Impact of stretching and shrinking on the thermal profile and efficiency of a wet and porous longitudinal fin in motion subject to convection and radiation

We consider heat transfer with convection and radiation effect on a longitudinal wet and porous fin. The trapezoidal fin moving at a constant speed is subject to stretching and shrinking, and their influence on the fin's heat transfer rate and thermal distribution is investigated. The governing equation of the model mentioned above is nondimensionalized, and the resultant second-order nonlinear boundary value problem is solved numerically using the Chebyshev collocation method and validated using the shooting technique. All the simulations are carried out using MATLAB software. The impact of the critical dimensionless parameters on the fin tip temperature, the thermal profile, and the base heat transfer rate are analyzed graphically. Fin efficiency is also computed, and the influence of the pertinent parameters on it is inferred. For a moving fin, the shrinking mechanism favors a faster base heat transfer, an uptick of about 9%, and the stretching fin enhances thermal distribution and efficiency by around 3% and 14%, respectively. The rise is further accelerated with the enhancement of the Peclet number. The fin tapering from that of a rectangular profile ($C=0$) helps achieve a faster heat transfer rate along the fin length, a gain of nearly 22%, when the fin taper ratio $C$ varies from 0 to 0.8.