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Ref.: Jaluria, Y., Design and Optimization of Thermal Systems, McGraw- Hill Inc.,

1998.

Acceptable Design of a Thermal System

Acceptable design

Engineering Quotes

“A common mistake that people make when trying to design something completely foolproof is to underestimate the ingenuity of complete fools.”

Douglas AdamsME TodaySeptember 2009 Issue - Volume 11

“The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong, it usually turns out to be impossible to get at and repair.”

Douglas AdamsDirector, Center for Systems IntegrityPurdue University

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Acceptable design

IntroductionThe various considerations that are involved in the development of an acceptable design of a thermal system lead to the following main steps:

• ► Formulation of the design problem

• ► Conceptual design

• ► Initial design

• ► Modelling of the system

• ► Simulation of the system

• ► Evaluation of the design

• ► Selection of an acceptable design

Acceptable design

Initial DesignThe initial design follows the formulation of the problem and the conceptual design; it is the first step in the quantitative design procedure. The analysis of the system, through modelling and simulation, and evaluation of the design for its acceptability are based on the initial design.

Commonly used methods for obtaining an initial design are:

• ► Selection of components to meet given requirements and constraints

• ► Use of existing systems

• ► Selection from a library of previous designs

• ► Use of current engineering practice and expert knowledge of the application

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Acceptable design

Initial Design

Expert knowledgeExpert knowledge is understood as information available on the particular application and corresponding types of thermal systems, along with current engineering practice, i.e., the information obtained from an expert in the area.Several ideas developed over the years form the basis of this knowledge and it plays a major role in determining what is feasible and what is not. Information from earlier problems and attempts to resolve them is also part of this knowledge.

In the following example is illustrated the use and application of expert knowledge.

Acceptable design

Initial Design

Expert knowledge (cont.)

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Acceptable design

Initial Design

Expert knowledge (cont.)

Fig. 1.8 (a) Vapor compression refrigeration system

Acceptable design

Initial Design

Expert knowledge (cont.)

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Acceptable design

Initial Design

Expert knowledge (cont.)

Acceptable design

Initial Design

Expert knowledge (cont.)

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Acceptable design

Initial Design

Expert knowledge (cont.)

Acceptable design

Design Strategies

Commonly Used Design Approach

An initial design is developed on the basis of the problem statement and of the modelling, simulation and evaluation of the corresponding system. If the given requirements and constraints are satisfied, the initial design is acceptable. Otherwise, a redesign process is undertaken until an acceptable design is obtained.

The initial design may be based on existing systems and processes and thus result in a design which is very close to the final acceptable design. However,other strategies have been developed and are used for a variety of applications.Two strategies that are based on numerical simulation are presented in what follows.

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Acceptable design

Design Strategies

Other Strategies

Adjusting design variables

This approach is based on using the analysis, which incorporates modeling and simulation to study a range of design variables and determine the resulting outputs from the system for a typical, fixed set of operating conditions. The basic concept is kept unchanged, and the design variables,such as dimensions, specifications and characteristics of components, geometrical configuration, and materials are varied over their given ranges and the effects on the important quantities in the problem are investigated.

An acceptable design is obtained by choosing the appropriate values for the various design variables on the basis of the problem statement and simulation results.

Acceptable design

Design Strategies

Other Strategies (cont.)

Different designs

Another strategy considers a collection of chosen designs, including different concepts, and employs modelling and simulation to study the system behaviour over the expected range of operating conditions. An initial design is not the starting point, and simulation results are obtained for a variety of designs.

An acceptable design is obtained from the various designs considered by comparing the simulation results with the problem statement, ensuring that all the requirements and constraints are satisfied.

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Acceptable design

Design StrategiesOther Strategies (cont.)Both these strategies are shown schematically in Fig 5.4.

Acceptable design

Design StrategiesOther Strategies (cont.)The main difference between these strategies and the approach discussed in “Basic Considerations in Design” is that an initial design is not the starting point for the design process. Extensive simulation results are obtained for the range of design variables for fixed operating conditions in one case and for a variety of designs under different operating conditions in the other. Thedesired acceptable designs are selected on the basis of these results and the formulation of the design problem. The following example illustrates design of a system without starting with an initial design.

Example

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Acceptable design

Design StrategiesExample (cont.)

Figure 5.10 Solar collector and storage tank system

Acceptable design

Design StrategiesExample (cont.)

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Acceptable design

Design StrategiesExample (cont.)

Acceptable design

Design StrategiesExample (cont.)

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Design of Systems from Different Application AreasThe subject of design of thermal systems spans a fairly wide spectrum of problems. A few examples from some of the important areas of application are given here to illustrate the synthesis of the various ideas and design steps. Some of these examples are taken from actual industrial systems.

Manufacturing ProcessesManufacturing processes represent one of the most important areas in which thermal systems are of interest. These systems are generally complicated, and involve features such as:

Acceptable design

Design of Systems from Different Application AreasManufacturing Processes (cont.)

The governing equations for manufacturing processes are typically partial differential equations that are coupled through the boundary conditions and material property variation.In the following example is discussed the design process for a system used for industrial thermal processing of materials.

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Acceptable design

Design of Systems from Different Application AreasManufacturing Processes (cont.)

The governing equations for manufacturing processes are typically partial differential equations that are coupled through the boundary conditions and material property variation.In the following example is discussed the design process for a system used for industrial thermal processing of materials.

Acceptable design

Design of Systems from Different Application AreasManufacturing Processes (cont.)

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Acceptable design

Design of Systems from Different Application AreasManufacturing Processes (cont.)

Acceptable design

Design of Systems from Different Application AreasManufacturing Processes (cont.)

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Acceptable design

Design of Systems from Different Application AreasManufacturing Processes (cont.)

Acceptable design

Design of Systems from Different Application AreasManufacturing Processes (cont.)

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Acceptable design

Design of Systems from Different Application AreasManufacturing Processes (cont.)

Acceptable design

Design of Systems from Different Application AreasManufacturing Processes (cont.)

Let us now consider the thermal system for this process.

A continuous movement of the plastic cords, wound on the mandrel, in a wide channel with electric heaters and air flow driven by a fan may be designed, as shown in Fig. 5.17. The mandrels are rotated to ensure uniform surface heating.

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Acceptable design

Design of Systems from Different Application AreasManufacturing Processes (cont.)

Fig. 5.18 depicts the condition for which the cords are heated at constant heat flux in the heating zone and then cooled by convection. An acceptable design can be obtained from this figure. For a mandrel traversing speed of 1cm/s, a heating region length of 1.1 m and a cooling region length of 1.4 mis obtained an acceptable design if the maximum temperature is kept at 300 ºF(148.9 ºC) for safety.

Acceptable design

Design of Systems from Different Application AreasCooling of Electronic Equipment

This is an important area for thermal design, electronic devices are generally very temperature sensitive and it is crucial to design efficient systems to remove the thermal energy dissipated in electronic equipment. Figure 5.19 shows the dependence of the difference between the surface temperature of the electronic device and the ambient as a function of the input heat flux.

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Acceptable design

Design of Systems from Different Application AreasCooling of Electronic Equipment (cont.)

Various modes of heat transfer for removal of the dissipated energy are also indicated, with natural cooling in air applicable at very low heat flux levels and liquid cooling with boiling at very high levels.

The main characteristics of the electronic systems and associated cooling methods are:

Acceptable design

Design of Systems from Different Application AreasCooling of Electronic Equipment (cont.)

In the design of thermal systems for the cooling of electronic equipment the typical fixed quantities, requirements, constraints, and design variables are as follows:

The design process is generally first directed at the cooling parameters, keeping the geometry of the electronic circuitry unchanged.

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Design of Systems from Different Application AreasCooling of Electronic Equipment (cont.)

A relatively simple design problem is considered in the following example to illustrate some of the basic considerations involved.

Acceptable design

Design of Systems from Different Application AreasCooling of Electronic Equipment (cont.)

Example

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Design of Systems from Different Application AreasCooling of Electronic Equipment (cont.)

Solution:

• By employing a given value of the convective heat transfer coefficient, the problem is considerably simplified, since the calculation of the fluid flow in the enclosure is not required.• It should be noted this is a simplification, because, in general, the conjugate (conduction + convection) problem in the boards requires the solution of coupled nonlinear partial differential equations.• In the present case, a simple mathematical model is derived to determine the temperature distribution in the board.

Acceptable design

Design of Systems from Different Application AreasCooling of Electronic Equipment (cont.)

Solution (cont.):

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Acceptable design

Design of Systems from Different Application Areas

Cooling of Electronic Equipment (cont.)

Solution (cont.):

Acceptable design

Design of Systems from Different Application AreasCooling of Electronic Equipment (cont.)

Solution (cont.):

The mathematical model yields a second-order ordinary differential equation which may be solved numerically.The results were obtained with a Newton-Raphsom correction scheme applied to the fourth order Runge-Kutta method.

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Acceptable design

Design of Systems from Different Application AreasCooling of Electronic Equipment (cont.)

Solution (cont.):

Acceptable design

Design of Systems from Different Application AreasCooling of Electronic Equipment (cont.)

Solution (cont.):

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Acceptable design

Design of Systems from Different Application AreasCooling of Electronic Equipment (cont.)

Solution (cont.):The effect of varying the width of the board for five components is shown in Fig. 5.23; if the width can be increased to 0.30 m, five components can be accommodated without violating the temperature limit. Similarly, an increase in the thickness and height of the board leads to reduction in temperature levels, allowing additional components to be located per board.

Acceptable design

Design of Systems from Different Application AreasEnvironmental Systems

Thermal systems related to environmental problems have gained considerable interest because of the need to design efficient systems for the disposal of rejected energy, chemical pollutants, and solid waste.

Examples of the flows generated by such discharges are shown in the Figure below.

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Acceptable design

Design of Systems from Different Application AreasEnvironmental Systems (cont)

Acceptable design

Design of Systems from Different Application AreasEnvironmental Systems (cont)

Let us consider thermal or mass discharges to ponds and lakes. The design problem may be formulated as

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Acceptable design

Design of Systems from Different Application AreasEnvironmental Systems (cont)

The heat transfer from a cooling pond such as a lake involves

Transport mechanisms are relatively involved and simplifications are usually used to estimate the resulting heat and mass transfer; however, all the transport rates may be combined into a single expression such as:

Acceptable design

Design of Systems from Different Application Areas Environmental Systems (cont)

Environmental Systems (cont)

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Acceptable design

Design of Systems from Different Application AreasEnvironmental Systems (cont)

Acceptable design

Design of Systems from Different Application AreasEnvironmental Systems (cont)

SolutionThe given quantities are the pond dimensions, the total amount of

heat rejected Q, the temperature difference ∆T between the intake and outfall, and the surface heat transfer parameters h and Te that characterize the local ambient conditions.

The requirement is that the temperature rise at the intake must not exceed 2.5ºC.

The main constraint is that the energy rejected to the pond must be rejected to the environment for steady-state conditions.

Assumptions

• The pond is shallow as the depth H is much less than the length L and width W, and uniform conditions over the depth are assumed. • The heat transfer from the pond occurs only at the surface and the total thermal energy rejected to the pond must be lost to the environment at the surface for steady-state conditions,

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Acceptable design

Design of Systems from Different Application AreasEnvironmental Systems (cont)

Let us first consider a very simple one-dimensional model with uniformity assumed over the pond width as well, as shown in the Figure .

FIGURE. Three-dimensional problem of heat rejection to a body of water, along with a simplified one-dimensional model.

Acceptable design

Design of Systems from Different Application AreasEnvironmental Systems (cont)

where u is the average discharge velocity in the x direction and T(x) is the temperature distribution in the pond. The governing equation for T(x) is

The total heat rejected Q is given as

where εh is the eddy thermal diffusivity. The boundary conditions are

where To is the temperature at the outfall, x = 0, and TL is the temperature at the intake, x = L. It is assumed that there is no heat loss beyond x = L, giving the zero gradient condition.

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Acceptable design

Design of Systems from Different Application AreasEnvironmental Systems (cont)

To calculate the temperature distribution over the pond surface the differential equation needs to be solved. A possible approach to solve it is by using the finite difference method.The Figure shows the computed results for different values of the total energyrejected to the pond.

FIGURE Temperature distribution from the one-dimensional slug flow model for different values of energy rejected Q.

Acceptable design

Design of Systems from Different Application AreasEnvironmental Systems (cont)

Observations

The temperature rise at the intake is less than the allowable value of 2.5°C for Q = 400 kW. Therefore, this is an acceptable design.

The temperature rise at the intake is within the given limit even for Q = 600 kW.

For still higher values of Q, the given requirements cannot be met and an additional heat rejection system, such as a cooling tower, will be needed.

For small values of Q, the intake temperature is unchanged. As Q increases, the flow rate and thus u increases, resulting in an

increase in the temperature level needed to lose the increased amount of energy by surface heat transfer. This gives rise to a larger intake temperature.

An increase in the eddy diffusivity εh, which represents the turbulence due to wind and the flow in the pond, also increases the intake temperature due to enhanced thermal diffusion.