Heat Transfer In Triangular Ducts With Axial Conduction,containing Porous Medium
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The objective of this study is to find a numerical solution for the velocity and temperature field in a duct of triangular cross-section area. A fully saturated porous medium is considered to be present in the duct. The study reports the contribution of axial conduction in heat transfer to flow passing through triangular porous passages. The terms in x-direction are retained in the energy equation due to the presence of axial conduction. Also, because of the geometrical asymmetry, non-orthogonal boundary conditions can exist and thus make the determination of heat transfer more difficult. The problem under consideration uses H2 boundary conditions namely locally constant wall heat flux circumferentially and in the axial direction as well. The placement of porous materials can enhance the transfer of heat to a flowing fluid. The problem is divided into two parts. The first part deals with the finding the velocity field expression with the help of Brinkman's Momentum Equation. The second part uses the Energy Equation for finding the temperature field. A fully developed flow is considered for the velocity field calculations and a thermally developing flow for the temperature calculations. There are different methods for calculating the velocity field, one of them the method of Variational Calculus. The Variational Calculus leads to a minimization technique that provides a methodology known as the Galerkin method. Thus in the first phase, a weighted residual method (WRM) specifically the Galerkin method is used for calculations. This method allows using a polynomial function form known as basis function, which is finite, continuous and single valued.Depending on the duct cross section, formation of the basis function under H2 boundary conditions needs special attention for triangular ducts. The calculations for the temperature field might be formidable. Thus a Mathematica program is used for calculating the eigenvalues and eigenfunctions and for calculating various parameters such as Nusselt Number (Nu) and the heat transfer coefficient. The Mathematica program is as shown in Appendix A.