Effect of a Point/Line Heat Source on Hydromagnetic Free Convection between Vertical Walls due to Induced Magnetic Field
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RESEARCH ARTICLE
Effect of a Point/Line Heat Source on Hydromagnetic Free Convection between Vertical Walls due to Induced Magnetic Field Naveen Dwivedi1
•
Ashok Kumar Singh1
Received: 13 February 2019 / Revised: 7 October 2020 / Accepted: 15 October 2020 Ó The National Academy of Sciences, India 2020
Abstract The hydromagnetic natural convective flow of an incompressible electrically conducting and viscous liquid amid non-conducting vertical walls with a constant point heat source/sink under the impact of the induced magnetic field has been studied. A wavelet function is used to formulate the point heat source. The considered problem is described by a group of simultaneous ODEs with significant boundary conditions, and their solutions have been acquired for the induced magnetic field, the velocity field and the temperature field by applying the Laplace technique. The skin friction, induced current density and mass flux have also been discussed. The influences of controlling parameters on the fluid flow are discussed with the tables and graphs. The valuable consequence of this investigation is that an enhancement in the length of point heat source enhances the induced magnetic field, velocity, induced current density and temperature field. Keyword Free convection Point/line heat source/sink Induced current density Magnetohydrodynamics Induced magnetic field Abbreviations a Arbitrary constant of wavelet function b Arbitrary constant of wavelet function d Distance between two vertical walls g Gravitational acceleration H0 Constant magnetic field hx Induced magnetic field & Naveen Dwivedi [email protected] 1
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
hx Ha Q0 S Tc T T u u0 u
Dimensionless induced magnetic field Hartmann number Volumetric rate of heat generation/absorption Heat source/sink parameter Temperature of both walls Temperature of the fluid Dimensionless temperature of the fluid Velocity of the fluid along x-axis Characteristic velocity of the fluid Dimensionless velocity
Greek letter b Thermal expansion coefficient j Thermal conductivity le Magnetic permeability t Kinematic viscosity of the fluid q Fluid density r Electrical conductivity s0 Skin friction coefficient in non-dimensional form at the left wall s1 Skin friction coefficient in non-dimensional form at the right wall
1 Introduction There are several uses of magnetohydrodynamics in the engineering, biological systems and medical sciences. Several hydromagnetic flows with different physical conditions have been investigated in the absence of the induced magnetic field. The hydromagnetic channel flow with a transverse magnetic field has been first investigated by Hartman [1]. Ostrach [2] considered the effect of frictional heating as well as the heat source on the combined forced and natural convective channel flow between
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vertical walls. Thereafter, Poots [3] described the consequence of the magnetic field on free convective flow in the cases of different physica
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