Comparisons Between Integral Transform, Finite Volumes and Combined Solution Strategies for Convective Heat Transfer Problems

Abstract

Both traditional discretization-based numerical methods and alternative hybrid analytical-numerical techniques have been successfully applied for solving a considerable number of convective heat transfer problems. Despite the number of studies dedicated to separately solving a given problem by one methodology or the other, there are very few studies dedicated to comparing the computational solution performance of these approaches. In this context, this paper presents a comparison of solutions using the Finite Volumes Method (FVM) and the Generalized Integral Transform Technique (GITT) for a three dimensional steady-state convective heat transfer problem. The selected problem is that of thermally developing laminar flow within a square duct. The flow is considered kinetically developed and a constant wall temperature condition is employed. Both solutions are computationally implemented using the Mathematica system and, in order to guarantee a fair comparison, both implementations employ the same numerical ODE integrator to handle the solution in the flow direction. The comparisons are made by observing the convergence behavior of the Nusselt number for different positions along the flow direction, for both methodologies. In addition to these comparisons, combined solution strategies are analyzed, in which the velocity is obtained by one methodology and the temperature by the other.