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Magneto-thermo analysis of oscillatory flow around a non-conducting horizontal circular cylinder

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Abstract

The present study is based on oscillatory mixed-convection flow of electrically conducting fluid around a non-conducting horizontal circular cylinder. By following the statement of the problem, a mathematical model is constituted, and then, the formulated model is transformed into convenient form for integration by using primitive-variable formulation. The behavior of oscillatory skin friction, heat transfer and magnetic flux for pertinent parameters involved in the flow model such as mixed-convection parameter \( \lambda \), magnetic force parameter \( \xi \), the magnetic Prandtl number \( \gamma \) and the Prandtl number Pr is discussed numerically. For this purpose, first velocity profile, temperature distribution and magnetic-field profile at various positions \( \alpha = \pi /6, \;\pi /3 \) and \( \pi \) of the non-conducting horizontal circular cylinder for steady state are secured and then are used to calculate oscillatory skin friction, heat transfer and current density. It is predicted that oscillatory behavior of skin friction, heat transfer and current density is increased at position \( \alpha = \pi /4 \) for increasing values of the various physical pertinent parameters. It is pertinent to mention here that the convective heat transfer is practically associated with oscillatory flow behavior.

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Abbreviations

u, v :

Velocity along \( xy \)-direction (m s −1)

\( H_{\text{x}} \), \( H_{\text{y}} \) :

Magnetic field along \( xy \)-direction (Tesla)

\( \mu \) :

Dynamic viscosity (kg m −1 s −1)

\( \nu \) :

Kinematic viscosity (m 2 s −1)

\( \rho \) :

Density (kg m −3), \( \tau \) Shear stress (P a)

\( g \) :

Gravitational acceleration (m s −2)

\( \beta \) :

Thermal expansion coefficient (K −1)

\( \nu_{\text{m}} \) :

Magnetic permeability (H m −1)

\( \alpha \) :

Thermal diffusivity (m 2 s −1)

T:

Temperature (K)

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

Specific heat (J kg −1 K −1)

\( T_{\infty } \) :

Ambient fluid temperature (K)

\( R_{{{\text{e}}_{\text{L}} }} \) :

Reynolds number

\( G_{{{\text{r}}_{\text{L}} }} \) :

Grashof number

\( \xi \) :

Magnetic force parameter

\( \lambda \) :

Mixed-convection parameter

\( \theta \) :

Dimensionless temperature

\( \gamma \) :

Magnetic Prandtl number

Pr:

Prandtl number

\( \sigma \) :

Electrical conductivity

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Sargodha, Sargodha, Pakistan

    Zia Ullah & Muhammad Ashraf

  2. Department of Mathematics, Faculty of Science, Aswan University, Aswan, 81528, Egypt

    A. M. Rashad

Authors
  1. Zia Ullah
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  2. Muhammad Ashraf
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  3. A. M. Rashad
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Correspondence to Muhammad Ashraf.

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Ullah, Z., Ashraf, M. & Rashad, A.M. Magneto-thermo analysis of oscillatory flow around a non-conducting horizontal circular cylinder. J Therm Anal Calorim 142, 1567–1578 (2020). https://doi.org/10.1007/s10973-020-09571-5

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