Effects of entrance region transport processes on free convection slip flow in vertical microchannels with isothermally heated walls

A boundary layer analysis for entrance region heat transfer in vertical microchannels within the slip flow regime

“…In order to compare the present numerical solutions with the results obtained from full-scale numerical computations, the variation of the non-dimensional entrance length with Rayleigh number (Ra), for different values of Knudsen number (Kn), are compared with those obtained by Biswal et al [3], as shown in the Fig. 2.…”

“…(14) is solved using the fourth order Runge Kutta method [3], to obtain the evolution of the boundary layer as a function of the axial coordinate, X. The results are parameterized in terms of the parameters A and B and Ra (as appearing in Eq.…”

“…These conclusions, however, were made by neglecting the momentum and heat transfer characteristics in the developing region of the microchannel. Appreciating the fact that the transport phenomena in the developing region might influence the characteristics of the fully developed natural convection in vertical microchannels in a rather profound manner, Biswal et al [3] have recently executed a comprehensive computational study on free convection heat transfer in the entrance region, followed by that in the fully developed region, in long vertical microchannels, for different values of Knudsen number and Rayleigh number. In their study, special implications of accommodating the effects of the developing region in the heat transfer analysis were discussed in details and some important conclusions based on the same were pinpointed.…”

Heat Transfer at Microscale

“…Chen and Weng afterwards extended their works by taking the effects of thermal creep (2008a) and variable physical properties (2008b) into account. Natural convection gaseous slip flow in a vertical parallel plate microchannel with isothermal wall conditions was numerically investigated by Biswal et al (2007), in order to analyze the influence of the entrance region on the overall heat transfer characteristics. Chakraborty et al (2008) performed a boundary layer integral analysis to investigate the heat transfer characteristics of natural convection gas flow in symmetrically heated vertical parallel plate microchannels.…”

Slip-flow and heat transfer of gaseous flows in the entrance of a wavy microchannel

“…This thin layer is called the Knudsen layer and the flow regime in this range of Knudsen numbers is known as slip-flow regime. In slip-flow regime the standard Navier-Stokes and energy equations can still be used with modifications to the boundary conditions allowing for velocity slip and temperature jump at the walls [1][2][3].…”