Entropy Analysis for MHD Flow Over a Non-Linear Stretching Inclined Transparent Plate Embedded in a Porous Medium Due to Solar Radiation

Abstract

Nomenclature a-absorption or extinction coefficient of fluid, m-1 ; B-magnetic field, tesla; B 0-magnetic rate, positive constant; Br-Brinkman number (= μu w (x) 2 /ΔTk); C(ε)-porous medium inertia coefficient, m-1 ; C f-Skin friction coefficient (=-(2(m+1)/Re x) 0.5 f ηη (0)); C p-specific heat at constant pressure, J/(kgK); d p-particle diameter, m; D p-geometric parameter of porous medium; Ec-Eckert number (= u w (x) 2 /C p (T w-T ∞)); f-dimensionless velocity variable (= Ψ(x,y)(Re x) 0.5 /u w (x)); g-gravitational acceleration, m/s 2 ; Gr x-Grashof number (= g(T w-T ∞)β/ν 2); Ha-Hartman number (= B 0 x(σ/μ) 0.5); K(ε)-porous medium permeability, m 2 ; k-thermal conductivity, W/(mK); m-index of power law velocity, positive constant; M-magnetic parameter (= 2σB 0 2 /ρ ∞ b(m+1)); Nu-Nusselt number (=-(0.5(m+1)Re x) 0.5 θ η (0)); N s-Entropy generation number; Pr-Prandtl number (= μC p /k); q rad-radiation flux distribution, W/m 2 ; R-Radiation parameter; Re x-local Reynolds number (= ρu w (x)x/μ); T-temperature, K; u-velocity in x-direction, m/s; v-velocity in y-direction, m/s; x-horizontal coordinate, m; x-vertical coordinate, m; γ-plate inclination angle, degrees; α-thermal diffusivity, m 2 /s; θ-dimensionless temperature variable (= (T-T ∞)/(T w-T ∞)); μ-dynamic viscosity, kg/(ms); υ-kinematic viscosity, m 2 /s; ρ-density, kg/m 3 ; σ-electrical conductivity, mho/s; Ω-dimensionless temperature difference (= ΔT/T ∞ =(T-T w)/T ∞); Ψ-stream function, m 2 /s; ηsimilarity variable (= (y/x)(0.5Re x (m+1)) 0.5); β-thermal expansion coefficient, 1/K.

Entropy Generation Minimization of Nanofluid Flow in a MHD Channel Considering Thermal Radiation Effect

“…They attributed this to the low conductivity of plasma compared to the liquid metal. Habibi Matin et al [7] and Dehsara et al [8] investigated the second law analysis of MHD flow of nanofluid over a stretching sheet in the regular and porous mediums. They showed that adding nano particles to the base fluids in forced, natural, and mixed convection would cause a reduction in shear force and a decrease in stretching sheet heat transfer coefficient.…”

Entropy Generation in Boundary Layer Flow of a Micro Polar Fluid Over a Stretching Sheet Embedded in a Highly Absorbing Medium

“…Using local similarity solution technique and shooting quadrature, he numerically obtained the velocity, temperature and entropy generation number. Dehsara et al (2012) numerically analyzed entropy generation for the mixed convection flow over a nonlinear stretching inclined transparent plate embedded in a porous medium due to solar radiation. Butt et al (2012a) Frontiers in Heat and Mass Transfer (FHMT), 6, 7 (2015) Global Digital Central DOI: 10.5098/hmt.6.7 ISSN: 2151-8629 2 discussed the boundary layer flow and heat transfer analysis of a second grade fluid over a stretching sheet through a porous medium and investigated the effect of viscoelasticity on entropy generation using the Homotopy analysis method (HAM).…”