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UPWIND DIFFERENCING SCHEME IN EIGENFUNCTION EXPANSION SOLUTION OF CONVECTIVE HEAT TRANSFER PROBLEMS

D. J. N. M. Chalhub
Dept. of Mechanical Engineering, PGMEC, Universidade Federal Fluminense - UFF, RJ, Brazil

Leandro A. Sphaier
Department of Mechanical Engineering – PGMEC, Universidade Federal Fluminense, Rua Passo da Patria 156, bloco E, sala 216, Niteroi, RJ, 24210-240, Brazil

Leonardo Alves
Departamento de Engenharia Mecânica - TEM Universidade Federal Fluminense - UFF

Abstrakt

A new methodology for solving convective heat transfer problems has been developed, and is herein presented. The proposed solution scheme is based on writing the unknown potential in term of eigenfunction expansions, as traditionally carried out in the Generalized Integral Transform Technique (GITT). However, a different approach is used for handling advective derivatives. Rather than transforming the advection terms as done in traditional GITT solutions, upwind discretization approximations are used prior to the integral transformation. With the introduction of upwind approximations, numerical diffusion is introduced, which can be used to reduce unwanted oscillations that arise at higher Péclet values. The solution methodology is illustrated by employing it for solving a two dimensional Burgers' equation, arising from the analysis of transient thermally-developing flow between parallel plates, with the presence of axial diffusion. The flow is dynamically developed and a robin boundary condition is prescribed at the solid wall. The simulation results show cases for which the dissipative error and the associated numerical diffusion can actually improve the GITT solution. It is seen that a proper usage of the upwind approximation parameter can effectively reduce solution oscillations for higher Péclet values.

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