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Computational study on the effects of variable viscosity of micropolar liquids on heat transfer in a channel

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Abstract

A numerical model is developed to study the effects of temperature-dependent viscosity on heat transfer in magnetohydrodynamic flow of micropolar fluid in a channel with stretching walls. The governing equations for linear and angular momenta and energy are transformed to a set of nonlinear ordinary differential equations by using similarity variables, and resulting problems are solved numerically by quasi-linearization. The effects of the various physical parameters on velocity, microrotation and temperature profiles are presented graphically and numerically. Finally, the effects of pertinent parameters on local skin-friction coefficient and local Nusselt number are also presented graphically. Some important observations regarding the effect of vortex viscosity parameter, microinertia density parameter, spin gradient viscosity parameter and couple stress on flow fields are noted and displayed. Numerical values of shear stress, couple stress and heat flux are computed and tabulated. The viscosity variation parameter enhances the shear stress and the couple stress. However, the heat transfer exhibits an opposite trend. The viscosity parameter is the most influential on thermal distribution. The magnetic field acts as a retarding force which reduces the normal and streamwise velocities as well as the microrotation distribution

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Abbreviations

\(\mu _{0}\) :

Characteristic viscosity (kg m−1 s−1)

\(\sigma\) :

Electric conductivity (s m−1)

\(\rho\) :

Fluid density (kg m−3)

p :

Fluid pressure (kg m−1 s−2)

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

Fluid temperature (K)

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

Heat flux (kg s−3)

\(\nu\) :

Kinematic viscosity (m2 s−1)

\(B_0\) :

Magnetic field intensity (m−1 A)

j :

Microinertia per unit mass (m2)

\(\phi\) :

Microrotation component (s−1)

K :

Porous permeability (m2)

T 1, T 2 :

Reference fluid temperatures (K)

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

Shear stress (kg m−1 s−2)

\({\mathrm{c}}_{\mathrm{p}}\) :

Specific heat (J kg−1 K−1)

b :

Stretching rate (m)

\(k_0\) :

Thermal conductivity (W m−1 K−1)

\(\kappa\) :

Vortex viscosity (Pa s)

2c :

Width of channel (m)

u, v :

x and y component of velocity (m s−1)

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

Couple stress coefficient

Ec:

Eckert number

M :

Magnetic field parameter

g :

Microrotation

f :

Normal velocity

\(f'\) :

Stream velocity,

\(\theta\) :

Temperature

Nu:

Nusselt number

\(N_2\) :

Parameter for microinertia density

\(N_3\) :

Parameter for skin gradient viscosity

\(N_1\) :

Parameter for vortex viscosity

Pr:

Prandtl number,

Re:

Reynolds number

\(\eta\) :

Similarity variable

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

Skin friction coefficient

\(\gamma\) :

Spin gradient viscosity

\(\mu \left( T_{\mathrm{f}}\right)\) :

Temperature-dependent viscosity

δ :

Viscosity variation constant

\(\epsilon\) :

Viscosity variation parameter

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Authors and Affiliations

  1. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan

    Shahid Rafiq & Zaheer Abbas

  2. Department of Applied Mathematics and Statistics, Institute of Space Technology Islamabad, Islamabad, Pakistan

    Muhammad Nawaz

  3. Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al Majma’ah, 11952, Saudi Arabia

    Sayer Obaid Alharbi

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  1. Shahid Rafiq
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Rafiq, S., Abbas, Z., Nawaz, M. et al. Computational study on the effects of variable viscosity of micropolar liquids on heat transfer in a channel. J Therm Anal Calorim 145, 3269–3279 (2021). https://doi.org/10.1007/s10973-020-09889-0

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