Key words Free-convection flow, thermal porous plate, and inverse Laplace transform MSC (2000) 80A20The unsteady free-convection flows of a viscous and incompressible fluid near a porous infinite vertical plate (or wall) are investigated under an arbitrary time-dependent heating of the plate. Exact solutions of this problem are obtained with the help of Laplace transform technique, when the plate is moving with an arbitrary time-dependent velocity and for special cases of the impulsive and the accelerated heating effects. These solutions are given in closed form for arbitrary Prandtl number of the fluid and for the thermal porous wall with or without suction or injection. The particular cases of the thermal plumes which are responsible for atmospheric pollution are also discussed.

In this paper, we consider the unsteady free-convection flows of a viscous and incompressible fluid near an oscillating porous infinite vertical plate (or wall) during the heating of the plate. The governing equations are solved in closed form by the Laplace transform technique, when the Prandtl number (Pr) of the fluid is arbitrary and the suction (or injection) is constant. This solution is applied for a special case of the constant heating effects from the harmonically oscillating plate. The resulting velocity and temperature are shown graphically and are also discussed for the case of air (Pr=0.71) or water (Pr=7.0) flows.

An exact solution of the problem of the unsteady free convection and mass transfer flow near an infinite vertical porous plate, which moves with time-dependent velocity in a viscous and incompressible fluid, is presented here by the Laplace transform technique. All expressions of the new solutions of the present problem were obtained in closed forms with arbitrary Prandtl number (Pr), Schmidt number (Sc), thermal Grashof number (Gr), and mass Grashof number (Gm). Two applications of physical interest for porous or nonporous plate are discussed. Applying numerical values into the expressions of analytical solution, we was also discussed the vertical air flows—the usual phenomenon at plumes into the atmosphere.

Laboratory-scale experiments were conducted to determine the influence of higher thermophilic temperatures on thermophilic aerobic digestion treatment of a simulated sludge. The efficiency of the process was evaluated in respect of solids removal and degradation rate constants at four thermophilic temperatures. Batch runs were operated at a retention time of one day and temperatures of 65, 70, 72 and 75 degrees C. The results indicated that temperature increase did not impart any significant benefits to the digestion operation in terms of suspended solids and biochemichal oxygen demand reduction. The findings from this research also suggested that the treatment would not appear to benefit from temperatures higher than 65 degrees C, as classically suggested by Van't Hoff-Arrhenius. Therefore, increase of thermophilic temperature in the tested 65-75 degrees C range does not enhance the efficiency of thermophilic, aerobic sludge digestion treatment.

The problem of boundary layer flow of an incompressible fluid over a moving porous flat plate is investigated, by taking into account the heat due to viscous dissipation. The governing boundary layer equations of this flow field were solved analytically using the Laplace transform technique. These new exact analytical solutions for velocity and temperature were obtained with arbitrary Prandtl number and dissipation parameter (or Eckert number Ec). The corresponding solutions for nonporous plate are discussed. Applying numerical values into the analytical expressions of the temperature and heat transfer coefficient, we also discussed the effects of the dissipation parameter in the cases of water, gas, and ammonia flow. We can finally deduce that the fluid temperature of the present problem will increase in the case of viscous dissipation with positive Ec, but this temperature will decrease with negative Ec.