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Numerical Simulation of MHD Stagnation Point Flow of Micropolar Heat Generating and Dissipative Nanofluid : SLM Approach

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Abstract

In the present paper, we study the magnetohydrodynamic stagnation point flow dealing with heat and mass transfer of a micropolar nanofluid influenced with heat generation and viscous dissipation. Nonlinear ordinary differential equations are obtained by applying suitable similarity transformation on the governing partial differential equations. These differential equations have been solved by successive linearization method (SLM). The effects of various dimensionless parameters, such as heat generation parameter, thermophoretic parameter and stagnation parameter on the flow field, are discussed through tables and graphs by accumulating sufficient data using SLM. Results show many important facts, including temperature distribution gradual increment with the increase of heat generation and microrotation parameters. Quadratic multiple regression analysis has been performed for skin friction coefficient, local Sherwood number and local Nusselt number. When free stream velocity and stretching velocity are equal, variation in microrotation and magnetic field leads to very low perturbation in skin friction, local Sherwood number and local Nusselt number, whereas when free stream velocity is dominant over stretching velocity, there occurs reverse heat flow at the surface of the sheet.

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Abbreviations

a, b :

Arbitrary constants

\({B_0}\) :

Magnetic field

C :

Fluid concentration

\({Cf_x}\) :

Skin friction coefficient

\({C_\mathrm{{w}}}\) :

Species concentration at the surface

\({C_\infty }\) :

Ambient species concentration

\({c_p}\) :

Specific heat at a constant pressure

\({D_{\mathrm{{B}}}}\) :

Coefficient of Brownian diffusion

\({D_\mathrm{{T}}}\) :

Coefficient of thermophoretic diffusion

\(\mathrm{{Ec}}\) :

Eckert number

f :

Stream function

\(j_\mathrm{{f}}\) :

Microinertia density

K :

Material parameter

k :

Vortex viscosity

\({k_\mathrm{{f}}}\) :

Thermal conductivity

Le:

Schmidt number

M :

Magnetic parameter

N :

Microrotation or angular velocity

Nb :

Brownian motion parameter

Nt :

Thermophoretic parameter

Nux :

Local Nusselt number

Pr:

Prandtl number

Q :

Heat generation coefficient

\({q_\mathrm{{w}}}\) :

Heat transfer rate

Rex :

Local Reynolds number

Shx :

Local Sherwood number

s :

Stagnation parameter

T :

Fluid temperature

\({T_\mathrm{{w}}}\) :

Fluid temperature at stretching sheet

\({T_\infty }\) :

Ambient fluid temperature

u :

Fluid velocity component in the x direction

\({u_\mathrm{{w}}}\) :

Stretching velocity

\({u_\infty }\) :

Free stream fluid velocity

v :

Fluid velocity component in the y direction

x, y :

Coordinate directions

\(\alpha \) :

Heat generation parameter

\({\gamma _\mathrm{{f}}}\) :

Spin gradient viscosity

\(\theta (\eta )\) :

Dimensionless temperature

\({\mu _\mathrm{{f}}}\) :

Dynamic viscosity

\({\upsilon _\mathrm{{f}}}\) :

Kinematic viscosity

\({(\rho {c_p})_\mathrm{{f}}}\) :

Heat capacity of base fluid

\({(\rho {c_p})_\mathrm{{p}}}\) :

Nanoparticle heat capacity

\({\rho _\mathrm{{f}}}\) :

Fluid density

\(\sigma \) :

Electric conductivity

\({\tau _\mathrm{{w}}}\) :

Surface shear stress

\(\phi (\eta )\) :

Dimensionless concentration

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Authors and Affiliations

  1. Department of Mathematics and Computing, Indian Institute of Technology (ISM) Dhanbad, Jharkhand, 826004, India

    G. S. Seth, B. Kumar & V. K. Sinha

  2. Department of Mathematics, National Institute of Technology Jamshedpur, Jharkhand, 831014, India

    R. Nandkeolyar

Authors
  1. G. S. Seth
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  2. B. Kumar
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  3. R. Nandkeolyar
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  4. V. K. Sinha
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Correspondence to G. S. Seth.

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Significance Statement

Investigation of MHD stagnation point flow of micropolar heat generating and dissipating nanofluid is significant due to its application in the manufacturing of plastic substance, polymer extrusion, lubricant, etc. Effect of the magnetic field, microrotation, heat generation, Brownian and thermophoretic diffusions along with viscous dissipation and Joule heating on the fluid flow is analysed. Governing equations are solved by successive linearization method (SLM). The numerical results are validated in the limiting sense with published research article. Magnetic field, thermophoretic and Brownian diffusions, viscous dissipation, heat generation and microrotation have a significant effect on the rate of heat and mass transfer.

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Seth, G.S., Kumar, B., Nandkeolyar, R. et al. Numerical Simulation of MHD Stagnation Point Flow of Micropolar Heat Generating and Dissipative Nanofluid : SLM Approach. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 91, 503–515 (2021). https://doi.org/10.1007/s40010-020-00704-x

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  • DOI: https://doi.org/10.1007/s40010-020-00704-x

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