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We report a theoretical study to determine the temperature profiles due to the continuous andconstant injection of hot water through a line source, into a homogeneous fluid-saturated porous medium which has had initially a constant temperature T∞. In our treatment we have taken in to account the simultaneous injection of constant fluxes of volume fluid, q, and of heat, φ. By using a far-field description, we found similarity solutions for the dimensionless temperature depending on the Peclet number, P e, as the single parameter of the problem.

Currently, very little is known about reliable phenomelogical correlations to estimate the gravity-driven mass flow rate, of dry non-cohesive granular material, outflowing from thin thickness slots in vertical sidewalls of rectangular silos. Here, we validate a simple and general formula that fits pretty well data published elsewhere, including the cases of vertically and horizontally elongated slots.

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In this work we report experiments carried out to describe the features of the mass flow rate of dry cohesionless granular material that flows, only due to gravity, out from circular orifices at the sidewall of silos with thin wall thickness, w. This study shows that the classical Hagen’s correlation for the mass flow rate is essentially correct for this case. Finally, we show graphically, in a three-dimensional plot, the evolution of the flow rate for continuous variations of the parameters D and w