Forced convection heat transfer from a plate stack embedded in a homogeneous porous medium

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Abstract
The current paper examines some novel and interesting aspects of the mathematical modelling of fluid flow and forced convection heat transfer from a plate stack embedded in a homogeneous porous media. Time-dependent forced convection heat transfer from some cylinders embedded in groundwater are explored numerically using finite difference methods. An algorithm was developed about rectangular heated solid objects with the same size placed in an in-line arrangement in homogeneous porous media. Central and one-sided finite difference formulae are used to discretize the domain. Applying the mathematical model, continuity, momentum, and energy equations are solved by the finite difference methods. Generally, analytical solutions are not possible for such problems, so most of the work is done numerically. The numerical results for the two-dimensional velocity potential and stream function have been calculated and the resulting fluid and temperature contours are represented graphically for various values of the parameters involved (e.g. length of the entrance, the fluid flow rates, coefficient of thermal diffusion and advection in the observed long-time plume behaviour, effect of time and temperature on heat transfer, etc.). It is observed that fluid and heat fluxes and fluid velocity depend upon the size, shape, burial depth, position of heated objects, and positions of the entrance and exit of the homogeneous porous media. Moreover, the hydraulic conductivity of the porous medium affects the pressure drops, fluid velocity as well as the heat transfer rates.

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