A General Analytical Solution for Fluid Flow and Heat Convection Through Arbitrary-Shaped Triangular Ducts: A Variational Analysis

Abstract

Abstract In this paper, an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts is presented for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Here, the functionals of flow and heat transfer equations are derived and the resulted Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. In addition, effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. Here, the problem is solved for the case of constant heat flux at walls by considering the viscous dissipation. The results reveal that the value of the Nusselt number decreases with increasing the Brinkman number both in the wall cooling and wall heating modes. Finally, the proposed technique is suggested to solve the flow and heat transfer problems in complicated geometries analytically.