Conduction: One Dimensional - 2 Chemical Engineering Notes | EduRev

Heat Transfer

Chemical Engineering : Conduction: One Dimensional - 2 Chemical Engineering Notes | EduRev

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

Fig. 2.4: Illustration 2.1

Conduction: One Dimensional - 2 Chemical Engineering Notes | EduRev

 

Illustration 2.2

Conduction: One Dimensional - 2 Chemical Engineering Notes | EduRev

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 Chemical Engineering Notes | EduRev

On putting all the known values,

Conduction: One Dimensional - 2 Chemical Engineering Notes | EduRev

Conduction: One Dimensional - 2 Chemical Engineering Notes | EduRev

Fig. 2.5: Illustration 2.2

Thus,

Conduction: One Dimensional - 2 Chemical Engineering Notes | EduRev

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 Chemical Engineering Notes | EduRev

Conduction: One Dimensional - 2 Chemical Engineering Notes | EduRev

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

 

The equivalent resistance of the wall will be,

Conduction: One Dimensional - 2 Chemical Engineering Notes | EduRev

where,

Conduction: One Dimensional - 2 Chemical Engineering Notes | EduRev

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

Conduction: One Dimensional - 2 Chemical Engineering Notes | EduRev

where, R is the equivalent resistance.

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