Boundary Integral Expression of Forced Convection Heat Transfer under Arbitrary Surface Temperature Distributions and Its Application to Heat Transfer Optimal Design

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Convection heat transfer characteristics depend not only on geometric and flow boundary configurations, but on also thermal boundary conditions. Thus, in order to evaluate the heat transfer rate under arbitrary thermal boundary conditions, we need to develop a general heat transfer expression instead of ordinary heat transfer coefficient defined in Newton's cooling law.From this reason, we have proposed a boundary integral expression of forced convection heat transfer, in which the heat transfer rate is expressed as a function of thermal boundary conditions. Moreover, we have extended this expression for natural and mixed convection heat transfer problems by using the perturbation method.The results obtained can be summarized as follows :(1) Local heat transfer rate in forced convection heat transfer problem can be expressed by a Fredholm-type boundary integral as a function of surface temperature distributions. This boundary integral expression, whose kernel can be obtained by a numerical simulation technique, also clarifies a detailed mechanism of forced convection heat transfer.(2) A numerical solution of adjoint problem for forced convection heat transfer enables us to calculate the mean heat transfer rate under arbitrary steady and unsteady thermal boundary conditions.(3) Introducing the perturbation principle and using the numerical solutions of base and perturbed adjoint problems, a kind of sensitivity function can be constructed for natural and mixed convection heat transfer. The sensitivity function gives the change of mean heat transfer rate for arbitrary thermal and flow boundary perturbations.