EXPERIMENT2 – RADIAL HEAT CONDUCTION

A: A Steady State Heat Conduction

B: The Fourier Rate Equation for Radial Heat Transfer

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SAFETY INSTRUCTIONS

All practical work areas and laboratories should be covered by local safety regulations which

must be followed at all times.

Hot Surfaces and Liquids

The unit incorporates a pumped electric water heater, and is capable of producing temperatures that could cause skin burns.

Before disconnecting any of the pipes or tubing:

 Leave time for the water to cool

 Check that the temperature is at a safe level

 Do not touch any surfaces close to ‘Hot Surfaces’ warning labels, or any of the interconnecting tubing, whilst the equipment is in use.

General Instructions

 If a spill occurs, turn off the pumps (if possible without injury) and immediately

get in touch with the Laboratory Instructor or Technician.

 Ensure that protective clothing (LAB coat) and gloves are worn when handling any of the substances used in the reactor.

 Shorts or skirts should not be worn to the lab.

 Sandals, high heels, or open-toe shoes are not acceptable.

 Safety glasses are a required item to be worn in all areas of the laboratories.

 Electrical – Burn / Shock: Care with electrical connections, particularly with grounding, and not using frayed electrical cords, can reduce hazard.

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Contents Theory …………………………………………………………………………………………………………………………………. 4

Experimental Objectives ………………………………………………………………………………………………………… 4

Safety Precautions ………………………………………………………………………………………………………………… 4

Equipment Description ………………………………………………………………………………………………………….. 4

Exercise A – A Steady State Heat Conduction ………………………………………………………………………….. 6

Procedure …………………………………………………………………………………………………………………………….. 6

Results …………………………………………………………………………………………………………………………………. 8

Discussion and Conclusion ……………………………………………………………………………………………………… 8

Exercise B – The Fourier Rate Equation for Radial Heat Transfer ……………………………………………….. 8

Procedure …………………………………………………………………………………………………………………………….. 8

Results …………………………………………………………………………………………………………………………………. 9

Discussion and Conclusion ……………………………………………………………………………………………………… 9

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Theory Heat transfers in different modes conduction, convection, and radiation. In this experiment you are

going demonstrate heat transfer in conduction. Conduction can take place in gasses, liquids, and solid.

In solids, conduction accrues due to vibrations of molecules, and in gasses and liquids due to collisions

and diffusion.

In general, heat conduction accrues in a diversity of engineering applications and can be calculated

using Fourier’s law of heat conduction:

�̇�𝑐𝑜𝑛𝑑 = −𝑘 𝐴𝑑𝑇

𝑑𝑟

For a steady- state conduction in a cylindrical wall (disk), heat transfers in radial direction of the

medium layers and will be depending on the radius of cylindrical layers and the temperature of each

layer. Taking the surface area of the cylinder 2𝜋𝑟𝐿 and after integrating then the appropriate form of

the general heat conduction in radial direction will be calculated by:

�̇�𝑐𝑜𝑛𝑑 = 2𝜋𝑘𝐿 (𝑇1 − 𝑇2)

ln (𝑟2𝑟1

)

Where: 𝑟1 𝑎𝑛𝑑 𝑟2 are the radius of inner and

outer surfaces, and 𝐿 is the total length of the

cylinder.

Experimental Objectives In this experiment you are going to demonstrate linear heat conduction according to the following:

A. To measure the temperature distribution for steady-state conduction of energy through a

uniform cylindrical wall (radial) and demonstrate the effect of a change in heat flow.

B. To investigate the Fourier Rate Equation in calculating heat transfer.

Safety Precautions 1. Do not touch any surface after operating the experiment!

2. Do not unplug any of the thermocouples. Thermocouples are sensitive devices and can be

damaged easily if they are mishandled!

3. Allow time for the equipment after it cool before handling any component.

4. Do not unplug any of water connection as it can cause overheat and serious damage!

Equipment Description See Figure 1. The radial heat conduction equipment comprises a heated disk (2) made of brass with

110mm diameter and 3.2 mm thickness with central copper core (5) of 14mm diameter. The entire

specimen is located in a plastic case (6) to provide insulation.

The central core is connected to the heating element (4) which can be controlled by using service unit

HT10XC. The disk is cooled by a flow of water through a coper tube (1), pressure regulator (11) is also

connected to control water flow.

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Six Thermocouples (7) are installed on the disk to measure temperature gradient from the heated

central core to the cooled section. They are positioned at different radii from the center disk according

to the following T1 7mm, T2 10mm, T4 30mm, T5 40mm, T6 50mm.

Figure 1: Radial Heat Conduction Device

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Figure 2: Section View Showing thermocouples

Exercise A – A Steady State Heat Conduction In this exercise you are going to measure the temperature distribution for steady-state conduction of

energy through a uniform cylindrical wall (radial) and demonstrate the effect of a change in heat flow.

Procedure 1. Start your experiment only after you receive operating and safety practice by your instructor!

2. Insure that water is supplied to the cold section.

3. Insure that the flexible water connection is directed to the drain.

4. Insure that each thermocouple is connected to its socket at part (K) of the service unit.

5. Insure that switch (B) on the service unit is toward the Manual setting.

6. Insure that you select V on the measurement selection switch (E).

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Figure 3: HT10XC Service Unit

7. Turn on the main standby switch (A)

8. Watch the voltage readings on top panel meter (D) (since you selected V on step number 6).

9. Starting from zero voltage increase the volt gradually to 12V.

10. At 13V change the measurement selection switch (E) to I, and read the corresponding current

value on meter (D).

11. Make sure that the temperature switch (G) is located at T1, as a start, you will change it later.

12. Wait for 10min (for a steady-state condition) and watch the temperature on the adjacent panel

meter (J).

13. After reaching a steady state, take the reading of T1 and change the temperature reading switch

to display other temperatures.

14. Fill the table below of the temperatures at different layers and don’t forget to mention the

units. Note that at the third layer you won’t be able to measure T3, this will be calculated later.

15. Repeat step 9 with changing the voltage at 14 and 16V.

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Results Fill the table below according to your experimental results.

Table 1: Temperatures recorded for each thermocouple vs position along the bar

T1 T2 T4 T5 T6

𝑟𝑖 (mm) 7 10 30 40 50

T at 13V (oC)

T at 14V (oC)

T at 16V (oC)

Discussion and Conclusion In this part, you will discuss and make a conclusion based on your own results in the lab.

Exercise B – The Fourier Rate Equation for Radial Heat Transfer In this exercise you need to use the data obtained from the previus section. You will investigate the

Fourier Rate Equation and calculate the rate of heat flow for steady-state conduction of energy

through the wall of a cylinder (radial energy flow).

The disk is considered to be constructed of a series of different layers. At each layer the temperature

is measured. Since the area of each layer increase with the radius, the temperature gradient will

decrease.

Figure 4: Diagram showing heat in radial direction.

Procedure Figure 4 represent the temperature distribution across the cylindrical bar.

1. Since we are assuming almost zero heat lost in the heat transfer process. Find the heat transfer

rate that is generated as electrical work to the disk by using 𝑄𝑒𝑙𝑒̇ = 𝑉 × 𝐼 use the readings

taking for the diferent voltage input and fill in table 2 (they will represent a theoritical values).

2. Since the material of the dicsk is brass use thernmal conductivity as 110W/m.C.

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3. Calculate the rate of heat transfer from the layer 1 to layer 6, using the proper equation at

different volatges used (they will represent experimental values).

Results Fill the table below according to your experimental results.

Table 2: Experimental Results

At 13V At 14V At 16V

Quantity Values Units Values Units Values Units

𝐼

T1

T6

𝑟1

𝑟6

𝐿

𝑘

�̇�𝑒𝑙𝑒.

�̇�𝑐𝑜𝑛𝑑.

Discussion and Conclusion In this part, you will discuss and make a conclusion based on your own results in the lab.

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Exercise

Givens:

L= 3.2×10-3 m, KBrass = 110 W/m.oC

T1 T2 T4 T5 T6

𝑟𝑖 (mm)

T at 13V (oC)

T at 14V (oC)

T at 16V (oC)

1. Plot temperature gradient (T vs r) for each electrical power input in separate graph.

2. From the graph, get the value of T3, exp. and fill in the table below:

T3, exp.

𝑟𝑖 (mm) 20

T at 13V (oC)

T at 14V (oC)

T at 16V (oC)

3. Fill the below table according to your calculations and readings:

At 13V At 14V At 16V

Quantity Values Units Values Units Values Units

𝐼 2.16 A 2.32 A 2.68 A

T1

T6

𝑟1

𝑟6

𝐿

𝐾

�̇�𝑒𝑙𝑒.

�̇�𝑐𝑜𝑛𝑑.

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4. Calculate T3, Theoretical using Fourier Rate Equation between layer 1 & 3 for the three-

power input theoretically.

T3, Theoretical

𝑟𝑖 (mm) 20

T at 13V (oC)

T at 14V (oC)

T at 16V (oC)

5. Find the percentage error in each value for the rate of heat transfer (�̇�𝑐𝑜𝑛𝑑.) and T3.

6. What are the major factors for these errors in this experiment?