Analytical solution of flow and heat transfer in a three-tube heat exchanger consisting of evaporator and condenser partially filled with porous media

A triple-tube heat exchanger composed of a condenser and evaporator was proposed in this study. Also, the heat exchanger is partly filled with metal foam for improving performance. So that in addition to heat transfer enhancement, the pressure drop does not exceed the value expected by the designer. A system of six differential equations is formed under the coupled interfacial boundary conditions; accordingly, the dimensionless relations of velocity and temperature for fluid and solid are analytically obtained using continuity, momentum, and energy equations in porous and clear regions. In the solution method, first by normalizing, linear combination, and the variable change method, the differential equations are decoupled, and then by forming the Bessel differential equations, the solutions are obtained in terms of the modified Bessel functions of the first and second kind. In the porous medium, the local thermal non-equilibrium and the Darcy-Brinkman models are used in the energy and momentum equations, respectively. Also, to validate the analytical solutions, numerical simulation using Ansys-Fluent software with UDF coding was employed. The results showed that at high values of pore density, the effect of porosity on pressure drop is relatively small. The porosity 0.97 as the optimum performance point and the dimensionless porosity radius 1.78 as the critical hydraulically point was obtained. One of the most important results of this research is that the performance of the partly porous triple-tube heat exchanger improves significantly nearly three times compared to the non-porous one.