Effect of point/line heat source and Hall current on free convective flow between two vertical walls
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Effect of point/line heat source and Hall current on free convective flow between two vertical walls NAVEEN DWIVEDI
∗
and ASHOK KUMAR SINGH
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221 005, India ∗ Corresponding author. E-mail: [email protected] MS received 25 January 2020; revised 16 June 2020; accepted 3 July 2020 Abstract. The influence of a point heat source and Hall current on the laminar hydromagnetic free convective flow of an incompressible and electrically conducting viscous liquid between two vertical walls has been studied. A wavelet function is utilised to mathematically formulate the point or line heat source. The incidental equations on the flow have been processed subject to the Boussinesq approximation. A unified analytical solution of basic equations like thermal energy and momentum has been derived by employing Laplace transform technique. The impacts of the pertinent physical parameters, such as Hall parameter, magnetic field and point heat source, on the velocity field are explained graphically. The valuable result from the investigation is that an increase in the length of the point heat source leads to the enhancement of the velocity profiles. Moreover, it is noticeable that an enhancement of Hall current has a direct connection with the primary factor of the volumetric flow rate and skin friction. Keywords. Magnetohydrodynamic flow; Laplace transformation; Hall current; point/line heat source. PACS Nos 44.25.+f; 47.65.−d; 52.65.Kj
1. Introduction Magnetohydrodynamics designates the frontier area combining electrodynamics and classical fluid mechanics. It deals with the flow of electrically conducting liquids which are subject to a magnetic field. Today, magnetohydrodynamics has developed into a broader field of fundamental as well as applied research in physical science and engineering. It has several uses in engineering and science, for example, solar energy collectors, nuclear reactors, astrophysics, aerospace, electromagnetics, geomechanics, electrical heaters, plasma confinement, oceanography, geophysics, magnetic drug targeting, etc. In natural convection, the liquid motion is produced by buoyancy effects because of the density differences caused by the differences in liquid temperature or because fluid–solid interfaces are at dissimilar temperatures or because of the changes in densities of distinct fluids adjoining to each other. MHD natural convective flow of an incompressible viscous liquid in the vertical walls has been the subject of numerous previous researches due to its potential relevance in several industrial processes. First of all, Osterl and Young [1] studied the influence of applied magnetic field and viscous dissipation on the 0123456789().: V,-vol
free convective flow of a liquid in two heated vertical walls. Poots [2] investigated laminar hydromagnetic free convective flow between two parallel plane surfaces and in a circular tube. The Couette flow of an electrically conducting and incom
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