Abstract
This paper addresses the impact of Darcy-Forchheimer flow of MHD viscous fluid over a linear stretchable surface. Inspection has been accomplished in the presence of Arrhenius activation energy, second order slip and chemical reaction which has not been considered earlier. Flow in the porous media is categorized by taking Darcy-Forchheimer model. In addition we considered electrically conducting flow which is induced by stretching sheet. Suitable similarity variables are employed to get the ordinary differential equations (ODE’s). The obtained mathematical expression are now solved numerically with the aid of bvp4c Matlab package which instigated three-stage Lobatto IIIa finite difference collocation procedure. Graphs are developed against convergence parameters like porosity parameter (Kp), local inertia coefficient (Fr) activation energy (E), chemical reaction rate constant (σ), Schmidt number (Sc), temperature difference ratio (Γ), exponentially fitted constant (m), magnetic parameter (M), radiation parameter (R), 1st-order (γ) and 2nd-order (δ) slip parameter, suction or injection parameter (S), Prandtl number (Pr). It is found that Sherwood number decreases in the presence of activation energy while opposite behaviour is seen for temperature difference ratio parameter, whereas temperature profile enhances for large value of inertia parameter and porosity parameter.
Highlights
The concept of fluid flow and heat transport analysis through porous structures has been receiving a great attention amongst engineers, geologist, mathematician and architectures due to its several scientific and practical situations such as nuclear waste repository, electronic cooling, packed bet heat exchanger, thermal insulation, drying technology, catalytic reactors and oil production, energy storage units, petroleum industries and geothermal systems and many others.[1–4] Henry Darcy did the pioneer work in 1856, for the homogenous fluids flow passing through porous medium
Because of the fact that porous media is to increase the resistance to the fluid motion, velocity of the fluid decrease whereas opposite trend in seen for temperature profile with the increase of porosity parameter
The resistive force is improved for the liquid, therefor lower velocity is obtained correspond to larger Forchheimer number
Summary
The concept of fluid flow and heat transport analysis through porous structures has been receiving a great attention amongst engineers, geologist, mathematician and architectures due to its several scientific and practical situations such as nuclear waste repository, electronic cooling, packed bet heat exchanger, thermal insulation, drying technology, catalytic reactors and oil production, energy storage units, petroleum industries and geothermal systems and many others.[1–4] Henry Darcy did the pioneer work in 1856, for the homogenous fluids flow passing through porous medium. Seddeek[9] performed the combined influence of thermophoresis and viscous dissipation effect under the saturating porous media of Darcy-Forchheimer flow. Bhatti et al.[17] employed numerical scheme to examine the viscous fluid flow over a permeable porous plate with MHD effects. MHD and radiation effects on viscous flow towards an exponential stretching sheet by utilizing HAM method. Ishak[20] considered combined impact of thermal radiation and MHD boundary layer flow over an exponential surface. And Madhu and Reddy[22] illustrated the thermal stratification effect on MHD viscous fluid flow and heat transfer towards an exponentially stretchable surface by using the finite difference scheme. From practical point of view Injection of fluid via porous surface has of application for boundary layer problem like polymer fiber coating, film cooling, coating of wires, etc. To formulate and investigate 2-D Darcy-Forchheimer model for viscous fluid induced by stretching surface. I have confirmed that the present numerical results provides a very good agreement as compared with the published work
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