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Novel solution for heat and mass transfer of a MHD micropolar fluid flow on a moving plate with suction and injection

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Abstract

Two new functions on the semi-infinite interval, namely Rational Gegenbauer (R) and Exponential Gegenbauer (E) functions are proposed to solve the heat transfer problem. The considered problem is flow of MHD micropolar over a moving plate with suction and injection boundary conditions. For applying Tau method efficiently, two matrices of derivative and product for both of rational and exponential Gegenbauer whose enable us to solve a system of nonlinear algebraic equations on the semi-infinite interval were introduced, and an error bound of these functions approximation was estimated which led to have an exponential convergence rate in this method. Moreover, the influence of the important physical parameters on heat and mass transfer phenomena are studied with details. Comparing the results of Rational Gegenbauer Tau and Exponential Gegenbauer Tau methods with available analytical and numerical solutions shows that the present methods are efficient and have fast convergence rate and high accuracy. This method can solve a set of coupled nonlinear and high-order differential equations on a semi-infinite domain by converting to a set of linear equations.

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Abbreviations

b :

Constant

\(B_0\) :

Uniform transverse magnetic field

\(c_\mathrm{f}\) :

Skin-friction coefficient

\(c_p\) :

Specific heat at constant pressure

Ec:

Eckert number

f :

Dimensionless velocity

G :

Microrotation parameter

g :

Dimensionless microrotation

\(G_1\) :

Microrotation constant

K :

Coupling constant parameter

\(k^*\) :

Mean absorption coefficient

M :

Magnetic field parameter

N :

Components of microrotation

Nu:

Nusselt number

Pr:

Prandtl number

\(q_\mathrm{r}\) :

Radiative heat flux

\(q_\mathrm{w}\) :

Surface heat flux

R :

Thermal radiation parameter

Re:

Reynolds number

s :

Constant characteristic of the fluid

T :

Temperature of fluid

u, v :

Velocity components along x and y directions, respectively

x, y :

Cartesian coordinates along the plate and normal to it, respectively

\(\eta\) :

Similarity variable

\(\gamma\) :

Constant

\(\kappa\) :

Thermal conductivity

\(\mu\) :

Dynamic viscosity

\(\nu\) :

Kinematic viscosity

\(\rho\) :

Density of the fluid

\(\sigma\) :

Electrical conductivity

\(\sigma ^*\) :

Stefan–Boltzmann

\(\tau\) :

Skin friction

\(\theta\) :

Dimensionless temperature

\(\varphi\) :

Stream function

\(\infty\) :

Ambient condition

w:

Condition of the wall

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Acknowledgements

The authors are very grateful to both reviewers for carefully reading this paper and for their comments and suggestions which have improved the paper.

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Authors and Affiliations

  1. School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

    F. Baharifard

  2. Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G. C., Tehran, Iran

    K. Parand

  3. Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G. C., Tehran, Iran

    K. Parand

  4. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada

    K. Parand

  5. Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, 4800 Cao An Rd., Jiading, 201804, Shanghai, China

    M. M. Rashidi

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  1. F. Baharifard
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Correspondence to F. Baharifard.

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Baharifard, F., Parand, K. & Rashidi, M.M. Novel solution for heat and mass transfer of a MHD micropolar fluid flow on a moving plate with suction and injection. Engineering with Computers 38, 13–30 (2022). https://doi.org/10.1007/s00366-020-01026-7

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