Analytical study on core flow in a novel scheme of cascade heat exchanger intensified with open foam partially filled in an annulus

Abstract

Due to the importance of energy-saving and efficiency in the industry, a novel scheme for waste heat recovery was utilized in the cascade refrigeration cycle. This system is composed of a cascade heat exchanger combined with a recuperator intensified with open foam. The exhaust air from the heat exchanger is used for the air handling unit. Also, core flow in an annular channel is proposed as an innovation to enhance heat transfer. An analytical study was performed to evaluate the impact of metal foam properties on the performance of the partially filled annular heat exchanger with asymmetric isothermal boundary conditions. The energy equations were decoupled by normalizing, linear combination, and the variable change method. Then by forming the Bessel differential equations, temperature solutions were achieved in terms of the modified Bessel functions of the first and second kinds. In the energy and momentum equations of the porous region, the local thermal non-equilibrium (LTNE) and the Darcy-Brinkman models were used, respectively. The analytical solutions of velocity, pressure drop, mass flow ratio, temperature, and Nusselt numbers were obtained. A hydraulically critical point exists at the nondimensional interfacial radius of 2.86 for Da=10−4. It revealed that the Darcy number and the thermal conductivity ratio are two crucial parameters for improving performance. Based on the Performance evaluation criterion (PEC) definition, the optimal porosity value of 0.91 was determined. Also, a design triangle in the range of metal foams was proposed to select the local Nusselt and Biot numbers. At a particular Biot number, the PEC value increases 3.76 times in the design range of metal foams. Results demonstrated that the core flow in an annular heat exchanger leads to high performance, several times greater than non-core flow.