Unsteady-State Heat Conduction in Various Geometries

3 UNSTEADY-STATE HEAT CONDUCTION IN VARIOUS GEOMETRIES 

In Section 5.2 we considered a simplified case of negligible internal resistance where the object has a very high thermal conductivity. Now we will consider the more general situation where the internal resistance is not small, and hence the temperature is not constant in the solid. The first case that we shall consider is one where the surface convective resistance is negligible compared to the internal resistance. This could occur because of a very large heat-transfer coefficient at the surface or because of a relatively large conductive resistance in the object. 

To illustrate an analytical method of solving this first case, we will derive the equation for unsteady-state conduction in the. x direction only in a flat plate of thickness 2H as shown in Fig. 5.3-1. The initial profile of the temperature in the plate at i = 0 is uniform at T = 7j . At time t = 0, the ambient temperature is suddenly changed to T, and held there. Since there is no convection resistance, the temperature of the surface is also held constant at T,. Since this is conduction in the x direction, Eq. (5.1-10) holds. 

5 Principles of Unsteady-State Heat Transfer 

Generally, it is convenient to define a dimensionless temperature Y so that it varies between 0 and 1. Hence, 

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Sec. 5.3 Unsteady-State Heat Conduction in Various Geometries... 

Charts for diffusion in various geometries. The various heat-transfer charts for unsteady-state conduction can be used for unsteady-state diffusion and are as follows. 

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