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Thermal analysis of an unsteady compressible flow in an asymmetric channel with joule heating: a finite difference approach

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Abstract

Thermal analysis of compressible flow under peristalsis is stimulated by its extensive utility in geophysics, thermal storage devices and in other industrial operations. With regard to these utilities, this work is aimed at heat transfer analysis of unsteady compressible flow of an electrically conducting viscous fluid under peristalsis. Considerations are made for an asymmetric channel with velocity and thermal slip conditions. Thermal analysis has been taking into account in the presence of viscous dissipation and joule heating effects. Mass and momentum conservation laws, equation of state and energy equation are employed to numerically model the current problem. Explicit finite difference method is used to numerically solve the resulting nonlinear partial differential equations. Graphical representations are used to show the effect of pertinent parameters on axial velocity, dimensionless temperature and heat transport rate. It has been demonstrated that the magnetic field trims down the fluid’s velocity. Also, higher Prandtl number exhibit lower thermal diffusivity which in turn causes the fluid temperature to fall. In general, the temperature rises along with the Mach number. This is because, in accordance with the ideal gas law, the compressibility effects increase the pressure and density, which in turn raises the temperature.

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Abbreviations

\(\left( {x,y} \right)\) :

Coordinate axis

\(\left( {u,v} \right)\) :

Velocity components

\(c\) :

Speed of wave

\(a*\) :

Speed of sound

\(a_{1}\) :

Wave amplitude on upper wall

\(a_{2}\) :

Wave amplitude on lower wall

\(p_{{\text{c}}}\) :

Reference pressure

\(p\) :

Pressure

\(t\) :

Time

\(T\) :

Temperature

\(S\) :

Extra stress tensor

\(B_{0}\) :

Magnetic flux density

\(J\) :

Electric current vector

\(k_{{\text{c}}}\) :

Compressibility of the liquid

\(K_{{\text{n}}}\) :

Knudsen number

\({\text{R}}\) :

Reynolds number

\(H\left( y \right)\) :

Magnetic number

\(M\) :

Magnetic field parameter

\({\text{Pr}}\) :

Prandtl number

\({\text{Ma}}\) :

Mach number

\(\rho\) :

Density

\(\rho_{0}\) :

Density at reference pressure

\(\lambda\) :

Wavelength

\(\mu\) :

Dynamic viscosity

\(\phi\) :

Phase difference

\(\theta\) :

Dimensionless temperature

\(\sigma\) :

Electric conductivity of the fluid

\(\alpha\) :

Wave number

\(\beta\) :

Thermal slip parameter

\(\varphi\) :

Viscous dissipation

\(\chi\) :

Compressibility parameter

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Funding

No funding, grants or other support was received for conducting this study.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan

    Rida Rafaqat & Ambreen Afsar Khan

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

    Rida Rafaqat

Authors
  1. Rida Rafaqat
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  2. Ambreen Afsar Khan
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Contributions

All authors contributed to the study conception and design. Material preparation and analysis were performed by RR and AAK. The first draft of the manuscript was written by RR and reviewed by AAK. All authors read and approved the final manuscript.

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Correspondence to Rida Rafaqat.

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Rafaqat, R., Khan, A.A. Thermal analysis of an unsteady compressible flow in an asymmetric channel with joule heating: a finite difference approach. J Therm Anal Calorim 148, 14243–14252 (2023). https://doi.org/10.1007/s10973-023-12585-4

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  • DOI: https://doi.org/10.1007/s10973-023-12585-4

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