Effect of Newtonian heating/cooling on free convection in an annular permeable region in the presence of heat source/sink

Abstract

The influence of Newtonian heating/cooling in the presence of heat source/sink has been investigated on laminar free convective flow in a vertical annular permeable region. The mathematical model for the K E Y W O R D S Free convective flow, heat source/sink, modified Bessel functions, Newtonian heating, vertical permeable annulus 1 | INTRODUCTION Flow in a porous medium is a subject of great interest to theorists and experimentalists alike due to its huge utility in various fields, such as filtration, trickle bed reactors, chromatography, adsorption/desorption, migration of contaminants in soil and groundwater, natural gas and oil production, flow of water in mines, tribology and lubrication, nuclear reactors, solidification or fusion of binary mixtures, sinterization, and collectivity of particles by compression and heating, and engineering sciences, among others. In free convection, the fluid motion occurs by free means, such as buoyancy. Since the magnitude of the fluid velocity associated with free convection is relatively low, the heat transfer coefficient encountered in free convection is also low. However, in the absence of convective currents, heat can be transferred by conduction only, whose rate is still much lower than heat transfer rate of convective currents. Convective flows occur under a variety of physical and engineering situations. Depending on the application being considered, free convective flows have been investigated in the literature corresponding to clear fluid media as well as flows that take place through permeable media. Our interest in this study is to investigate the free convection in an annular permeable region in which the flow takes place under the influence of Newtonian heating or cooling at the inner boundary of the annulus. It is also assumed that the flow is subjected to the additional influence of heat source/ sink in the flow domain. Research on flows through porous media is a topic of great interest and relevance to the scientific and engineering community. Considerable work has been reported in the literature on convective flows through porous media in which researchers have studied the effects of different physical, chemical, and geometric features. Flow and heat transfer problems through porous media have numerous engineering applications, such as geothermal energy recovery, crude oil extraction, petroleum reservoirs, electronic cooling, drying processes, groundwater pollution, nuclear reactor, thermal energy storage, and flow-through filtering media. A majority of the studies on convection heat transfer in the porous media are based on Darcy's law, 1,2 which, in general, corresponds to low permeability of the medium. The accuracy of this result is restricted to specific ranges of the Darcy number and the Reynolds number. On the other hand, in the case of flows taking place in permeable media of higher permeability, one has to consider modified models of porous media, such as the Brinkman model or the Forchheimer model. For instance, in a forced convection study, Vafai...

Influence of Heat Source/Sink on Free Convection in Annular Porous Region

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Role of heat source/sink in transient free convective flow through a vertical cylinder filled with a permeable medium: An analytical approach

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