Abstract

FREE CONVECTIVE FLOW OF HEAT GENERATING/ABSORBING ON TRANSIENT NATURAL CONVECTION IN A VERTICAL CHANNEL: THE RIEMANN-SUM APPROACH

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Abstract This article investigates the of heat generation/absorption on an unsteady free convective flow in channel formed by two vertical parallel plates. Equation of energy and momentum that describe the flow situations are solved using the Laplace transform method. Due to the difficulties that are associated with the analytical inversion of the obtained results from the Laplace to the time domain, the Riemann-Sum approach is employed to do the inversion, thus obtaining the temperature, velocity, skin-friction and rate of heat transfer. To validate the Riemann-sum approach used, the steady state solution for velocity and temperature are obtained analytically. An excellent agreement is found between the steady state solutions and the transient solutions at large values of time. Keywords: free convection; heat generation; suction/injection; Riemann-sum approximation. Nomenclature - acceleration due to gravity [ms-2] - width of the channel [m] - Prandtl number - dimensionless heat sink parameter - dimensional time - dimensionless time - dimensional fluid temperature - channel wall temperature - initial temperature of fluid at - dimensionless fluid temperature. - dimensional velocity [ms-1] - dimensionless velocity - co-ordinate perpendicular to the plate [m] - dimensionless co-ordinate perpendicular to the plate - coefficient of thermal expansion [K-1] - coefficient of viscosity [Kgm-1s-1] - kinematic viscosity [m2s-1]

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