FREE-CONVECTION FROM A VERTICAL PLATE IN A POROUS-MEDIUM SUBJECTED TOA SUDDEN CHANGE IN SURFACE HEAT-FLUX

An analysis is made of the transient free convection from a vertical f lat plate which is embedded in a fluid-saturated porous medium. It is assumed that for time <(tau)over bar> < 0 a steady state temperature o r velocity has been obtained in the boundary-layer which occurs due to a uniform flux dissipation rate q(1) ''. Then at time <(tau)over bar> = 0 the heat Bur on the plate is suddenly changed to q(2) '' and main tained at this value for <(tau)over bar> > 0. An analytical solution h as been obtained for the temperature/velocity field for small times in which the transport effects are confined within an inner layer adjace nt to the plate. These effects cause a new steady boundary layer. A nu merical solution of the full boundary-layer equations is then obtained for the whole transient from <(tau)over bar> = 0 to the steady state, firstly by means of a step-by-step method and then by a matching tech nique. The transition between the two distinct solution methods is alw ays observed to occur very near to the turning point of the plate surf ace temperature, a time at which the fluid temperature is close to its steady state profile. The solution obtained using the step-by-step me thod shows excellent agreement with the small time analytical solution . Results are presented to illustrate the occurrence of transients fro m both small and large increases and decreases in the levels of existi ng energy inputs.