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Combined Effect of Radiation and Inclined MHD Flow of a Micropolar Fluid Over a Porous Stretching/Shrinking Sheet with Mass Transpiration

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Abstract

The present investigation is focused on the study of a micropolar flow in a porous medium subject to inclined magnetic field, mass transpiration and internal radiation. The analytical solutions of the flow and temperature fields were derived in closed forms for the first time here by using similarity transformations. The transformed velocity, microrotation and temperature fields were plotted and analyzed for a number of relative dimensionless parameters, while skin friction coefficient and Nusselt number were also calculated and discussed. The results showed that the micropolar flow may accelerate or decelerate depending on the effect of porous medium, the mass transpiration, the radiation and the inclined applied magnetic field. Moreover, heat transfer may enhanced or diminished depending on the same phenomena. The present analytical results are anticipated to be of great significance regarding the effect of important MHD and heat transfer parameters on micropolar fluids and they can be used in a variety of industrial applications.

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Abbreviations

c p :

Specific heat coefficient \(\left(J{ kg}^{-1}{K}^{-1}\right)\)

d :

Stretching/Shrinking parameter

Da − 1 :

Inverse Darcy number

f :

Dimensionless stream function

g :

Dimensionless microrotation

j :

Microinertia per unit mass \(\left({kg m}^{2}\right)\)

K :

Material parameter/micropolar parameter

k :

Medium permeability \(\left({m}^{2}\right)\)

k 1 :

Absorption coefficient

N r :

Thermal radiation parameter

Pr :

Prandtl number

Q :

Chandrasekhar number

q r :

Radiative heat flux \(\left(W {m}^{-2}\right)\)

T :

Temperature \(\left(K\right)\)

T w :

Temperature at the sheet \(\left(K\right)\)

T ∞ :

Free-stream temperature \(\left(K\right)\)

u :

Velocity component in \(x\) direction \(\left(m {s}^{-1}\right)\)

u w :

Stretching/Shrinking velocity of the sheet \(\left(m {s}^{-1}\right)\)

v :

Velocity component in \(y\) direction \(\left(m {s}^{-1}\right)\)

V c :

Wall mass transfer parameter

v k :

Kinematic viscosity \(\left({m}^{2}{ s}^{-1}\right)\)

v w :

Wall mass transfer velocity \(\left(m {s}^{-1}\right)\)

x :

Distance along the sheet \(\left(m\right)\)

y :

Distance perpendicular to the sheet \(\left(m\right)\)

α :

Non-negative sheet constant \(\left({s}^{-1}\right)\)

γ :

Spin-gradient viscosity \(\left(kg m{ s}^{-1}\right)\)

δ :

Wall coefficient \(0\le \delta \le 1\)

∆ :

∆=Qsin2τ+Da−1

η :

Similarity variable

θ:

Dimensionless temperature

κ :

Gyro-viscosity \(\left(kg {m}^{-1}{ s}^{-1}\right)\)

λ :

Thermal conductivity \(\left(W{ m}^{-1}{K}^{-1}\right)\)

μ :

Dynamic viscosity \(\left(kg {m}^{-1}{ s}^{-1}\right)\)

ρ :

Fluid density \(\left(kg {m}^{-3}\right)\)

σ* :

Strefan-Boltzman constant \(\left(W{ m}^{-2}{K}^{-4}\right)\)

τ :

Angle of the inclined magnetic field \(\left(rad\right)\)

ψ :

Stream function \(\left({m}^{2}{ s}^{-1}\right)\)

Ω:

Microrotation \(\left({s}^{-1}\right)\)

w :

Boundary condition at the sheet

∞:

Free stream boundary condition

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Funding

This work has been supported by the Special Account for Research Grants (SARG), University of West Attica (grant number 80781/54613).

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of West Attica, Athens, Greece

    Kyriaki-Evangelia Aslani & Ioannis E. Sarris

  2. Department of Mathematics, Davangere University, Davangere-577 007, Shivagangotri, India

    Ulavathi Shettar Mahabaleshwar

  3. Department of Mathematics, Guru Nanak Dev University, Amritsar, 143005, India

    Jitender Singh

Authors
  1. Kyriaki-Evangelia Aslani
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  2. Ulavathi Shettar Mahabaleshwar
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Contributions

Conceptualization and methodology were made by U.S.M. and J.S. Literature review was made by U.S.M. and K-E.A. Validation of the mathematical model, results and original draft preparation were made by K-E.A. Review, editing and supervision were made by I.E.S. All authors read and approved the final manuscript.

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Correspondence to Kyriaki-Evangelia Aslani.

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Aslani, KE., Mahabaleshwar, U.S., Singh, J. et al. Combined Effect of Radiation and Inclined MHD Flow of a Micropolar Fluid Over a Porous Stretching/Shrinking Sheet with Mass Transpiration. Int. J. Appl. Comput. Math 7, 60 (2021). https://doi.org/10.1007/s40819-021-00987-7

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