Exploring Darcy dissipation modulation of nanofluid with titanium dioxide (TiO2) and copper (Cu) for enhanced thermal performance in a vertical sheet

Abstract

Progressing an effective heat conductivity of base fluids poses a significant challenge faced by industries today, leading to growing interest in nanofluids. As conventional fluids are unsatisfactory for effective heat transmission compared to nanofluids, this article attempts to shed some light on to scrutinize the heat transmission and flow behaviours of nanofluid based on Titanium dioxide and Copper in the context of Darcy dissipation past a vertical stretching sheet. In the context of mathematical modeling, using the correspondence alteration method (similarity transformation), the leading equations were renewed into a system of nonlinear ODEs. The measured results of nonlinear ODEs are solved using the Homotopy perturbation method (HPM). The effects of distinct significant parameters on different distributions are exemplified through the graphs. The skin friction and Nusselt number are computed and compared for the bvp5c and HPM for different parameters. The important and intriguing features of this investigation is that, for dominant estimations of Grashoff number, the nanofluid velocity profile improves. Due to high Lorentz force and porosity effects near the walls of vertical sheet decreases the velocity profile for both Bvp5c and HPM cases. The temperature gets rises with higher values of magnetic, porosity, dissipation, heat generation and Biot factors. Nanoparticles enhance thermal diffusion, leading to steeper temperature gradients. Overall, Runge-Kutta fourth-order provides a highly accurate numerical solution, while HPM offers an efficient analytical approximation.