Nonlinear convection in a porous medium with internal heat sources (Q1063499)

The present paper deals with the study of nonlinear thermal convection at small amplitude in a horizontal porous layer of fluid with the boundaries almost insulated in the presence of internal heat source. Earlier theoretical works on this topic were based upon the assumption that the internal heat source was uniform. In many practical problems the internal heat source is not necessarily uniform. The author has dealt with the problem very well by considering the heat source to be non-uniform which produces a nonlinear basic temperature gradient. The author has theoretically confirmed that increase in cell's width occurs because of non uniformity of heat source which has already been observed in the experiment conducted by \textit{Tritton} and \textit{Zarraga} [J. Fluid Mech. 30, 21-31 (1967)] and suggested by \textit{Robert} [ibid., 33-49 (1967)].