The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell (UCM) model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration (suction) and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration (suction) and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.
In this paper, we have developed an inventory models for deteriorating items with non-linear price dependent demand and frequency of advertisement of items. It is allowed and partially backlogged with a exponential rate on the duration of waiting time up to the arrival of next lot. In this model, the deterioration rate follows three-parameter weibull distribution and the transportation cost is considered explicitly for replenishing the order quantity. The transportation cost is dependent on the lot-size as well as the distance from the source to the destination of the located shop. The corresponding nonlinear model are formulated and solved by considering the transportation cost for replenishing the items. A numerical example is given to illustrate the results and the significant features of the result are discussed. Finally, we have performed the sensitivity analysis taking one or more parameters at a time.
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