Laminar forced convection with viscous dissipation in a Couette–Poiseuille flow between parallel plates (original) (raw)
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-In this study, analytical solutions are obtained to predict laminar heat convection in a plane Couette flow between two parallel plates with a zero pressure gradient and an axial movement of the upper plate. A Newtonian fluid with constant properties is considered with an emphasis on the viscous dissipation effect. Both hydrodynamically and thermally fully developed flow cases are investigated. The axial heat conduction in the fluid, and through the wall are neglected. Three different orientations of thermal boundary conditions are considered: different constant heat fluxes, equal constant heat fluxes and an insulated lower plate. For different values of relative velocity of the upper plate, the effect of the modified Brinkman number and Brinkman number on the temperature distribution and the Nusselt number are discussed.NOMENCLATURE 13 aa Constant U Dimensionless velocity Br Brinkman number p U Velocity of the moving plate (m/s) m Br Modified Brinkman Number x Axial coordinate direction (m) p c Specific heat at constant pressure (J/gK) y Vertical coordinate direction (m) 1 h Heat transfer coefficient at upper plate (W/m 2-K) Y Dimensionless vertical coordinate H Channel height (m) Greek Symbols k Thermal conductivity (W/mK) Dimensionless temperature H Nu Nusselt number at the upper plate m Dimensionless bulk mean temperature 1 q Upper wall heat flux (W/m 2) Dynamic viscosity (kg/m-s) 2 q Lower wall heat flux (W/m 2) Density (kg/m 3)
Numerical simulations of heat transfer to a third grade fluid flowing between two parallel plates
Canadian Journal of Physics, 2018
This investigation deals with numerical treatment of heat transfer flow of a third grade fluid between two infinite parallel plates subject to no-slip condition at boundary and no-temperature jump. Three flow configurations, Couette, Poiseuille, and plane Couette–Poiseuille, have been discussed. Approximate solutions using Lagrange–Galerkin method to Couette, Poiseuille, and Couette–Poiseuille flow problems are computed and delineated. It has been substantiated that the fluid rheology and heat transfer phenomenon are greatly influenced by the third grade flow parameters, Brinkman number, and pressure gradient. A rigorous mathematical exposition of the numerical scheme is provided. Because no a priori assumptions are made on pertinent flow parameters, apart from those due to thermodynamic stability, the results presented in this investigation are also valid for their large values.