Unsteady separated stagnation-point flow and heat transfer of a viscous fluid over a moving flat surface

摘要

In this paper, we have investigated numerically the laminar unsteady separated stagnation-point flow and heat transfer of a viscous fluid over a moving flat surface in the presence of a time dependent free stream velocity which causes the unsteadiness of this flow problem. The plate is assumed to move in the same or opposite direction of the free stream velocity. The flow is therefore governed by the velocity ratio parameter lambda (ratio of the plate velocity to the free stream velocity) and the unsteadiness parameter beta. When the plate surface moves in the same direction of the free stream velocity (i.e., when lambda 0), the solution of this flow problem continues for any given value of beta. On the other hand, when they move in opposite directions (i.e., when lambda 0), the solution does not exist after a certain value of lambda depending upon the values of beta. In this case, separation appears inside the layer only for a negative value of beta, and for a positive value of beta, the boundary layer solution is terminated after a certain distance from the plate surface with an attached flow solution with no point of inflection. The concerning issue of the steady flow (beta = 0) case has also been considered and two types of attached flow solutions have been found-one with a point of inflection and the other with no point of inflection, in a definite range of lambda (-1.246 58 = lambda = -1.07). However, this range decreases with an increase in vertical bar beta vertical bar when beta 0. A novel result which arises from the heat transfer analysis is that for a given value of lambda (= 0), first the heat transfer rate increases with the increase of the Prandtl number Pr and after attaining a maximum value, it decreases and finally tends to be zero for large values of Pr depending upon the values of beta 0. On the contrary, for a given value of beta (= 0), the rate of heat transfer increases consistently with the increase of Pr. Publ