Two Key Problems of Convection

A constant property fluid having velocity V and upstream temperature To flows steadily through an infinitely long tube of cross sectional area A and periphery P. The upstream half of the tube is insulated, while the downstream half either transfers heat with a coefficient h to an ambient at temperature T,x [Fig. 2.38(a)] or is subjected to a peripheral heat flux q [Fig. 2.38(b)]. The wall thickness of the tube is negligible. Based on a radially lumped analysis, we wish to know the axial temperature distribution in the fluid. 

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Figure 2.38 Two key problems of convection, (a) Heat transfer to ambient, (b) prescribed heat flux.

In terms of the knowledge gained so far, we are ready now for a study of two key problems which will be utilized frequently in the chapters on convection. 

Computer modeling of convection has had mixed success. Many convection problems, particularly those involving laminar flow, can readily be solved by special computer programs. However, in situations where turbulence and complex geometries are involved, computer analysis and modeling are still under development. Mass transfer analogies can play a key role in the study of convective heat transfer processes. Two mass transfer systems, the sublimation technique and the electrochemical technique, are of particular interest because of their convenience and advantages relative to direct heat transfer measurements. 

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