Electronic edition ISSN 1574-0579

Thermodynamic and response surface assessment of MHD Maxwell nanofluid flow with convective heating over a Darcy--Forchheimer stretching sheet

Ratnamanjari Sahoo¹ - Bharat Keshari Swain² - Apul Narayan Dev³

¹ Center for Data Science, ITER, Siksha 'O' Anusandhan (deemed to be University), 751030, Odisha, India
² Department of Mathematics, Agarpara College, Agarpara, Bhadrak, 756115, Odisha, India
³ Department of Mathematics, ITER, Siksha 'O' Anusandhan (deemed to be University), Bhubaneswar,751030, Odisha, India

Abstract
This study investigates the magnetohydrodynamic (MHD) mixed convection flow of a Maxwell nanofluid over a vertically stretching sheet embedded in a Darcy-Forchheimer porous medium, incorporating viscous dissipation, internal heat generation/absorption and homogeneous chemical reaction. The Buongiorno model is employed to account for Brownian diffusion and thermophoresis, while temperature-dependent viscosity and thermal conductivity, along with concentration-dependent Brownian diffusivity are considered to enhance physical realism. The governing nonlinear boundary layer equations for momentum, energy and species transport are formulated and transformed into a coupled system of ordinary differential equations using appropriate similarity transformations. The resulting boundary value problem is solved numerically using the shooting technique combined with a fourth-order Runge-Kutta method. Furthermore, response surface methodology (RSM) and ANOVA are implemented to analyze parameter sensitivity and optimize the Nusselt number. Effects of the Forchheimer number, chemical reaction parameter, Biot number and Eckert number on velocity, temperature, concentration, entropy generation, Bejan number, skin friction coefficient, Nusselt number and Sherwood number are examined. The results show that increasing Fr suppresses velocity and heat transfer due to enhanced porous resistance, whereas increasing Rc decreases velocity, temperature and concentration profiles while significantly enhancing mass transfer. Higher Ec increases velocity and temperature because of viscous dissipation, whereas larger Bi strongly enhances heat transfer through intensified convective heating. Entropy generation increases with Fr, but decreases with increasing Rc, Ec and Bi. The ANOVA analysis confirms that the developed RSM model is highly significant, with excellent predictive capability (R₂ = 0.99938). The Biot number is identified as the dominant parameter, contributing approximately 86.99 percent to the Nusselt number variation. The study provides useful thermodynamic information for porous thermal systems and reactive nanofluid transport applications. Keywords: Maxwell nanofluid, slip effect, MHD viscous dissipation, Darcy-Forchheimer porous medium, chemical reaction. Tables 10, Figs 19, Refs 34.