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Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

Document Description: Conduction: One Dimensional - 2 for Mechanical Engineering 2022 is part of Steady State Heat Conduction for Heat Transfer preparation. The notes and questions for Conduction: One Dimensional - 2 have been prepared according to the Mechanical Engineering exam syllabus. Information about Conduction: One Dimensional - 2 covers topics like and Conduction: One Dimensional - 2 Example, for Mechanical Engineering 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Conduction: One Dimensional - 2.

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Illustration 2.1
The two sides of a wall (2 mm thick, with a cross-sectional area of 0.2 m2) are maintained at 30oC and 90oC. The thermal conductivity of the wall material is 1.28 W/(m·oC). Find out the rate of heat transfer through the wall?
Solution 2.1
Assumptions
1. Steady-state one-dimensional conduction
2. Thermal conductivity is constant for the temperature range of interest
3. The heat loss through the edge side surface is insignificant
4. The layers are in perfect thermal contact
Given,

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

Fig. 2.4: Illustration 2.1

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

 

Illustration 2.2

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

Solution 2.2
Assumptions:
1. Steady-state one-dimensional conduction.
2. Thermal conductivity is constant for the temperature range of interest.
3. The heat loss through the edge side surface is insignificant.
4. The layers are in perfect thermal contact.

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

On putting all the known values,

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

Fig. 2.5: Illustration 2.2

Thus,

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

The previous discussion showed the resistances of different layers. Now to understand the concept of equivalent resistance, we will consider the geometry of a composite as shown in fig.2.6a.

The wall is composed of seven different layers indicated by 1 to 7. The interface temperatures of the composite are T1 to T5 as shown in the fig.2.6a. The equivalent electrical circuit of the above composite is shown in the fig 2.6b below,

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

Fig.2.6. (a) Composite wall, and (b) equivalent electrical circuit

 

The equivalent resistance of the wall will be,

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

where,

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

Therefore, at steady state the rate of heat transfer through the composite can be represented by,

Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering

where, R is the equivalent resistance.

The document Conduction: One Dimensional - 2 Notes | Study Heat Transfer - Mechanical Engineering is a part of the Mechanical Engineering Course Heat Transfer.
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