Abstract
This article describes a new method for the numerical solution of the generalized Graetz problem. The method involves the use of boundary integral concepts over subintervals or elements in the radial direction to eliminate the radial heat conduction operator. This leads to a new discretization scheme whereby the problem is reduced to a set of ordinary differential equations for the nodal temperatures and their radial gradients as a function of the axial distance. This set of equations is then solved by axial marching using the implicit Euler method. The method yields accurate solutions both in the entry region as well as for the fully developed regions of the pipe, and an example problem of heat transfer with a constant wall temperature is used for numerical testing of the computational scheme.
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