Conduction unsteady-state: with convection

Fig. 4-20 Nomenclature for numerical solution of unsteady-state conduction problem with convection boundary condition.

Figure 5.3-3, calculated using Eq. (5.3-7), is a convenient plot used for unsteady-state heat conduction into a semiinfinite solid with surface convection. If conduction into the solid is slow enough or h is very large, the top line with h /ailk = oo is used. 

EXAMPLE 5.4-3. Unsteady-State Conduction with Convective Boundary Condition... 

In many cases the temperature of a process that is varying continuously with time is determined experimentally by measuring the temperature in the slowest-heating region. In cans this is the center of the can. Methods given in Chapter 5 for unsteady-state heating of short, fat cylinders by conduction can be used to predict the center temperature of the can as a function of time. However, these predictions can be somewhat in error, since physical and thermal properties of foods are difficult to measure accurately and often can vary. Also, trapped air in the container and unknown convection effects can affect the accuracy of predictions. 

Another important technical task is to design an appropriate cooling capacity for the mold. The object itself and its unsteady-state cooling are part of what must be considered. In addition, the convective and conductive heat transfer from the mold cavity must be dealt with correctly. 

Conduction is most easily understood by considering heat flow in homogeneous isotropic solids because in these there is no convection and the effect of radiation is negligible unless the solid is translucent to electromagnetic waves. First, the general law of conduction is discussed second, situations of steady-state heat conduction, where the temperature distribution within the solid does not change with time, are treated third, some simple cases of unsteady conduction, where the temperature distribution does change with time, are considered. 

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