swing. This method uses a low and high temperature setpoint in a time-defined equation, which allows for an overall optimum response for medium thermal mass (5 cm).

The half-sinusoid setpoint control equation is:

[ ]{ },( ) cos ( ( ) / 2) /( )sp sp low sp end start end startT t T T t t t t tπ= + ∆ − + − (3)

where:

spT = setpoint temperature as a function of time t

,sp lowT = lowest setpoint temperature

startt = starting time (for this case 3 am)

endt = ending time (for this case 11 am)

“Impact of Surface Characteristics on Radiant Panel Output”, Lindstrom et al., (1998), took a close look at the effects of surface texture and different covering materials on the output of radiant panels. The study measured the hemispherical and angular emittance of various construction materials. The results found that the surface texture and conditions tested did not have a significant effect on the rate of the transfer from the radiant panels in the office sized test space. The research was performed to test the emissivity of non-metal building materials and quantify the assumption that 0.9 emissivity is applicable to materials that not found in literature. It concluded that surface texture has no effect on the rate of heat transfer from a surface and all materials tested have similar emissivity properties.

“Basic Study of Radiative and Convective Heat Exchange in a Room with Floor Heating”, Hanibuchi and Hokoi (1998), compares a computer model of an enclosure with the recorded measurements of a built environment to the same specifications. The computer model calculated the radiative and convective heating results independently,


9

which showed that convective heat exchange accounts for 48% of the heat transfer with a radiant system. Modeling and experimentation also found that there is uniform temperature distribution except in areas near windows where drafts can lower the air temperature. The numerical results accurately predicted the temperature within 1.8°F when compared to the experimental recordings.

“A Three-Dimensional Numerical Investigation of the Effect of Cover Materials on Heat Transfer in Floor Heating Systems”, by Chen and Athienitis (1998), used a numerical investigation to examine the effects of different floor covering materials on a radiant heating floor system. This study focused on the temperature distribution and energy consumption with a floor heating system. The study shows the cover layer has a significant effect on thermal performance of floor heating systems, using a three-dimensional finite-difference model to evaluate the partial and full cover of electric panel floor heating. It takes 2.25 hrs to achieve the surface operating temperature for a 5 cm concrete floor. However, the same floor with 2 cm of carpet on the entire surface takes 4.75 hrs to reach the operating temperature. The carpeted surface also showed an increase in energy consumption, requiring 9% more energy than the uncarpeted floor to achieve the same floor temperature. The increased thermal resistance of covering materials leads to increased energy requirements, higher back losses, higher temperature variations of the floor surface for partially covered floors, and higher lag times to achieve operating conditions.

“Radiant Panel Perimeter Heating Options: Effectiveness and Thermal Comfort” by Freestone and Worek (1996) studied the effects of placing radiant ceiling panels in the perimeter of an enclosure to control the local MRT in that region, creating a hybrid system with the forced air heating system. Local perimeter heating can make up for heat loss from perimeter walls or areas near windows. The configuration studied was an office building with space above and below the office. They found that by placing radiant heating in the ceiling and removing the insulation above the panel allowed the office above to receive radiant subfloor heating in that region. Coupled with partitioning the air plenum of the forced-air heating system to divert air to areas of the office not controlled with radiant panels, increased the MRT and the operative temperature of the office.

The “Case Study: Seven-System Analysis of Thermal Comfort and Energy Use for a Fast-Acting Radiant Heating System” by Watson, Chapman, and DeGreef (1998) analyzed heating system operation before and after retrofitting units of a large single-family housing community with various radiant systems. The pre- and post-retrofit energy data were monitored for two to four years. There were 19 different housing designs for the 100 units studied. The association found lower installation and maintenance costs for the radiant systems installed than with forced air-heating systems. This study focused only on radiant heating because all of the units had separate air-conditioning systems for cooling. The range of savings in energy use varied greatly, not considering the initial thermal comfort before installing the radiant systems. The highest savings was 36.3% when compared to the previous energy usage for heat loads only, and the lowest savings was -3.1%. The average energy


10

savings was 14.6%, indicating the many design factors that encompass radiant panel systems. The thermal requirements and usage as well as the building configuration including: windows, flooring materials, insulation, and spatial consideration can have a dramatic effect on the thermal results of radiant systems.

“Development of a Mathematical Model and Computer Simulation of Radiant Panel Heating Systems” by Khan and Coutin-Rodicio (1990) modeled transient heat transfer from a hydronic ceiling panel. The development of separate transient equations for the elements of the enclosure resulted in a set of coupled, non-linear differential equations. Numerical analysis was able to determine the mean ceiling water temperature and local heat transfer rate of the ceiling as a function of the water supply temperature and the room comfort conditions.

Summary: This literature review has provided of knowledge for the design of radiant panel test chamber used in this research project. The most disconcerting result is that there are numerous parameters that impact the heat transfer rate from the radiant conduit system. Also apparent, and well within the scope of this research project is that the radiant system operation significantly depends on the design of the system, the installation, and the local construction materials adjacent to the panel, and that the numerical models created up to now have been validated repeatedly with radiant panel operation.


TEST SETUP

Tests were completed experimentally and numerically to cover the widest range of common applications. The complete list is provided in Table 2.

Table 2. Matrix of Physical and Numerical Tests

Experimental Numerical Configuration Insulation

5/8 in. below panel

Insulation 2 in. below panel Concrete Slab

No Plates Test 1 Test 3 ---

Plates Test 2 Test 4 ---

Concrete, h=5 W/m2-K, ½ in Test 5

Concrete, h=5 W/m2-K, ¾ in --- --- Test 6

Concrete, h=10 W/m2-K, ½ in --- --- Test 7

Concrete, h=10 W/m2-K, ¾ in --- --- Test 8

11

Experimental: The experimental tests were conducted with a hydronic heating system, although as specified earlier, the results are presented in a conduit-neutral way to apply equally to electrical cable systems. Since there are numerous ways to design and install a radiant panel system, the research team and PMS focused on the most common, generically available techniques. The PMS specifically determined that testing and evaluating proprietary systems was outside the scope of this project. The selection criteria used to determine the panel types include that would be tested are:

Is the panel commonly used in industry?

Is the panel generic (non-proprietary)?

Is it possible to install the panel in the test cell within the scope of the current project?, and

Is it possible to instrument the panel in the test cell?


12

With input from the Project Monitoring Subcommittee, the decision was made to utilize a hydronic system with PeX that would function in the different configurations shown in columns two and three of Table 2. The parameters under investigation were the impact of heat transfer plates and the position of insulation below the PeX tubing.

Numerical: One of the more common radiant systems in use today is a system with hydronic tubes or electric cables embedded in concrete. This type of system was impractical to install in the test cell but fortunately is easily modeled using several common numerical techniques. The radiant system embedded in concrete transfers heat by conduction, turning the entire concrete slab into a radiant panel heating the occupied space. The numerical studies, listed in column three of Table 2, investigated the impact of the depth of the radiant conduit as well as the impact of the surface convective heat transfer coefficient on the ultimate heat transfer rate from the radiant panel. The numerical model that was used for these studies has been validated and used for several commercial- and industrial-type heating applications (Chapman et al., 1992).

Experimental Setup

Figure 2 shows the inside of the upper region of the test chamber. The near full-size test chamber, equipped with instrumentation to measure a variety of temperatures and water flow rates, was built to provide for the consistent collection of data under varying installation situations. The chamber had the capability to accept the panel system determined to be of most significance by the Project Monitoring Committee. This test chamber design precluded back losses with the heavy insulating material below the radiant conduit, ensuring 100% energy transfer through the floor system. This test chamber was constructed with materials typical to that of residential construction.

Several companies involved in the radiant heating industry donated equipment used with the test cell. All equipment was of the generic nature to ensure that test results were not biased toward a certain proprietary type. The test cell as a whole consisted of four main sections:

1. Pre-Panel Equipment

2. Panel Equipment

3. Loading Equipment

4. Instrumentation


13

Pre-Panel Equipment The pre-panel equipment is defined as all equipment required to circulate heated water throughout the hydronic panel. Figure 3 shows a schematic of the pre-panel and panel equipment. A water-heating device was required for the hydronic systems and a boiler was chosen for the method of heating water for delivery to the hydronic tubing. A heat exchanger warmed the water returning to the boiler high enough to prevent the boiler from experiencing thermal shock. Copper piping connected all pre-panel equipment and an expansion tank accounted for water expansion when heated. A pressure-relief valve operated the heating circuit within critical pressure limits and a circulation pump provided water flow through the system. Several shut-off valves and flow control valves isolated the required areas of the circulating system. An in-line flow meter measured the water flow rate in the system. Copper compression fittings connected the pre-panel equipment to the cross-linked polyethylene tubing of the hydronic panel.

Figure 2. A photo of the inside of the test chamber


PaneThctTs

Figure

3. Schematic of the Pre-Panel Equipment and Panel Equipment used for Hydronic Test Panel

l Equipment he panel equipment is considered equipment used to transfer heat from the eating equipment to the occupied space. A hydronic panel contains several omponents to make the heating system. The tubing selected for heat transfer in his hydronic system was ½ inch inner-diameter cross-linked polyethylene tubing. his type of conduit is commonly used in radiant heating systems and a chematic of the tubing layout in the test cell floor is shown in Figure 4.

Flow Rate, Tin

Tout

HYDRONIC FLOOR PANEL

HYDRONIC TURBING RUNS

FLOOR JOISTS Figure 4. Schematic of the hydronic tubing runs

14


Ontrasyswitsysarrsys

Fig

F

ure 5. Hydronic Subfloor Heating System with Extruded Heat Transfer Plates.

15

e major question in the application of these hydronic systems is whether heat nsfer plates are necessary to provide the heat output required by these tems. This experiment uses the same arrangement for the hydronic system

h heat-transfer plates as for that without. The identical application of both tems presents the opportunity to compare the operation of both types of angements with varying insulation depths. Figures 5 and 6 show the hydronic tem configurations.

igure 6. Generically installed hydronic subfloor heating system


16

Loading Equipment Experimentally testing radiant panels properly requires a known load to act as the weather conditions. An insulated room provided a test chamber to better simulate the built environment and enclose the radiant system under controlled conditions. An air cavity in the wall directly behind the wall gypsum and two inches of insulation in the wall framing created a barrier to isolate the test chamber from ambient conditions of the laboratory.

An air handler and air conditioning system supplied temperature controlled air to the cavity of the walls. This cool air barrier provided load to the enclosed test for the radiant systems. Tests performed by Falke (1999) showed that an R-19 wall on a 0°F day will have an inside wall temperature of 60°F. This conclusion therefore provided the basis for simulating 0°F conditions to the test chamber in Kansas in the middle of summer. The control setpoint for the air conditioning system was 60°F as measured on the interior surface temperature of the test chamber walls.

Instrumentation Selecting instrumentation for the test cell first required an understanding of the rate of energy transfer necessary to operate the radiant heating panels. Also need is a measure of the rate that energy transfers from the panel surface to the conditioned space. The rate of energy supplied to the hydronic heating system was measured using the water flow rate, as well as the supply and return temperatures of the water flowing through the radiant panel as shown in Figure 4. With this measured data, the instantaneous power required was calculated as follows:

( )sys supply returnP mc T T= −! ! (4)

sysP! = power to panel

inT = supply water temperature (inlet)

outT = return water temperature (outlet)

m! = water mass flow rate

c = specific heat capacity of the circulating water

Although only hydronic systems were tested, the rate that electrically powered radiant panels consume energy is calculated by measuring the current and voltage that would be supplied to the panel. The power consumed by an electrical panel is then:


17

sysP V I= ×! (5)

V = voltage supplied to the radiant panel

I = current required to operate the panel

The rate that heat energy transfers from the panel surface to the conditioned space is calculated by measuring the heat flux (BTU/hr·ft² or W/m²) at the panel surface. The temperature gradient measured at the panel surface and the heat flux of the panel surface is related through Fourier’s Law (Incropera and DeWitt, 1996):

surfacedTq kdy

′′ = − (6)

surfaceq′′ =heat flux at the surface

dTdy

= temperature gradient between two points

Rearranging this equation yields the thermal conductivity of the instrumentation by measuring the temperature difference across two points from a known heat source.

To reduce the possibility of instrumentation error and to evaluate the uniformity of the radiant heating panel, the temperature gradient was measured and recorded at four different locations. Because the flooring surface was plywood, it was impractical to embed the thermocouples in the floor. Therefore, a 5/8” sheet of gypsum drywall was placed on top of the radiant panel for easier installation of the thermocouples. Though the gypsum adds resistance to the radiant panel, the system was calibrated after the drywall was installed to account for this extra resistance. Because the drywall covered the entire panel and the thermocouples were precisely placed, the results are not affected by the drywall. Eight thermocouples were embedded in “plugs” made of the same 5/8” gypsum drywall as that of the heating panel. Figure 7 illustrates the heat flux sensors (plugs) used to measure the surface temperature gradients of the radiant panel.

The thermocouples were precisely spaced inside of the plugs. The measurements from the thermocouples were used to calculate the temperature gradient at the radiant panel surface. Conservation of energy requires that the surface heat flux calculated from the surface temperature gradient be equal to the heat flux leaving the heater surface by convection and radiation.


The signal gconditioningsignal condshown in Fi

The signal fsignal to a lcurrent is necomputerizevoltage andthe data acqinformation

Figure 7

Embedded thermocouples

GypsumInstrumentation connector

. Heat Flux Sensor used for recording temperature

gradient / heat flux at the surface of the radiant heatingpanel.

enerated by the thermocouples was transmitted to a signal station and to a computerized data collection system. A single itioner is illustrated in Figure 8 and the data collection station is gure 9.

rom a thermocouple travels to a 4-20mA converter that converts raw inear milliamp current as seen in Figure 10. This conversion to cessary for delivery to the data acquisition board of the d data system. A shunt resistor then converts the input current to each signal conditioner is calibrated. The voltages are transmitted to uisition card of the computer for monitoring and the substantial related to the heat transfer rate of these heating systems.

Figure 8. Temperature Signal Conditioning Circuit

18


19

Figure 9. Data acquisition system


TESTING METHODS

Calibration

Calibration of any system is very important to ensure reliable data collection. A cross-sectional diagram of the test cell is shown in Figure 10. The thermocouples were evenly spaced in the arrangement shown in order to increase the accuracy of the readings. Two of the thermocouple plugs were placed on top of floor joists and two plugs were placed between the floor joists. This verified the placement of the thermocouples did not affect the readings. The thermocouple depths vary to eliminate the cause for errors from placement in the drywall.

Each thermocouple transmitter was run to a 4-20 mA transmitter that converted the thermocouple readings to a linearized current. After the transmitter, the signal was again converted to a linear voltage by use of 500-kOhm shunt resistor.

Each conditioned thermocouple circuit was calibrated with a digital-multimeter and thermocouple calibrator. This thermocouple calibrator generated a voltage to simulate a thermocouple at a specific temperature and each transmitter was then adjusted to generate the proper voltage across the shunt resistor. The ideal

Hot Plate

Plywood Subfloor

Thermocouples inGypsom Board

Subfloor Airspace Floor Joists

Figure 10. Cross sectional diagram of test chamber

20


21

equation for each calibrated circuit would therefore be:

18.50 5.0T V= × − (7)

Not all of the shunt resistors were exactly 500-kOhm so the above equation for the each of the channels of the data acquisition system was adjusted for the calibration results. The 15 equations corresponding to the 15-thermocouple circuits used for the data acquisition system are included in Appendix B. Temperature readings from the calibrated channels are shown in Figure 11. After calibrating the thermocouple circuits, the data acquisition system recorded the measured readings (voltages) in a data table. To ensure the operating range of the calibration was valid for different temperature measurements and there

was no drift, the previous calibration procedure was repeated throughout testing.

The next step in calibrating the system was to obtain the thermal conductivity of the radiant panel. This was accomplished by loading the system with a known power and measuring the heat transfer through the panel. A typical stovetop burner or hotplate supplied with a known voltage created a radiant heat source with known power output. A radiant heat shield placed over the top of the hotplate ensured the temperature difference across the panel would not depend on the hotplate’s placement. Two different hotplates with different resistance

Channel Mesurements at 32°FAfter Calibration

32.0

31.7

31.6 31

.6

32.3

32.2

31.7

32.0

31.0

32.2

31.5

31.6

31.9

31.9 31

.9

31.4

30

30.5

31

31.5

32

32.5

Ideal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Data Acquisition Channel

Tem

pera

ture

(°F)

Figure 11. Measured Differences of Calibrated Channels


22

characteristics were used with two different voltages, creating three scenarios of power. The power scenarios were 534W, 1049W, and 1626W (approximately 500W, 1000W, and 1500W).

While applying the radiant source from the hotplate in the subfloor airspace the data system recorded temperatures from the thermocouple plugs. The thermal conductivity of the radiant panel is calculated by knowing the temperature difference between the two thermocouples of the thermocouple plugs, and the known input of the radiant system, the energy from the hotplate. Rearranging Equation 5 yields the thermal conductivity of the radiant panel. The results from this calibration of the radiant panel are shown in Figure 12.

In the legend, the letters A thru D represent a particular thermocouple stack.

Data set “A” corresponds to the measurement of thermocouple (channel) number 2 minus the measurement of thermocouple number 1. “B” is channel 4 minus channel 3, “C” is channel 6 minus channel 5 and data set “D” represents channel 8 minus channel 7.

The trendlines clearly show a similar slope for thermocouple stacks A&B and C&D due to placement in the panel surface. The thermocouple stack selected for data reduction is channels 6 minus 5 due to its low error in comparison of

Delta-T vs. Power

0.0

1.0

2.0

3.0

4.0

5.0

6.0

400 600 800 1000 1200 1400 1600 1800Power (W)

Del

ta T

(°F)

Thermocouple Stack A Thermocouple Stack B Thermocouple Stack C Thermocouple Stack D

Figure 12. Temperature difference in thermocouple plugs.


23

calculated thermal delivery and actual thermal delivery. The thermal resistance for this stack is 1748.91 BTU/hr-°R.

Testing Procedure

Each test started from ambient lab conditions, and allowed the heating and cooling systems time to achieve operating equilibrium. The flow rate of the system was set at 0.4 GPM for each test. The data acquisition system recorded temperatures of the test chamber every moment the air conditioning and heating systems supplied energy to the test chamber. A data table was created for each radiant test and the data was compiled after completion of the testing.

Numerical Methods

The numerical method used to analyze the impact of radiant conduit in concrete slabs is well-developed and has been in use for a variety thermodynamic and heat transfer systems. The research team utilized a finite-difference technique that is well-described by Patankar (1980). The method was two-dimensional heat conduction with the boundary conditions set as:

• Bottom: Insulated from the ground

• Left and Right of the Tube: Symmetrical, since additional radiant conduits will be to the left and right of the conduit under analysis

• Surface: Heat transfer coefficients of 5 and 10 W/m2-K.

The numerical mesh is illustrated in Figure 13. The results are provided as contour plots of the temperature distribution throughout the slab, and the surface heat transfer rates for each of the four cases.

Figure 13. Numerical mesh used to analyze radiant conduit in concrete slabs.


24

RESULTS AND ANALYSIS

Data Reduction

The data acquisition system measured the temperatures of the test chamber at one –second intervals and recorded the voltages to a data table . With the calibration equations for the channels listed in Appendix B, the voltages recorded in the data tables were converted to temperatures. This data was then reduced to evaluate the thermal signatures of the radiant panels. All test data is included on the attached CD.

Analysis

The primary deliverables of this project are the heat transfer models. These can be used to predict the heat transfer rate from the surface of various types of radiant heating panels based on the panel construction materials and the operating parameters. The heat transfer models have been validated by the data sets collected in this task and can be applied to several other types of radiant heating systems. There are two forms of heat transfer models, depending on whether the heating system is electrically or hydronically powered.

The model for the electrically powered systems was expected to have the form:

ds

VIqA

′′ = (8)

dq = heat transfer rate from the panel surface per unit surface area

sA = panel surface area

VI = the power supplied to the panel, the product of voltage and current

The specific form of the heat transfer model for the hydronic radiant heating panel was expected to be:

( )in out

ds

mc T Tq

A−

′′ =!

(9)

inT = water inlet temperature

outT = water outlet temperature


25

m! = water mass flow rate

c = specific heat capacity of the circulating water

The heat transfer models listed in equations (8) and (9) are for an easily characterized ideal case. Since most installations are not ideal, these models were calibrated using the data sets collected in this task.

Heat flux The data recorded at steady-state operations provides the operating characteristics of the hydronic radiant systems. Evaluating the temperature difference between the thermocouples and knowing the thermal conductivity of the heat flux sensors provides the measured heat flux of the panel. Each test configuration was repeated to compare results and assure the validity of the measurements. Figure 14 in the appendices lists the results of the comparing tests for each of the test configurations. The nomenclature is as follows:

! With or Without heat transfer Plates

! Insulation distance from tubing to insulating material

! Test run number (#)

As can be seen in the figure, the heat flux between each of the different runs is within 3.4 BTU/hr ft².

Thermal Delivery with Heat Transfer Plates Each of the configurations delivered energy to the upper portion of the test chamber. At steady state conditions, certain configurations delivered energy at higher rates, while others took significantly longer to reach steady state operating conditions than the other three.

By maintaining the water inlet temperature and water flow rate, the supplied input energy was constant for each of the four experimental configurations. To ensure that each configuration was tested in comparable configurations, the upper portion of the test cell was loaded consistently throughout the tests.

The steady state results for each of the configurations are illustrated in Figure 14. The bar graphs show the results from each of the tests, including the redundant test that was completed for each configuration. The primary result from these four configurations is that the heat transfer plates increase the heat that is transferred to the occupied by space by between 160% and 172%, depending on where the insulation was positioned. The percent increase is 172% when the insulation is backing the tubes at 5/8” from radiant panel and 160% when the insulation is 2 inches below the panel.


26

The steady state results for each of the configurations are illustrated in Figure 14. The bar graphs show the results from each of the tests, including the redundant test that was completed for each configuration. Depending on the position of the insulation these configurations increased the heat transferred to the occupied space by between 160%-172%. The heat transfer plates significantly enhanced the delivered thermal energy as shown in Figure 14. The first test with the insulating material 5/8” below the bottom of the radiant panel produced a heat flux of 45.0 (BTU/hr-ft²). With the insulating material 2 inches below the hydronic panel the heat flux is 43.6 (BTU/hr-ft²) for the hydronic system. The measured difference of the heat flux for these two systems is within the tolerance of the thermocouples used in the measurements, showing no significant difference between the systems.

The configuration resulting in the highest heat transfer rate to the occupied space is with the insulation 5/8” below the bottom of the panel and with the heat transfer plates installed. The configuration with the heat transfer plates, but with the insulation positioned 2 inches below the panel performed almost as well.

Heat Flux for Each Test Configuration

24.7

22.4

45.0

47.6

24.2

28.1

43.6

40.3

0.0

10.0

20.0

30.0

40.0

50.0

60.0

No Plates

/ 5/8"

Air gap

#1

No Plat

es / 5

/8" Air g

ap #2

Plates

/ 5/8"

Air gap

#1

Plates / 5

/8" Air g

ap #2

No Plates

/ 2" A

ir gap #

1

No Plat

es / 2

" Air g

ap #2

Plates /

2" A

ir gap

#1

Plates

/ 2" A

ir gap

#2

Test Configuration

Hea

t Flu

x (B

TU/h

r•ft

²)

Figure 14. Test results for the four experimental configurations.


27

A qualification necessary on these tests concerns the type of insulation that used in the system. All cases used blue board foam insulation used for these experiments. Expectations are that if fiber glass insulation had been used instead, the results for the case with 5/8” air gap may have performed more like the case where the insulation was positioned 2 inches below the panel. The reason for this qualification is that it is common knowledge that convection loops can form inside the fibers of the fiberglass insulation. Depending on the magnitude of the convection loops, the overall system may perform as if the insulation were positioned lower. This qualification is listed at the end of the report as an area for further study.

Ramp-up time to steady-state The time required to achieve thermal equilibrium varied between the different radiant panel configurations. Figure 15 demonstrates the time required to achieve a thermal balance for a system without heat transfer plates and 5/8” air gap. Each test configuration in the test chamber possessed different time requirements to achieve thermal balance. While this portion of the investigation was outside the scope of this project, the results were recorded and included as an extra data point to assess which configuration to use in a particular application.

As shown in Figure 16, the position of insulation has an enormous impact the on the time required to reach steady state. When the insulation is positioned so that it is 5/8” below the panel surface, observations showed that the heat transfer plates had little impact on the time to reach equilibrium. However, when the insulation is placed two inches below the tube, the time to reach equilibrium increases by a factor of 2.36, from 4.26 hours to 10.05 hours.

Comparing the right-most bars shows that this increase in time can be offset by installing heat transfer plates. In this case the time to reach equilibrium decrease by a factor of two, from 10.05 hours to 5.04 hours.

The configuration that reached equilibrium in the shortest amount of time includes heat transfer plates and has the insulation positioned 5/8” below the radiant surface.


Ramp-up Time for Thermal Delivery

0.0

500.0

1000.0

1500.0

2000.0

2500.0

3000.0

3500.0

4000.0

4500.0

5000.00.

0

1.0

2.0

3.0

4.0

5.0

6.0

Time (hours)

Ther

mal

Del

iver

y (B

TU/h

r)

Steady-state conditions begin

Figure 15. Time Interval to Achieve Thermal Equilibrium

Hydronic Panel Ramp-up Time

4.26

3.89

10.05

5.04

0.0

2.0

4.0

6.0

8.0

10.0

12.0

No Plates / 5/8" Air gap

Plates / 5/8" Air gap

No Plates / 2" Air gap

Plates / 2" Air gap

Test Configuration

Tim

e to

Ste

ady-

Stat

e (h

ours

)

Figure 16. Transient Test Results

28


Numerical Results Numerical methods were used to determine the impact of separate concrete / tube / cable configurations. In each of these studies, the conduit temperature was maintained at 140°F.

Figure 17 illustrates the temperature distribution within the concrete slab for each of the four cases. This figure is primarily shown to provide confirmation that the calculations provide expected results, and to demonstrate the information that can be determined with finite-difference modeling of radiant panel systems. The temperature scale is identical for each of the four panels. The two top contour plots compare the impact of the heat transfer coefficient on the temperature distribution for the case where the radiant conduit is ¾ inch below the surface of the concrete. The only difference between each of the plots is the convective heat transfer coefficient at the surface of the concrete. The temperature distribution shows that the convective heat transfer coefficient has a large impact

Figure 17.
Temperature distribution within the concrete slab.
29


30

on the temperature distribution within the concrete slab. The two bottom panels illustrate the same comparison, except that the radiant conduit is two inches below the surface of the concrete. In general, the cooler the concrete near the surface, the higher the heat transfer rate from the surface to the conditioned space.

Figure 18 illustrates the information that is pertinent to this project, namely the surface heat transfer rate from the slab to the occupied space. The results for each of the four cases are compared on the same plot. The vertical axis represents the localized heat flux and the horizontal axis represents the distance between the line of symmetry between the radiant conduit. Also included on the graph are the average heat fluxes for the total width above the single radiant conduit.

Figure 18. Surface heat flux from the concrete slab for the four different configurations.


31

Of interest is that the local heat flux varies substantially with distance from the radiant conduit, especially when the conduit is close to the surface of the concrete (refer to the ¾ inch lines on the graph in Figure 18). Also of importance is that the convective heat transfer coefficient has a large impact on the surface heat flux, making it impossible to develop a single correlation that can be used to determine the expected heat flux from the surface of a radiantly heated concrete slab. Instead, a more sophisticated approach is necessary that couples the conditions in the conditioned space to the operation of the radiant slab.

Finally, Figure 18 shows that the depth of the radiant conduit substantially impacts the heat flux from the surface, and becomes more significant with an increasing heat transfer coefficient. For example, when the convective heat transfer coefficient is 5 W/m2-K, changing the radiant conduit depth from ¾ inch to 2 inches only decreases the average heat flux from 32 Btu/hr-ft2-°R to 27 Btu/hr-ft2-°R, a reduction of 15%. However, when the convective heat transfer coefficient is 10 W/m2-K, the increasing the radiant conduit depth from ¾ inch to 2 inches decreases the average heat flux from 49 Btu/hr-ft2-°R to 38 Btu/hr-ft2-°R, a percentage change of 22%.


32

CONCLUSION

The most significant conclusion from this research project is that the heat flux from the surface of a radiant panel is impacted by numerous variables, several of which were outside the scope of this project. Because of these numerous variables, it is impossible, at this time, to develop simple formulae that can be used to determine the heat flux from a particular radiant panel system. Instead, the research team and PMS conclude that the results from this project provide a guideline that can be used by designers and installers. Specifically:

• The use of heat transfer plates dramatically increased the heat flux emitted from a radiant panel by better distributing the thermal load to the radiant surface. The difference in thermal delivery for a system with heat transfer plates to that without heat transfer plates provides designers practical data showing the power requirements and the potential delivery from like systems;

• Varying the insulation depth below the radiant conduit provided the opportunity to compare the two configurations. The advantage to mounting an insulating material near the radiant surface is seen when comparing a system with heat transfer plates to that without. The experimental data shows that mounting the insulating material 2” below the radiant panel increases the time required to achieve steady-state operation for a radiant system with or without heat transfer plates;

• The experimental data shows the use of heat transfer plates with a radiant system significantly increases the heat flux to the occupied environment. The mounting distance of an insulating material to the radiant element does not greatly affect the heat transfer characteristics of the radiant system when back losses are minimized or eliminated. The thermal resistance of the radiant panel system depends solely on the installation and construction materials;

• The numerical model of the radiantly heated concrete slab showed that the surface heat flux is a strong function of the convective heat transfer coefficient at the slab surface, and of the depth of the radiant conduit below the concrete surface. The results showed that the convective heat transfer coefficient may impact the heat flux more than the depth of the radiant conduit.

The goal of this project was to form a system equation using the construction materials as the input requirements, and was found to be far outside the original scope of work. The results provide comparative information of the thermal delivery from similar hydronic systems. Evaluating the insulation depth below the panel surface, and the use of heat transfer plates with this radiant system offers


33

designers operating data from an experimental setup comparable to that of installations in buildings and homes. Additional work with the experimental setup and heat flux delivery measurements will further the applied information required for system designers.


34

FUTURE WORK

The following items are potentially significant areas identified for future work:

• Convective loops created in fiberglass insulation will most undoubtedly be different from those developed in this report using blue-board insulation. Studies should be completed on the thickness and position of fiberglass insulation to assess the potential benefits that exist by manipulating the construction. An extremely wide variety of installations of radiant conduit are available for comparison.

• Conducting studies on all of the identified variations was beyond the scope of this project and, therefore, it is important to understand the impact of parameters such as tube spacing, tube depth, and moisture content of the concrete. The construction materials and their assembly are critical to radiant performance.

• Creating a database from exhaustive testing of different radiant systems in an identical environment would provide a rich database of information that can then be analyzed using statistical techniques to identify the most important design and operating parameters for evaluating radiant systems. This database can be developed from experimental data or by numerically modeling radiant systems. Modeling radiant systems to an equation with input parameters, design requirements, construction materials and installation will only occur from the comparison of different configurations in an identical environment.


35

ACKNOWLEDGEMENTS

The research team gratefully acknowledges the guidance and support of Mr. Richard D. Watson, Mr. Lawrence Drake, and Mr. Gary Hayden. These individuals played a large role in helping to guide the research project and in helping to interpret some of the results. The team also acknowledges the support of Dale Pickard and Radiant Engineering Inc. for donating the ThermoFin plates for the experiments, and of Gary Hayden for establishing contacts that culminated in the donations of the PeX tubing, the boiler, and several other pieces of equipment that were necessary to complete the experiments. Finally, but not least, we recognize the technical support and assistance of the Radiant Panel Association.


36

REFERENCES

ASHRAE, 1999. ASHRAE Applications Handbook.

ASHRAE, 1992. ASHRAE Standard 55-1992. Thermal Environmental Conditions on Human Occupancy.

Athienitis, A. K. and Tingyao C., 1997. “Numerical Study of Thermostat Setpoint Profiles for Floor Radiant Heating and the Effect of Thermal Mass,” ASHRAE Transactions 103(I).

Chapman, K.S., and DeGreef, J. M., 1998,Design Factor Development to Obtain Thermal Comfort with Combined Radiant and Convective In-Space Heating and Cooling Systems. Final Report of ASHRAE Research Project RP-907. Atlanta, Georgia: ASHRAE.

Chen, Y. and Athienitis, A. K., 1998. “A Three-Dimensional Numerical Investigation of the effect of Cover Materials on Heat Transfer in Floor Heating Systems,” ASHRAE Transactions 104(II).

Freestone, M. D. and Worek, W. M., 1996. “Radiant Panel Perimeter Heating Options: Effectiveness and Thermal Comfort,” ASHRAE Transactions 102(I).

Hanibuchi, H. and Hokoi, S., 1998. “Basic Study of Radiative and Convective Heat Exchange in a Room with Floor Heating,” ASHRAE Transactions 104(1).

Howell, J.R. 1988, A Study to Determine Methods for Designing Radiant Heating and Cooling Systems. Final Report of ASHRAE Research Project RP-394. Atlanta, Georgia: ASHRAE

Incropera, F. P. and DeWitt, D. P., 1996, Fundamentals of Heat and Mass Transfer, John Wiley and Sons, New York.

Jones, B. and Chapman, K. S., 1994, Simplified Method to Factor Mean Radiant Temperature (MRT) into Building and HVAC System Design. Final Report of ASHRAE Research Project RP-657. Atlanta, Georgia: ASHRAE.

Khan, A. Y., Coutin-Rodicio, S., 1990. “Development of a Mathematical Model and Computer Simulation of Radiant Panel Heating Systems,” American Society of Mechanical Engineers, Vol. 10. pp 47-53.

Kilkis, Birol I., and T. L. Ritter, 1998. “An Analytical Model for the design of in-slab electric heating panels,” ASHRAE Transactions 104(I).

Kilkis, I. B., and M. Sapçi, 1995. “Computer-Aided Design of Radiant Subfloor Heating System,” ASHRAE Transactions 101(I).


37

Lindstrom, P. C., Fisher, D. E., and Pedersen, C., 1997, Impact of Surface Characteristics on Radiant Panel Output. Final Report of ASHRAE Research Project RP-876. Atlanta, Georgia: ASHRAE.

Lindstrom, P. C., Fisher, D. E., and Pedersen, C., 1998. “Impact of Surface Characteristics on Radiant Panel Output,” ASHRAE Transactions 104(I).

Patankar, S.V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, First Edition.

Simmonds, P., 1996. “Practical Applications of Radiant Heating and Cooling to Maintain Comfort Conditions,” ASHRAE Transactions 102(I).

Watson, R. D., Chapman, K., and DeGreef, J. M., 1998. “Case Study: Seven-System Analysis of Thermal Comfort and Energy Use for a Fast-Acting Radiant Heating System,” ASHRAE Transactions 104(I).


APPENDIX A

FIGURE A.1

Tin and Tout vs Time

38

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

Time (hour)

Tem

pera

ture

(°F)

Tin Tout


39

APPENDIX B TEMPERATURE CHANNEL CALIBRATION EQUATIONS

Ideal Equation: T = V * 18.500 - 5.000

T is the calculated temperature

V is the measured voltage from the thermocouple circuit

T = V * 18.659 - 5.598

T = V * 18.527 - 5.440

T = V * 18.730 – 5.835

T = V * 18.412 – 4.492

T = V * 18.574 – 4.925

T = V * 18.519 – 5.296

T = V * 18.644 – 5.289

T = V * 18.787 – 6.607

T = V * 18.551 – 4.878

T = V * 18.571 – 5.681

T = V * 18.504 – 5.397

T = V * 18.492 – 5.040

T = V * 18.583 – 5.258

T = V * 18.692 – 5.439

T = V * 18.589 – 5.809

Documents

Develop Simplified Methodology to Determine Heat Transfer ... · flooring system based on the particular installation method. The flooring system tests investigated the use of insulation