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Influence of isoflux boundary condition on forced convection due to arbitrary orientation of magnetohydrodynamic flow in cylindrical geometry

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Abstract

The impact of the isoflux boundary condition on forced convection magnetohydrodynamic flow past a cylinder subjected to an arbitrarily oriented external magnetic field is examined numerically. A fourth-order compact finite difference scheme is developed using cylindrical geometry to discretize the governing Navier–Stokes transport equation together with the energy equation and subsequently solve it utilizing the pseudo-time iterative technique. The flow and heat transfer properties are demonstrated with respect to the parameters such as Reynolds number (\({\text{Re}}\)), interaction parameter (M), magnetic inclination angle (\(\alpha \)) and Prandtl number (\(\text {Pr}\)). The magnitude of the local Nusselt number and surface pressure behave non-monotonically with increasing M for streamwise magnetic field (\(\alpha = 0^\circ \)). Conversely, for other magnetic angles (\(\alpha \ne 0^\circ \)), both the values display a monotonic trend on the cylinder surface. The critical interaction parameter (\(M_{\rm cr}\)) for the mean Nusselt number (\({\overline{\text {Nu}}}\)) is determined in case of the streamwise magnetic field. A non-monotonic behavior in the \(M_{\rm cr}\) values is observed depending upon the values of \(\text {Pr}\) and \({\text{Re}}\). The heat transfer under the isoflux boundary condition is significantly enhanced throughout the cylinder surface when compared to the isothermal boundary condition.

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Data Availability Statement

No data are associated in the manuscript.

Abbreviations

\(C_{\rm dv},C_{\rm dp},C_D\) :

Coefficient of viscous, pressure and total drag

\(C_{\rm p}\) :

Surface pressure

\(c_{\rm p}\) :

Fluid specific heat capacity (\(\text{J}\,\text{kg}^{-1}\text{K}^{-1}\))

d :

Diameter of cylinder (m)

\({\mathcal {H}}_{\infty }\) :

Uniform magnetic field (\(\mathrm{wb\,m}^{-2}\))

M :

Interaction parameter

\(M_{\rm cr}\) :

Critical interaction parameter

\(\text {Nu}\) :

Local Nusselt number

\({\overline{\text {Nu}}}\) :

Average/mean Nusselt number

p :

Non-dimensional pressure

\(\text {Pr}\) :

Prandtl number

\((r,\theta )\) :

Cylindrical polar co-ordinates

\({\text{Re}}\) :

Reynolds number

T :

Non-dimensional temperature (K)

\(U_{\infty }\) :

Uniform velocity of fluid (\(\text {ms}^{-1}\))

\({\mathcal {V}}_r\) :

Radial velocity components

\({\mathcal {V}}_\theta \) :

Angular velocity components

\(\alpha \) :

Magnetic inclination angle

\(\beta \) :

Volumetric thermal coefficient (\(\text {K}^{-1}\))

\(\Theta \) :

Temperature (K)

\(\lambda \) :

Thermal diffusivity (\(\text {s}^{-1}\text {m}^2\))

\(\nu \) :

Kinematic viscosity (\(\text {m}^2\text {s}^{-1}\))

\((\xi , \eta )\) :

Modified coordinates (\(r=\text {e}^{\pi \xi }, \theta =\pi \eta \))

\(\rho \) :

Density of fluid (\(\text {kg}\,\text {m}^{-3}\))

\(\sigma \) :

Electrical conductivity (\(\text {S}\, \text {m}^{-1}\))

\(\psi \) :

Non-dimensional stream function

\(\omega \) :

Non-dimensional vorticity function

\(\text{cr}\) :

Critical value

D :

Total drag

dp, dv :

Pressure and viscous drag

s :

Surface of cylinder

\(\theta \) :

Angular component

\(\infty \) :

Free stream

\('\) :

Dimensional parameter

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  1. Department of Mathematics, National Institute of Technology Silchar, Silchar, Assam, 788010, India

    Rupam Saha & B. Hema Sundar Raju

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Saha, R., Raju, B.H.S. Influence of isoflux boundary condition on forced convection due to arbitrary orientation of magnetohydrodynamic flow in cylindrical geometry. Eur. Phys. J. Plus 139, 422 (2024). https://doi.org/10.1140/epjp/s13360-024-05229-5

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