Analytical investigation of porous pin fins with variable section in fully-wet conditions

The present work investigates the temperature distribution, heat transfer rate, efficiency and optimization of porous pin fins in fully wet conditions. The thickness varies along the length of the fin and the lateral surface equation is defined as functions that include diversification fins (rectangular, triangular, convex parabolic and concave parabolic sections). Fins are made of aluminium and the tips of fins are insulated. Furthermore, it is assumed that the heat transfer coefficient depends on temperature and in the fin it changes according to temperature changes. In order to derivethe heat transfer equation, energy balance and Darcy model are used. After presenting the governing equation to obtain the temperature distribution, least squares method (LSM) is applied. Comparison of the results between analytical solution and numerical outcome (fourth order Runge–Kutta method) shows that LSM is a convenient and powerful method in engineering problems. Then the effects of various geometric and thermophysical parameters (power index for geometry (n), porosity, Biot number and relative humidity) on the dimensionless temperature fin, efficiency and heat transfer rate are examined. Optimum design analysis was also carried out.