Thermal Boundary Condition Effects on Forced Convection Heat Transfer. Application of Numerical Solution of Adjoint Problem.

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Abstract

A numerical approach based on the adjoint formulation of forced convection heat transfer is proposed, to evaluate the total or mean heat transfer rate under arbitrary thermal boundary conditions. Using the numerical solution of the adjoint problem under the uniform Dirichlet condition, which can be computed by a slightly modified CFD code, an influence function of the local surface temperature can be obtained. As a result, the total heat transfer for arbitrary surface temperature distributions can be calculated by the influence function. In a similar fashion, using the numerical solution of the adjoint problem under the Neumann condition, the mean surface temperature can also be expressed as an influence function of the local heat flux distributions. The influence functions for a circular cylinder and for an in-line square rod array are presented to illustrate the present method.

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