Numerical treatment of heat transfer in a moving porous fin depending on different geometries of the nanofluid

In this paper, we applied wavelet collocation method to study the second-order boundary value problem of non-linear differential equation of a fully wetted moving porous fin depending on different geometrical configuration of nanofluids, such as spherical, needle and disk. We compared the exact solution in a particular case using numerical method to validate the results and found good agreement. The novelty of the work is a highly nonlinear problem solved by a hybrid numerical method, i.e., the Legendre wavelet collocation method. This method gives a percentage error of \(10^{-7}\) with exact results, which demonstrates the method’s accuracy. We also observed that when sphere-shaped nanoparticles are present, the heat transfer rate in the fin is enhanced. Detailed investigations are done to determine the impact of various factors. The findings and error analysis are displayed in the form of figures and tables.