MHD boundary layer flow and heat transfer of micropolar fluid past a stretching sheet with second order slip

Abstract

Skin friction coefficient c p Specific heat (J kg −1 K −1) f Dimensionless stream function g Dimensionless microrotation function j Micro-inertia density k Thermal conductivity of fluid (W m −1 K −1) K n Knudsen number ι = min[ 1 K n , 1] M Magnetic parameter N Microrotation component normal to xy-plane (s −1) n Microrotation parameter Nu x Local Nusselt number Pr Prandtl number q w Surface heat flux (W m −2) Re x Local Reynolds number T Temperature of the fluid inside the boundary layer (K) T w Temperature at the surface of the sheet (K) T ∞ Ambient temperature (K) u, v Velocity component along x-and y-direction (m s −1) Greeks α Momentum accommodation coefficient β Material parameter γ First order slip parameter δ Second order slip parameter η Dimensionless similarity variable θ Dimensionless temprature µ Coefficient of dynamic viscosity (Pas) υ Coefficient kinematic viscosity of (m 2 s −1) σ Electrical conductivity ψ Stream function (m 2 s −1) The molecular mean free path (m) Thermal diffusivity (m 2 s −1) ρ Fluid density (kg m −3

Physical aspects on unsteady MHD‐free convective stagnation point flow of micropolar fluid over a stretching surface

“…The governing equations of the problem are (see Chen and Ibrahim) …”

“…Ramzan et al discussed the heat and mass transfer features of MHD non‐Newtonian liquid over a stretching surface with stratification and radiation. The influence of variable thermal conductivity on the boundary layer flow of a non‐Newtonian liquid due to the stretching of a bidirectional surface was studied by Lu et al The influence of second‐order velocity slip on Newtonian fluid flow across a convectively heated surface was analyzed by Fang et al Ibrahim discussed the influence of slip parameter on micropolar fluid over an extending surface and said that the velocity distribution is a reducing function of slip parameter. The influence of radiation on MHD stagnation point flow past a melting surface in the presence of slip was scrutinized by Mabood et al It was reported that the melting parameter has a propensity to enhance the rate of thermal transport.…”

Numerical solution of micropolar nanofluids with Soret, Dufor effects and multiple slip conditions

“…Ibrahim [27] and Ibrahim [28] presented the investigation on micropolar fluid taking into account various determing parameters like Hartmann number, second order slip and passive control of nanoparticles. The results designated that the flow field and the engineering aspects of the study are sturdily affected by slip and material parameters.…”

Significance of the nonlinear radiative flow of micropolar nanoparticles over porous surface with a gyrotactic microorganism, activation energy, and Nield's condition

“…Ion‐slip condition in the micropolar fluid under Hall effects were investigated by Ojjela and Kumar . The implementation of second order slip caused by stretching surface by using micropolar fluid was conducted by Ibrahim . A numerically targeted exploration of micropolar with heat transfer over a cylinder has been disclosed by Prasad et al…”

“…specific heat of fluid and nanoparticles 1); dy(2,1) = y(3,1); dy(3,1) = (y(2,1)^2-y(1,1)*y(3,1)-K*y(5,1) + (K1)*y(2,1)-lmda*(y(6,1)-Nr*y(8,1)-Nc*y(10,1))/ (1 + K)); dy(4,1) = y(5,1); dy(5,1) = (y(2,1)*y(4,1) + K*(2*y(4,1) + y(3,1))-y(1,1)*y(5,1))/(1 + 0.5*K); dy(6,1) = y(7,1); dy(8,1) = y(9,1); dy(7,1) = -((eps + 4*Rd*(theta-1)*(1 + (theta-1)*y(6,1))^2)*y(7,1)^2 + Pr*y(1,1)*y(7,1) + Pr* (Nb*y(7,1)*y(9,1) + Nt*y(7,1)^2))/(1 + eps*y(6,1) + 1.3333*Rd*(1 + (theta-1)*y(6,1))^3); dy(9,1) = -(Nt./Nb)*dy(7,1)-Pr*Le*y(1,1)*y(9,1) + Pr*Le*sigma*y(8,1)*((1 + dlta*y(6,1))^n)* (exp(-E./(1 + dlta*y(6,1)))); dy(10,1) = y(11,1); dy(11,1) = -Lb*(y(1,1)*y(11,1)) + Pe*(y(9,1)*y(11,1) + dy(9,1)*(y(10,1) + dta1)); end Boundary conditions: global m gmaNbNt S res = [ya(1)-S, ya(2)-1, ya(4) + m*ya(3), ya(7) + gma*(1-ya (6)), Nb*ya(9) + Nt*ya (7),ya (10) (6);Nr = vec (7);Rd = vec (8);theta = vec(9);Le = vec(10); sigma = vec(11);dlta = vec(12);eps = vec(13);n = vec (14);E = vec(15);m = vec(16);gma = vec (17);lmda = vec(18);Lb = vec (19);…”