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Influence of heat transfer on MHD Carreau fluid flow due to motile cilia in a channel

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Abstract

Mucus transport mediated by motile cilia in the airway is an important defense mechanism for prevention of respiratory infections. Cilia motility can be affected by temperature difference and magnetic field. In this research, we investigate the combined effects of magnetic field and buoyancy force due to temperature difference. In the present study, mixed convective flow of a Carreau fluid model through a ciliated channel is modeled and analyzed by a symplectic metachoronal wave. The momentum and energy equations for the Carreau fluid are modeled and simplified by the stream function and small Reynold’s number approximation. The influence of magnetic parameter, Carreau fluid parameter, Brinkmann number and Weissenberg number on velocity, temperature and pressure gradient are presented via graphs. It is observed that Hartmann number helps to decelerate the flow, whereas Weissenberg number, Grashof number and Carreau fluid parameter are responsible for the accelerated flow. The heat transfer rate rises by increasing the values of Hartmann number, Weissenberg number, Carreau fluid parameter and Brinkmann number.

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Abbreviations

\(\varvec{V}\) :

Velocity field

\(\dot{U}\),\(\dot{V}\) :

Longitudinal and transverse velocities in fixed frame

\(u,v\) :

Longitudinal and transverse velocities in moving frame

\(\dot{X}\),\(\dot{Y}\) :

Coordinates of fixed frame

\(x,y\) :

Coordinates of moving frame

\(\rho\) :

Fluid density

\(\beta_{1}\) :

Coefficient of thermal expansion

\(\varvec{S}\) :

Cauchy stress tensor

\(\varvec{\tau}\) :

Extra stress tensor

\(T\) :

Fluid temperature

\(c_{\text{p}}\) :

Specific heat

\(k\) :

Thermal conductivity of the material

\(\varPhi\) :

Viscous Dissipation

\(n\) :

Power law index

\(\mu_{\infty }\) :

Infinite shear rate

\(\mu_{0}\) :

Zero shear rate viscosity

\(\mu\) :

Viscosity of the fluid

\(\varGamma\) :

Time constant

\(\dot{\varvec{\gamma }}\) :

Shear rate

\(\varvec{b}_{\text{f}}\) :

Body force

\(P\) :

Pressure

\(\psi\) :

Stream function

\(c\) :

Wave speed

\(a\) :

Wave amplitude

\(M\) :

Hartmann number

\(\alpha\) :

Eccentricity of the elliptical motion

\(\beta\) :

Wave number

\(\varepsilon\) :

Cilia length

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Authors and Affiliations

  1. Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan

    Khadija Maqbool, Naeema Manzoor & Rahmat Ellahi

  2. Center for Communications and IT Research, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia

    Sadiq M. Sait

Authors
  1. Khadija Maqbool
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  2. Naeema Manzoor
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  4. Sadiq M. Sait
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Correspondence to Khadija Maqbool.

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Maqbool, K., Manzoor, N., Ellahi, R. et al. Influence of heat transfer on MHD Carreau fluid flow due to motile cilia in a channel. J Therm Anal Calorim 144, 2317–2326 (2021). https://doi.org/10.1007/s10973-020-10476-6

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