An analytical method for the numerical calculation of the heat transfer coefficient in arbitrarily shaped ducts with constant wall temperature at the boundary is presented. The flow is considered to be laminar and fully developed, both thermally and hydrodynamically. The method presented herein makes use of Galerkin-type functions for computation of the Nusselt number. This method is applied to circular pipes and ducts with rectangular, isosceles triangular, and right triangular cross sections. A three-term or even a two-term solution yields accurate solutions for circular ducts. The situation is similar for right triangular ducts with two equal sides. However, for narrower ducts, a larger number of terms must be used.

A generalized method is presented that accommodates the linear form of the diffusion equation in regions with irregular boundaries. The region of interest many consist of subregions with spatially variable thermal properties. The solution function for the diffusion equation is decomposed into two solutions: one with homogeneous and the other with nonhomogeneous boundary conditions. The Galerkin functions are used to provide a solution for a diffusion problem with homogeneous boundary condition and linear initial condition. Problems with nonhomogeneous boundary conditions can be dealt with by many other schemes, including the standard Galerkin method. The final solution is a combination of these two solutions.

No abstract