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Soran University

Faculty of Engineering

Chemical Engineering Department

2015 -2016

Title: Radial heat conduction. Group: B. Names: Abdulsamad Alhamawande,Payam

Abdulrazaq and Rezhin M.Karem.

Date of experiment: 2015-12-19.

Data of Submission: 2016-01-04

Supervision: Mr. Ribwar K. Abdulrahman.

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The List of Contents:

Abstract …………………………………………………….(3)

Aim ……………………………………………………………(4)

Introduction ………………………………………………(5-6)

Equipment and components used.……………..(7)

Procedure ….………………………………………….……(8)

Data and Calculation (results)……………………..(9)

Discussion …………………………………………………(10-11)

Conclusion ………………………………………………..(12)

Reference ………………………………………………….(13)

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Abstract:

In this experiment there is a detailed explanation of heat transfer, thermal

conductivity and conduction through cylindrical shells.

And device user to measure thermal conductivity cylindrical shells and how it works.

And the relationship between thermal conductivity and temperature, length, radius,

heat.

And how to calculate thermal conductivity.

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Aim:

Measurement of linear thermal conductivity along the z-direction for radial system

heat transfer.

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Introduction:

Heat transfer is the exchange of thermal energy between physical systems,

depending on the temperature and pressure, by dissipating heat. The fundamental

modes of heat transfer are conduction or diffusion, convection and radiation.

Heat transfer always occurs from a region of high temperature to another region of

lower temperature. Heat transfer changes the internal energy of both systems

involved according to the First Law of Thermodynamics. The Second Law of

Thermodynamics defines the concept of thermodynamic entropy, by measurable

heat transfer.

Thermal equilibrium is reached when all involved bodies and the surroundings reach

the same temperature. Thermal expansion is the tendency of matter to change

in volume in response to a change in temperature.

Thermal conduction is the transfer of internal energy by microscopic diffusion and

collisions of particles or quasi-particles within a body or between contiguous bodies.

The microscopically diffusing and colliding objects include molecules, atoms,

electrons, and phonons. They transfer disorganized microscopic kinetic and potential

energy, which are jointly known as internal energy. Conduction takes place in all

phases of ponderable matter, such as solids, liquids, gases and plasmas, but it is

distinctly recognizable only when the matter is undergoing neither chemical reaction

nor differential local internal flows of distinct chemical constituents. In the presence

of such chemically defined contributory sub-processes, only the flow of internal

energy is recognizable, as distinct from thermal conduction. A net flow of energy

solely because of a temperature gradient is recognized as a flow of heat.

Heat spontaneously flows from a hotter to a colder body. For example, heat is

conducted from the hotplate of an electric stove to the bottom of a saucepan in

contact with it. In the absence of external drivers, within a body or between

bodies, temperature differences decay over time, and thermal equilibrium is

approached, temperature becoming more uniform.

In conduction, the heat flow is within and through the body itself. In contrast, in heat

transfer by thermal radiation, the transfer is often between bodies, which may be

separated spatially. Also possible is transfer of heat by a combination of conduction

and thermal radiation. In convection, internal energy is carried between bodies by a

moving material carrier. In solids, conduction is mediated by the combination of

vibrations and collisions of molecules, of propagation and collisions of phonons, and

of diffusion and collisions of free electrons. In gases and liquids, conduction is due to

the collisions and diffusion of molecules during their random motion. Photons in this

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context do not collide with one another, and so heat transport by electromagnetic

radiation is conceptually distinct from heat conduction by microscopic diffusion and

collisions of material particles and phonons. But the distinction is often not easily

observed, unless the material is semi-transparent.

In the engineering sciences, heat transfer includes the processes of thermal

radiation, convection, and sometimes mass transfer. Usually, more than one of these

processes occurs in a given situation. The conventional symbol for the material

property, thermal conductivity, is .

Cylindrical shells:

Conduction through cylindrical shells (e.g. pipes) can be calculated from the internal

radius, 𝑟1, the external radius, 𝑟2, the length, , and the temperature difference

between the inner and outer wall, 𝑇2 − 𝑇1

The surface area of the cylinder is

When Fourier's equation is applied:

and rearranged:

then the rate of heat transfer is:

the thermal resistance is:

And:

mean radius.-is important to note that this is the log𝑟𝑚

[1]

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Equipment and components used:

1-display and control unit.

2-measuring object.

3-experimental set-up for radial heat conduction.

4-experimental set-up for linear heat conduction .

[2]

Fig.1: Radial heat conduction.

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Procedure:

1. Set up the unit and adjust the cooling water flow rate.

2. Connect up the power and data cables appropriately.

3. Switch on the unit and adjust the desired temperature drop via the power setting

on the control and display unit.

4. When the thermal conduction process has reached a steady state condition, I.e.

the temperature at the individual measuring points are stable and no longer

changing, note the measurement results at the individual measuring points and the

electrical power supplied to the heater.

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Data and Calculations ( Results ) :

Q = 40w , L= 0.04m

K

(𝒘 𝒎.⁄ º𝐜)

ln( 𝒓𝒐𝒖𝒕

𝒓𝒊𝒏) ΔT(ºc) T(ºc) r(m) NO.

_

_

_

_

_ 1

_

_

_

50

0.01 2

16.98

0.693

-6.5

43.5

0.02 3

13.45

0.4055

-4.8

38.7

0.03 4

9.54

0.2877

-4.8

33.9

0.04 5

88.81

0.2231

-0.4

33.5

0.05 6

Q =−2πKL∆T

ln (rout rin⁄ ) K =

Qln (rout rin⁄ )

−2πL∆T

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Discussion:

1-Why we neglect the first rate of temperature ?

Because of the distance is zero and read temperature as minus.

2-What are the factors that affect the rate of conduction?

a)Temperature difference: The greater the difference in temperature between the

two ends of the bar, the greater the rate of thermal energy transfer, so more heat is

transferred. The heat, Q, is proportional to the difference in temperature:

b) Cross-sectional area: A bar twice as wide conducts twice the amount of heat. In

general, the amount of heat conducted, Q, is proportional to the cross-sectional

area, A, like this:

c)Radius (distance heat must travel): The longer the bar, the less heat that will make

it all the way through. Therefore, the conducted heat is inversely proportional to the

length of the bar.

d) Time: The amount of heat transferred, Q, depends on the amount of time

that passes, t — twice the time, twice the heat. Here’s how you express this

idea mathematically:

[3]

3-What is the relationship between thermal conductivity and temperature

difference, and length ? and ln (rout rin⁄ ) ?

K =Qln (rout rin⁄ )

−2πL∆T

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By increasing length and ΔT, thermal conductivity decrease. But by increasing

ln (rout rin⁄ ), thermal conductivity increase.

4-The thermal conductivity of an object depends on what?

The thermal conductivity of an object is dependent on its composition and dimensions(cross-sectional area and length). for two connected objects of the same dimension connected to hot and cold

reservoirs, the higher the temperature drop, the lower the thermal conductivity.

5-Why the temperature decreases?

Because there is resistance.

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Conclusion:

In this experiment we proved that thermal conductivity is inversely proportional with

temperature difference and length. By increasing temperature difference and length,

thermal conductivity decrease. By decreasing temperature difference and length,

thermal conductivity increase.

And thermal conductivity is directly proportional whit heat and ln(rout rin⁄ ). By

increasing ln (rout rin⁄ ) and heat, thermal conductivity increase. By decreasing

ln (rout rin⁄ ) and heat, thermal conductivity decrease.

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References: 1)(en.wikipedia)(2016)heat transfer. Available from: http://www.en.wikipedia.org

2)(gunt)(2016)Radial heat conduction. Available from: http://www.gunt.de

3)(dummies)(2016) understanding heat conduction and the factors. Available from:

http://www. dummies.com