Correction to ‘Free convection effect on the oscillatory flow past an infinite, vertical, porous plate with constant suction. I’ (Soundalgekar, V. M. 1973)

Abstract

In the paper noted in the title we have found a few mistakes and wish to correct them in this note. First we infer from the non-dimensional temperature θ (= ( T ' - T ' ∞ ) / ( T ' w - T ' ∞ )) and the Grashof number G (= ( T ' w - T ' ∞ ) / ∆ T with ∆ T = U 0 v 2 0 / vg x β ) that T ' ∞ only is kept constant and as G varies so does T ' w . For example, as G , being positive, takes increasing values T ' w increases and hence the fluid subsequently gets heated up as a result of heat-balance. Consequently we expect the fluid temperatures θ 0 (say, for a fixed Y ) to increase with positive G and to decrease with negative G and these results are not in evidence from figures 5-7 of Soundalgekar (1973), which are incorrect. That the results incorporated in and depicted by figures 5-7 cannot be all correct may be understood by a simple mathematical reasoning, namely: if E > 0, θ 0 cannot have a minimum as shown in figure 5 because from equation (20) of the reference, θ H 0 < 0 when θ ' 0 = 0 and if E < 0, θ 0 cannot have a maximum as shown in figure 7. Further it is necessary to know the quantitative nature of the errors committed in the paper. Therefore we have reworked out the problem and evaluated on I. B. M. 1620 the numerical values of the dimensionless mean velocity u 0 , the mean skin friction τ and the mean temperature θ 0 . We have found that the mean velocity diagrams, the values of the mean skin friction and the expression (37) for θ 0 are all correct. But the mean temperature profiles as shown in figures 5-7 are all incorrect! The correct values of the dimensionless mean temperature θ 0 have been presented in this note through figures 1-3. It is quite clear that θ 0 , as expected, increases with positive G significantly in the case of air ( P = 0.71). Physically it means that as the plate temperature T ' w increases (positive G increases) the fluid-temperature increases. This behaviour of θ 0 gets duly reversed when G , being negative, takes increasing values (see figure 3, P = 0.71). In the presence of free convection parameter G the mean temperature θ 0 increases as the frictional heating (positive E ) increases, a result in contrast to that reported by Soundalgekar. Moreover when the Prandtl number P is large, the effect of G (positive or negative) on θ 0 is almost insignificant - a result contrary to the one obtained by Soundalgekar.