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MHD Mixed Convection Flow of Couple Stress Fluid Over an Oscillatory Stretching Sheet with Thermophoresis and Thermal Diffusion Using the Overlapping Multi-domain Spectral Relaxation Approach

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Abstract

In this work, we introduce and apply the overlapping multi-domain bivariate spectral relaxation method (OMD-BSRM) to scrutinize the unsteady MHD flow of a couple stress fluid over an oscillatory stretching surface with thermophoresis, electric field and Soret effects. The uniform magnetic field and an electric field are considered perpendicular to the stretching surface. The nonlinear partial differential equations modelling the fluid flow problem are non-dimensionalized and then solved using the OMD-BSRM. Error analysis is presented to ascertain how accurate and convergent is the numerical approach. Simulations show that the numerical scheme converges to sufficiently accurate solutions after few iterations and utilizing less grid points. The repercussions of diverse flow variables on the fluid properties and transport phenomena are determined. Amongst other findings, we found that the amplitude of velocity improves with buoyancy force, but diminishes due to strengthening of the magnetic intensity and inertia parameter. The couple stress fluid motion accelerates with the inertia coefficient and electric field. The amplitude of mass transport augments with buoyancy forces and thermophoresis particle deposition but decreases with the Soret effect.

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Abbreviations

u, v :

Velocity components along \({\bar{x}}\) and \({\bar{y}}\) directions

\({\bar{x}},{\bar{y}}\) :

Cartesian coordinates

t :

Time

f :

Dimensionless stream function

\(B_0\) :

Magnetic strength

\(D_B\) :

Brownian motion coefficient

T :

Fluid temperature

C :

Concentration

\(T_\infty \) :

Ambient values of temperature

\(C_\infty \) :

Ambient values of concentration

Q :

Volumetric heat transfer

\(E_0\) :

Applied electric field

\(T_m\) :

Mean fluid temperature

\(D_m\) :

Mass diffusion coefficient

\(k_t\) :

Ratio of thermal diffusivity

\(c_p\) :

Specific heat capacity

\(c_b\) :

Form of drag coefficient

\(V_t (= -\frac{k_{1}\nu _{\infty }}{T_{r}}\frac{\partial T}{\partial {\bar{y}}})\) :

Thermophoretic velocity

\(k_1\) :

Thermophoretic coefficient

\(T_r\) :

Reference temperature

Fs :

Local inertia coefficient

\(E_1\) :

Local electric field parameter

y :

Similarity variable

\( Gr_x \) :

Local Grashof number

\( C_f, Nu, Sh \) :

Skin friction, Nusselt number and Sherwood number

\(\omega \) :

Oscillation frequency

\(\rho _\infty \) :

Fluid density

\(\nu _\infty \) :

Kinematic viscosity further from the sheet

\(\mu \) :

Dynamic viscosity

\(\lambda \) :

Heat source/sink parameter

\(\gamma _0\) :

Material constant for the couple stress fluid

\(\sigma \) :

Electrical conductivity of the fluid

\(\beta _T\) :

Coefficient of thermal expansion

\(\beta _C\) :

Coefficient of concentration expansion

\(\gamma \) :

Thermophoretic parameter

\(\delta \) :

Mixed convection parameter

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg, 3209, South Africa

    M. P. Mkhatshwa, S. S. Motsa & P. Sibanda

  2. Department of Mathematics, Faculty of Science and Engineering, University of Eswatini, Private Bag 4, Matsapha, Eswatini

    S. S. Motsa

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  1. M. P. Mkhatshwa
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  2. S. S. Motsa
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  3. P. Sibanda
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Correspondence to M. P. Mkhatshwa.

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Mkhatshwa, M.P., Motsa, S.S. & Sibanda, P. MHD Mixed Convection Flow of Couple Stress Fluid Over an Oscillatory Stretching Sheet with Thermophoresis and Thermal Diffusion Using the Overlapping Multi-domain Spectral Relaxation Approach. Int. J. Appl. Comput. Math 7, 93 (2021). https://doi.org/10.1007/s40819-021-01043-0

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