Darcy-Forchheimer relation in Casson type MHD nanofluid flow over non-linear stretching surface

Ghulam Rasool ^a,*, Ali J. Chamkha ^b, Taseer Muhammad ^c, Anum Shafiq ^d, Ilyas Khan ^e

a.  School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang, 310027, China
         b.  Mechanical Engineering Department, Prince Mohammad Bin Fahd University, Al-Khobar, 31952, Saudi Arabia
         c.  Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
         d.  School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China
         e.  Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, 72915, Vietnam

Abstract: Present article aims to discuss the characteristics of Casson type nanofluid maintained to flow through porous medium over non-linear stretching surface in the perspective of heat and mass transfer developments. A Casson type incompressible viscous nanofluid passes through the given porous medium via Darcy-Forchheimer relation. Slip boundary conditions are used for velocity, temperature and concentration of the nanoparticles. Brownian diffusion and Thermophoresis is attended. An induced magnetic field effect is involved to accentuate the thermo-physical characteristics of the nanofluid. The model incorporates boundary layer formulations and small magnetic Reynolds for practical validity. A fourth order Runge-Kutta (RK) scheme is enforced to solve the system numerically. Graphs are prepared for various progressive values of non-dimensionalized parameters whereas; variation in wall drag factor, heat and mass transfer rates is analyzed through numerical data. Results indicate that momentum boundary layer reduces for stronger inertial impact and the resistance offered by the porous media to the fluid flow. Temperature is found as a progressive function for the Brownian motion factor and Thermophoresis. The magnitude of wall drag factor, heat transfer and mass transfer rates shows reduction for progressive values of slip parameters.

Keywords: Casson type nanofluid; Darcy-Forchheimer model; Magnetohydrodynamics (MHD); Nonlinear stretching surface; Slip-boundary conditions