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Numerical Study of Unsteady MHD Second Grade Fluid Flow and Heat Transfer Within Porous Channel

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Abstract

The present investigation incorporates a detailed study of unsteady MHD flow and heat transfer of a second grade fluid between two infinitely long porous plates. With the aid of implicit finite difference scheme the pertinent partial differential equations are transformed and framed as system of algebraic equations. The resulting equations are solved numerically by the help of damped-Newton method, thereafter coded using MATLAB. The impact of variations in dimensionless parameters such as \(m^2\), \(\alpha \), Re for constant acceleration \((n = 1)\) and variable acceleration \((n = 0.5)\) on velocity and temperature is illustrated. It is noted that the magnetic parameter and Reynolds number have significantly opposite effect on the temperature and velocity profiles for both the instances. Increasing values of Ec and \(m^2\) plays a key role in enhancing the temperature at any point of the fluid whereas higher values of Re and \(\alpha \) has a pronounced effect on the velocity profile of the fluid.

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Abbreviations

p :

Pressure

V :

Velocity of suction/injection

\(\rho \) :

Density

\(\mu _{1}\) :

Dynamic viscosity

\(\mu _{2}\) :

Elastic coefficient

\(\nu _{1}\) :

Kinematic Viscosity \((\frac{\mu _{1}}{\rho })\)

t, T :

Reference time

Re :

Reynold’s number

\(\alpha \) :

Second grade viscoelastic parameter

\(m^2\) :

Magnetic parameter

\(B_{0}\) :

Magnetic field Strength

A :

Constant having dimension \(LT^{-1}\)

c :

Specific heat

\(\theta \) :

Temperature at any point

k :

Thermal conductivity of the liquid

\(\sigma \) :

Electrical conductivity of the medium

Ec :

Eckert number

Pr :

Prandtl number

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Authors and Affiliations

  1. Veer Surendra Sai University of Technology, Burla, Odisha, 768018, India

    Sukanya Padhi & Itishree Nayak

Authors
  1. Sukanya Padhi
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  2. Itishree Nayak
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Contributions

The problem was suggested by IN. The literature study was done by SP. Both the authors contributed in writing the code and analysing the results. SP majorly contributed in manuscript writing.

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Correspondence to Sukanya Padhi.

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Padhi, S., Nayak, I. Numerical Study of Unsteady MHD Second Grade Fluid Flow and Heat Transfer Within Porous Channel. Int. J. Appl. Comput. Math 7, 255 (2021). https://doi.org/10.1007/s40819-021-01196-y

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  • DOI: https://doi.org/10.1007/s40819-021-01196-y

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