Refrigeration efficiency analysis for fully wet semi-spherical porous fins

In this study, temperature distribution equation for a fully wet semi-spherical porous fin is presented by a new modified fin parameter introduced by Sharqawy and Zubair which can be calculated without needing to fin tip conditions. The driving forces for the heat and mass transfer are considered temperature and humidity ratio differences, respectively. It is assumed that heat and mass convective coefficients are temperature-dependent and heat transfer through the porous media is simulated by using the passage velocity from the Darcy’s model. After introducing the governing equation, Least Square Method (LSM) and fourth order Runge–Kutta method (NUM) are applied to predict the temperature distribution in a Si3N4 porous fin. Also, the effects of porosity, Darcy number, Rayleigh number, Lewis number, etc. on the fin efficiency are investigated. As a main outcome, results confirm that Lewis number should be significantly more than unit to make high refrigeration efficiency.