Abstract
This paper proposes analytical approximations for solving extended Graetz problems with axial diffusion in infinite domains. A general formulation, valid for both parallel-plates channels and circular ducts, is employed, and a discontinuous Dirichlet condition is applied at the wall. The adopted methodology consists of transforming the 2D convection equation into simpler one-dimensional forms, using approximation rules provided by the Coupled Integral Equations Approach. This technique is employed for producing expressions for the bulk temperature, and different levels of approximations are analyzed. The results are compared with an exact analytical solution to the problem and an expression obtained with the classical lumped system analysis (CLSA). While the results obtained with the CLSA are demonstrated to be substantially discrepant compared to the exact solution, the proposed improved formulas are equivalently simple and are shown to provide very good estimates for calculating the bulk temperature distribution. In addition, estimates for the length through which heat is diffused backward are also calculated with the derived approximate formulations and a practically perfect agreement is obtained with the higher-order approximation and the exact solution data.
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