Enhancement in Thermal Energy and Solute Particles Using Hybrid Nanoparticles by Engaging Activation Energy and Chemical Reaction over a Parabolic Surface via Finite Element Approach

TLDR

Hybrid nanoparticles have been extensively studied for their significant applications in thermal transport across various industrial processes. This study investigates the flow of a Powell–Eyring fluid containing hybrid nanoparticles over a melting parabolic stretched surface. Boundary‑layer equations for the Powell–Eyring fluid were derived, transformed into ordinary differential equations via similarity variables, and solved numerically using a finite‑element procedure in MAPLE 18.0, with grid‑independent validation and computation of surface drag and heat transfer coefficients. The finite‑element approach proved highly effective and readily applicable to other nonlinear problems; results show that the temperature profile increases with the magnetic parameter while decreasing with the Prandtl number.

Abstract

Several mechanisms in industrial use have significant applications in thermal transportation. The inclusion of hybrid nanoparticles in different mixtures has been studied extensively by researchers due to their wide applications. This report discusses the flow of Powell–Eyring fluid mixed with hybrid nanoparticles over a melting parabolic stretched surface. Flow rheology expressions have been derived under boundary layer theory. Afterwards, similarity transformation has been applied to convert PDEs into associated ODEs. These transformed ODEs have been solved the using finite element procedure (FEP) in the symbolic computational package MAPLE 18.0. The applicability and effectiveness of FEM are presented by addressing grid independent analysis. The reliability of FEM is presented by computing the surface drag force and heat transportation coefficient. The used methodology is highly effective and it can be easily implemented in MAPLE 18.0 for other highly nonlinear problems. It is observed that the thermal profile varies directly with the magnetic parameter, and the opposite trend is recorded for the Prandtl number.