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Influence of Non-linear Thermal Radiation on MHD Double-Diffusive Convection Heat and Mass Transfer of a Non-Newtonian Fluid in a Porous Medium

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Abstract

The present paper deals with the problem of steady, magnetohydrodynamic laminar double-diffusive convection heat and mass transfer of a micropolar fluid over a vertical permeable semi-infinite plate embedded in a uniform porous medium in the presence of non-linear thermal radiation. In addition, the present model allows the influence of heat generation/absorption and first-order chemical reaction. The governing equations are solved efficiently by Runge–Kutta–Fehlberg method with shooting technique. The effects of thermal buoyancy ratio, Schmidt number, chemical reaction parameter, heat generation/absorption and surface suction/injection on the fluid velocity, microrotation, temperature and solute concentration are analyzed. It is found that increase in the inverse Darcy number results in decrease in the velocity and microrotation distributions whereas reverse effects are seen on the temperature and concentration distributions. Also, it is observed that with increase in the magnetic parameter there is decrease in the velocity and microrotation gradient whereas reverse effects are noticed on the temperature and concentration distributions.

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Abbreviations

A :

Constant for wall temperature and concentration

B :

Microrotation material constant \((B=\nu /(j(g\beta _T A)^{1/2}))\)

\(B_{0}\) :

Strength of applied magnetic field

C :

Concentration at any point in the flow field

\(C_{f}\) :

Local skin-friction coefficient defined by Eq. (25)

\(C_m\) :

Local mass transfer coefficient defined by Eq. (27)

\(c_{p}\) :

Specific heat at constant pressure

\(C_q\) :

Local heat transfer coefficient defined by Eq. (26)

\(C_r \) :

Local wall microrotation coefficient \((C_r=\xi C_r^{*})\)

\(C_w\) :

Concentration at the wall

\(C_\infty \) :

Concentration at free stream

D :

Mass diffusivity

d :

Mean particle diameter

\(Da^{*}\) :

Inverse Darcy number (\(Da^{*}\)=\(\nu /(K(g\beta _T A)^{1/2})\))

f :

Dimensionless stream function \((f=\psi /((g\beta _T A\nu ^{2})^{1/4}x))\)

\(f_0\) :

Dimensionless wall mass transfer coefficient \((f_0=-V_w/(g\beta _T A\nu ^{2})^{1/4})\)

g :

Gravitational acceleration

Gr :

Buoyancy ratio (\(Gr=\beta _C(C_w-C_\infty )/(\beta _T(T_w-T_\infty ))\))

j :

Microrotation per unit mass

K :

Permeability of the porous medium

k :

Dimensionless chemical reaction parameter \((k=R/(g\beta _T A)^{1/2})\)

\(K^{*}\) :

Vortex viscosity

M :

Magnetic parameter

N :

Angular velocity or microrotation

\(P_r\) :

Prandtl number \((P_r=\rho \nu c_p/\kappa _e)\)

\(Q_0\) :

Heat generation or absorption coefficient

\(q_r\) :

Heat flux \(q_{r}=-\frac{4\sigma ^{*}}{3k^{*}}\frac{\partial T^{4}}{\partial y}\)

R :

Chemical reaction parameter

\(R_d\) :

Radiation parameter

S :

Porous medium thermal dispersion parameter \((S{=}c_p \sigma d(g\beta _T A)^{1/2}/(g\beta _T \alpha ))\)

\(S^{*}\) :

Local porous medium thermal dispersion parameter \((S^{*}=S\xi )\)

\(S_c\) :

Schmidt number \((S_c=\nu /D)\)

T :

Temperature at any point

\(T_w\) :

Wall temperature

\(T_\infty \) :

Free stream temperature

u :

Tangential or x-component of the Darcian velocity

v :

Normal or y-component of the Darcian velocity

\(V_w\) :

Dimensional wall mass transfer

x :

Distance along the plate

y :

Distance normal to the plate

\(\alpha \) :

Molecular thermal diffusivity

\(\alpha _e\) :

Effective thermal diffusivity of the porous medium

\(\alpha _d\) :

Thermal diffusivity of the porous medium due to thermal dispersion

\(\beta _C\) :

Concentration expansion coefficient

\(\beta _T\) :

Thermal expansion coefficient

\(\Delta \) :

Microrotation material parameter \((\Delta =K^{*}/(\rho \nu )\))

\(\delta \) :

Dimensionless heat generation or absorption parameter \((\delta =Q_0/(\rho c_p(g\beta _T A)^{1/2}))\)

\(\epsilon \) :

Porosity

\(\phi \) :

Dimensionless concentration \((\phi =(C-C_\infty )/(C_w-C_\infty ))\)

\(\gamma \) :

Spin gradient viscosity

\(\eta \) :

Dimensionless distance normal to the plate, \((\eta =(g\beta _T A/\nu ^{2})^{1/4}y)\)

\(\kappa _e\) :

Porous medium effective thermal conductivity

\(\lambda \) :

Microrotation material constant \((\lambda =\gamma /(\rho \nu j))\)

\(\nu \) :

Fluid kinematic viscosity

\(\psi \) :

Stream function

\(\theta \) :

Dimensionless temperature \((\theta =(T-T_\infty )/(T_w-T_\infty ))\)

\(\theta _w\) :

Temperature ratio

\(\rho \) :

Fluid density

\(\sigma \) :

Thermal dispersion constant

\(\xi \) :

Dimensionless distance along the plate \((\xi =g\beta _T x/c_p)\)

\(\omega \) :

Dimensionless microrotation \((\omega =N/(g\beta _T A/\nu ^{2/3})^{3/4})\)

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Authors and Affiliations

  1. Department of Mathematics, Siksha Bhavana, Visva-Bharati University, Santiniketan, West Bengal, 731 235, India

    Dulal Pal

  2. Department of Mathematics, Panchra High School (XII), Birbhum, West Bengal, 731133, India

    Bhuban Chandra Das

  3. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Kuppalapalle Vajravelu

  4. Department of Mechanical, Material and Aerospace Engineering, University of Central Florida, Orlando, FL, 32816, USA

    Kuppalapalle Vajravelu

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  1. Dulal Pal
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Correspondence to Dulal Pal.

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Pal, D., Das, B.C. & Vajravelu, K. Influence of Non-linear Thermal Radiation on MHD Double-Diffusive Convection Heat and Mass Transfer of a Non-Newtonian Fluid in a Porous Medium. Int. J. Appl. Comput. Math 3, 3105–3129 (2017). https://doi.org/10.1007/s40819-016-0281-5

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  • DOI: https://doi.org/10.1007/s40819-016-0281-5

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