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In this work, the effect of the second-order term to the velocity-slip/temperature-jump boundary conditions on the solution of four cases in which the driving force is fluctuating harmonically was studied. The study aims to establish criteria that secure the use of the first order velocity-slip/temperature-jump model boundary conditions instead of the second-order ones. The four cases studied were the transient Couette flow, the pulsating Poiseuille flow, Stoke's second problem, and the transient natural convection flow. It was found that at any given Kn number, increasing the driving force frequency, increases the difference between the first and second-order models. Assuming that a difference between the two models of over 5% is significant enough to justify the use of the more complex second-order model the critical frequencies for the four different cases were found. For the cases for which the flow is induced by the fluctuating wall as in cases 1 and 3, we found that critical frequency at Kn=0.1 to be [omega]=8. For the cases of flow driven by a fluctuating pressure gradient as in case 2, this frequency was found to be [omega]=1, at the same Kn number. In case 4, for the temperature-jump model the critical frequency was found to be [omega]=7 and for the velocity-slip model the critical frequency at the same Kn number was found to be [omega]=1.35. [DOI: 10.1115/1.4001970]

In the present work, the Jeffery--Hamel flow problem has been studied using both first-and second-order velocity-slip models, and then compared with the no-slip model. The objectives are to observe the behavior of the flow predicted by the two slip models and to establish criteria for using the two velocity-slip models. The study concentrates on examining the effect of the change in the Knudsen number (Kn) on the velocity profiles, magnitude of slip at the wall, and skin friction coefficient. Assuming that a difference between the two slip models of the order of 10% or less justifies the use of the simple first-order model, the transitional Kn numbers have been found. These Kn numbers depend on the flow direction, being either inflow or outflow. Also, there are three distinct regions that specify where to use each of the no-slip, first-order, and second-order slip models. Further, the reversal of the flow has been investigated as a function of the Kn number and for different Re. a, where Re is Reynolds number and a is the wall angle. Using the second-order slip models, it is found that as the Kn number increases, reversal occurs at Re. a smaller than the 10.31 value at which flow reversal happens in the no-slip model, and increasing the Kn number leads to a reduction in the skin friction coefficient in all cases except when reversal occurs. [DOI: 10.1115/1.4000918]

A two-dimensional melting process of a solid phase change material is investigated theoretically. The material contained in a rectangular enclosure heated from one side, while all the other sides are assumed to be adiabatic ones. In this study convection mode was considered to be the dominant mode of heat transfer within the melted region, except within the region very close to the solid surface at the bottom where conduction mode was only taken into considerations. It was found that the obtained results are in good agreement with previous ones. Finally the present analysis was used to predict the melted fraction of the phase change material and hence the amount of stored energy.

The transmission of heat from cylindrical pin fin arrays is influenced by the space between the fins, the clearance of the shroud and the missing pin in an unevenly organized fins and in-line arrays. The minute spanwise space between fins results in their contact with each another. The array and shroud clearance do not affect the constant interfin spacing, both spanwise and streamwise. The in-line arrays are more independent of the missing pin than the uneven arrays.