Abstract
Investigation of the effect of thermal radiation on a fully developed magnetohydrodynamic (MHD) convective flow of a Newtonian, incompressible and electrically conducting fluid in a vertical microchannel bounded by two infinite vertical parallel plates with constant temperature walls through a lateral magnetic field of uniform strength is presented. The Rosseland model for the conduction radiation heat transfer in an absorbing medium and two plates with slip-flow and no-slip conditions are assumed. In addition, the induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The non-dimensional governing equations are solved numerically using Runge–Kutta–Fehlberg method with a shooting technique. The channel is optimized based on the Second Law of Thermodynamics by changing various parameters such as the thermal radiation parameter, the temperature parameter, Hartmann number, Grashof to Reynolds ratio, velocity slip length, and temperature jump.
Highlights
Heat transfer in free and mixed convection in vertical channels takes place in many applications such as the design of cooling systems for electronic devices [1], chemical processing equipment [2], microelectronic cooling [3], and solar energy [4], etc
There is some research that deals with the assessment of the temperature and velocity fields for the vertical fully developed flow without considering the effect of thermal radiation [5,6], but heat transfer by simultaneous radiation and convection is important in various cases including combustion flows [7], furnaces [8], high-temperature reactors [9] and heat exchangers [10], combustion [11], solar energy [12], thermal radiative loading [13], and many others [14,15,16]
Industrial application of this combination in microchannels is in the flow of metal vapors [21,22], plasma chemical vapor deposition (CVD) [23], electrohydrodynamic mixers [24], rhombus microchannels [25], and laser-driven radiative shock experiments [26]
Summary
Heat transfer in free and mixed convection in vertical channels takes place in many applications such as the design of cooling systems for electronic devices [1], chemical processing equipment [2], microelectronic cooling [3], and solar energy [4], etc. Slip effects under boundary conditions and thermal radiation in the fluid is the topic of many researches [20] Industrial application of this combination in microchannels is in the flow of metal vapors [21,22], plasma chemical vapor deposition (CVD) [23], electrohydrodynamic mixers [24], rhombus microchannels [25], and laser-driven radiative shock experiments [26]. In the slip flow regime the flow is dense enough to be considered a continuum but the no-slip boundary condition is not valid In this regime a sub-layer on the order of one mean free path, known as the Knudsen layer, starts to become dominant between the bulk of the fluid and the wall surface. In the slip flow regime the flow is ruled by the Navier–Stokes equations, and rarefaction properties are simulated by the limited slip at the wall using Maxwell’s velocity slip and von Smoluchowski’s temperature jump boundary conditions
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