ANALYSIS OF HEAT AND NANOPARTICLE TRANSPORT INWALTER'S-B FLUID SUBJECTED TO CONVECTIVE BOUNDARYCONDITIONS

Abstract

The study of non-Newtonian fluid flow and heat transfer has gained considerable attention due to its widespread applications in polymer processing, lubrication systems, chemical engineering, biotechnology, and thermal management technologies. Among various non-Newtonian fluid models, Walter's-B fluid is particularly important because it effectively describes viscoelastic fluids exhibiting short memory effects. The interaction of nanoparticles with such fluids further enhances thermal conductivity and heat transfer characteristics, leading to the development of nanofluids that are increasingly used in advanced cooling systems and industrial heat exchange applications. Understanding the combined effects of viscoelasticity and nanoparticle transport is therefore essential for improving the performance of modern thermal systems. The present study investigates the analysis of heat and nanoparticle transport in Walter's-B fluid subjected to convective boundary conditions. The mathematical model is developed using the boundary layer approximation for a two-dimensional steady incompressible flow. Heat transfer and nanoparticle concentration distributions are analyzed by incorporating Brownian motion and thermophoretic diffusion effects. Convective heating at the surface is considered through a Biot number parameter, which characterizes the interaction between the fluid and the surrounding thermal environment. Similarity transformations are employed to convert the governing partial differential equations into a system of nonlinear ordinary differential equations. The transformed equations are solved numerically using the Runge–Kutta fourth-order method combined with the shooting technique. The influence of various dimensionless parameters including Deborah number, Prandtl number, Lewis number, Brownian motion parameter, thermophoresis parameter, and Biot number on velocity, temperature, and nanoparticle concentration profiles is examined. Numerical results reveal that viscoelastic effects significantly influence momentum transport, while convective heating strongly enhances thermal boundary layer thickness. The thermophoretic parameter is found to increase nanoparticle concentration within the boundary layer, whereas Brownian motion enhances thermal transport mechanisms. The findings of this investigation provide valuable insights into the complex interaction between fluid viscoelasticity, heat transfer, and nanoparticle transport under convective boundary conditions. The results contribute to the optimization of industrial processes involving polymeric nanofluids, thermal insulation systems, cooling technologies, and advanced manufacturing operations. Furthermore, the study establishes a useful framework for future investigations involving magnetic fields, thermal radiation, chemical reactions, and hybrid nanofluid systems in non-Newtonian fluid environments.