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Analysis of magnetohydrodynamic squeezed viscous fluid flow in a porous medium

磁流体动力压缩黏性流体在多孔介质中的流动分析

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Abstract

In this numerical analysis, the significance of features of squeezed viscous fluid flow in the presence of inclined magnetic field effect has been scrutinized. For the efficient heat transfer phenomenon, the viscous dissipation and Joule heating effects have also been incorporated in the temperature equation. The dimensionless conservation equations are tackled with the help of shooting method. The behavior of particular parameters contemplated in the model on the fluid motion, energy distribution rate of heat transfer and surface drag coefficient are presented graphically and discussed in detail. Significant importance of the inclined magnetic field effect is noticed in the fluid velocity and heat transfer rate. From the performed simulations, it is noticed that as Prandtl number is increased from 1 to 5, the rate of heat transfer is increased by 56%, whereas when the inclined magnetic parameter γ is increased from π/8 to π/2, the rate of heat transfer is declined by 9.7%. It is also observed that the rate of heat transfer diminishs as the squeezing parameter is hiked whereas stretching parameter of lower plate has an opposite trend.

摘要

本文通过数值分析, 讨论了倾斜磁场效应下压缩黏性流体流动特征的意义。对于高效传热现 象, 温度方程中还考虑了黏性耗散和焦耳热效应。利用打靶法求解了无量纲守恒方程。对模型中所考 虑的特定参数对流体运动、传热能量分配率和表面阻力系数的行为进行了图解和详细讨论。倾斜磁场 效应对流体速度和换热速率的影响非常重要。从模拟结果可知, 当普朗特常数从1 增加到5 时, 热传 导率增加了56%, 而当倾斜磁参数γ 从π/8 增加到π/2 时, 热传导率下降了9.7%。实验还发现, 随着挤 压参数的增大, 换热速率减小, 而下板拉伸参数的增大则趋势相反。

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Abbreviations

B 0 :

Magnetic field (kg/(s2 · A))

S b :

Suction/injection parameter

Da :

Darcy number

T H :

Upper plate temperature (K)

Ec :

Eckert number

T 0 :

Lower plate temperature (K)

g :

Gravitational acceleration (m/s2)

T ∞ :

Free stream temperature (K)

c p :

Specific heat capacity (J/(kg · K))

U s :

Velocity of lower plate (m/s)

u, v :

Velocity components (m/s)

k :

Thermal conductivity

v H :

Velocity of upper plate (m/s)

M :

Magnetic number

Nu :

Nusselt number

(x, y):

Cartesian coordinates

p :

Dimensional pressure (kg/(m · s2))

α :

Thermal diffusivity (m2/s)

Pr :

Prandtl number (v/α)

β :

Thermal expansion coefficient (K−1)

q x :

Radiative heat flux along x-direction (W/m2)

q y :

Radiative heat flux along y-direction (W/m2)

γ :

Magnetic inclination angle

φ :

Dimensionless concentration

θ :

Dimensionless temperature

η :

Dimensionless distance

k* :

Mean absorption coefficient

R :

Lower plate stretching parameter

ρ :

Nanofluid density (kg/m3)

Ra :

Rayleigh number

σ :

Electrical conductivity

R d :

Thermal radiation parameter

μ :

Dynamic viscosity (kg/(m · s))

Re x :

Local Reynolds number

v :

Kinematic viscosity (m2/s)

S :

Squeeze number

σ* :

Stefan-Boltzman constant (kW/(m2 · K4))

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, P.O. Box 2713, Doha, Qatar

    Shafqat Hussain

  2. Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan

    Shafqat Hussain, Shahzada M. Atif, Muhammad Sagheer & Ibraheem Jahangeer

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Correspondence to Shahzada M. Atif.

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Hussain, S., Atif, S.M., Sagheer, M. et al. Analysis of magnetohydrodynamic squeezed viscous fluid flow in a porous medium. J. Cent. South Univ. 30, 844–854 (2023). https://doi.org/10.1007/s11771-023-5262-3

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