Flow Behaviour Of Non-darcian Magnetohydrodynamic Casson Nanofluid Over A Stretching Or Shrinking Sheet With Slips And Convective Heating

Investigations of electrically conducting Magnetohydrodynamic (MHD) Casson nanofluidrnflow are important areas of research due to their applications in industries and engineeringrnfor industrial coolant, brake fluid, MHD generator, nanodrug delivery, and others. Several studiesrnconcerning heat and mass transfer of MHD nanofluids have been reported in literature. However,rnmost of the existing related works do not consider the combined effects of nonlinear radiation andrnnon-Darcian porous medium. If the fluid velocity is high and the temperature differences withinrnthe fluid are sufficiently large, both Darcy and linearized radiative heat flux models may notrnaccurately determine the fluid flow and thermal structure. Therefore, this study was aimed atrnanalysing the effect of nonlinear radiation, binary chemical reaction, Arrhenius activation energy,rnvariable viscosity and thermal conductivity on convective non-Darcian MHD dissipative Cassonrnnanofluid flow past a stretching or shrinking sheet with slip and convective heating. The objectivesrnof the study were to: (i) determine the flow behaviour of a non-Darcian MHD dissipative Cassonrnnanofluid over a stretching or shrinking sheet with multiple slip boundary conditions; (ii) examinernthe influence of variable viscosity and variable thermal conductivity on natural convective flow ofrnnon-Darcian MHD Casson nanofluid flow with velocity slip and convective heating; and (iii)rnanalyse the effect of binary chemical reaction and Arrhenius activation energy on forcedrnconvective flow of non-Darcian MHD Casson nanofluid in the presence of non-Navier velocityrnslip condition.rnThe mathematical equations governing the flow, heat and mass transfer of Cassonrnnanofluid in a non-Darcian porous medium are:rn= 0,rnu vrnx yrn rn+rn rn2 2 *rn2rn0rn2rn1 ( ) 1rn= 1 1 , B Brnf f f p prnu u u B x brnu v u u urnx y y k krn  rn    rn      rn+  +  − −  +  −rn      rn2 2rn2rn2rn1rn= 1rn( )rnT BrnBrnp frnT T T C T D T urnu v D andrnx y y y y T y C yrnrn rn  rn             rn+ +  +    +  +  rn               rn2 2rn2 2 = . TrnBrnC C C D Trnu v Drnx y y T yrn   rn+ +rn   rnWhere 0 ( , ) , , , , , , , , , , , , , , B f p B p T u v     B k b T   D C C D  are respectively velocityrncomponents in x and y directions, dynamic viscosity, fluid density, Casson parameter, electricrnconductivity, magnetic field, porous medium permeability, Forchhiemer inertial coefficient, fluidrntemperature, fluid thermal diffusivity, heat capacity ratio, Brownian diffusion coefficient,rnnanoparticle concentration, heat capacity and thermophoretic diffusion coefficient. The aboverngoverning equations were reduced to nonlinear ordinary differential equations using similarityrntransformation and then solved by employing weighted residual method. The computational procedure was implemented by writing codes in MATHEMATICA Software.rnThe findings of the study were that: [label=()]rn1. an increase in non-Darcian porous medium parameter resulted into a reduction in velocity, while it enhanced both temperature and nanoparticle volume fraction;rn2. a hike in temperature dependent viscosity and thermal conductivity parameters contributed to a decrease in both temperature and nanoparticle volume fraction profiles and a rise in velocity profile;rn3. nanoparticle volume fraction profile was reduced as a result of an increase in chemical reaction parameter, while increasing activation energy parameter led to an increase in nanoparticle volume fraction profile; andrn4. an increase in radiation parameter resulted into a decrease in temperature profile.rnThe study concluded that the thermal radiation, Forchheimer, variable viscosity, variable thermal conductivity, chemical reaction and activation energy parameters have significant effects on the velocity, temperature, nanoparticle volume fraction, Nusselt number and the Sherwood number of Casson nanofluid. It is therefore recommended that those parameters are necessary and should be considered when carrying out a design involving Casson nanofluid flow.

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