The self-heating of damp cellulosic materials: II. On the steady states of the spatially distributed case

The effects of wall transpiration on the unsteady free convection boundary-layer flow near a stagnation point in a heat generating porous medium

“…8 we plot values of the wall temperature h w hð0; tÞ against t obtained from the numerical solution of initial-value problem (7,8) for representative values of c. We see that these curves approach at large times the constant, nontrivial value given by the corresponding steady state solution shown in Fig. 1.…”

“…In (8), c [ 0 gives fluid injection from the boundary (blowing) and c\0 gives fluid withdrawal from the boundary (suction).…”

“…These represent possible large time limit of the initialvalue problem (7,8) and, for a general value of p, are given by…”

“…We solved initial-value problem (7,8) numerically using the scheme described in [10,12] for example, taking as our initial condition of oy ¼ a 0 e Ày and prescribing a value for a 0 [ 0.…”

“…This can set up a convective flow within the material which may help to dissipate the heat or alternatively can lead to enhanced heat generation and even thermal runaway with possibly disastrous consequences. Examples include the spontaneous ignition in stock piles of coal [1][2][3][4], in bagasse (the cellulose waste left after the extraction of sugar from sugar cane) [5,6] or in the wetting of cellulosic materials [7][8][9]. Previously we have modelled this problem assuming local heat generation at a rate proportional to ðT À T 1 Þ p , where T 1 is the (constant) ambient temperature and the exponent p !…”