The heat transfer coefficient of convection from the wall to the flow depends on flow type, on surface temperature distribution in a stream-wise direction, and in transient cases also on time. In so-called conjugated problems, the surface temperature distribution of the wall and flow are coupled together. Thus, the simultaneous solution of convection between the flow and wall, and conduction in the wall are required because heat transfer coefficients are not known. For external and internal flows, very accurate approximate analytical expressions have been derived for heat transfer in different kinds of boundary conditions which change in flow direction. Due to the linearity of the energy equation, the superposition principle can be adopted to couple with these expressions the surface temperature and heat flux distributions in conjugated problems. In the paper, this type of approach is adopted and applied to a number of industrial applications ranging from flat plates of electroluminecence displays to the optimization of heat transfer in fins, fin arrays and mobile phones.

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