Analysis of Gaseous Flow Between Parallel Plates by Second‐ Order Velocity Slip and Temperature Jump Boundary Conditions

Abstract

In this study the momentum and energy equations are solved to analyze the flow between two parallel plates by employing second-order velocity slip and temperature jump conditions. The flow is considered to be laminar, incompressible, hydrodynamically/thermally fully developed, and steady state. In addition to the isoflux condition, viscous dissipation is included in the analysis. Closed form expressions for the temperature field and Nusselt number are obtained as a function of the Knudsen number and Brinkman number. The Nusselt number obtained by employing the second-order model is found to be lower compared to the continuum value and agrees well with the other theoretical models.

Effects of Viscous Dissipation and Rarefaction on Parallel Plates with Constant Heat Flux Boundary Conditions

“…It is observed that the temperature jump has an antagonist effect compared with velocity slip as far as heat transfer is concerned. The effect of second-order velocity slip and temperature jump boundary conditions on the heat transfer characteristics of gaseous flow between isoflux micropipe/parallel plates has been reported elsewhere [44,45]. The present study intends to quantify the influence of second-order velocity slip, viscous dissipation, and different heat fluxes boundary conditions on heat transfer characteristics of hydrodynamically and thermally fully developed flow between parallel plates.…”

“…Numerous second-order slip models [37][38][39][40][41][42][43] were proposed to analyze the fluid flow and heat transfer characteristics with the choice of different slip coefficients. Recently, closed form expressions were stated for the Nusselt number using second-order velocity slip and temperature jump condition [44,45].…”

“…Numerous studies include second-order velocity slip and temperature jump boundary conditions to analyze the fluid flow and heat transfer in microdevices [36][37][38][39][40][41][42][43][44][45]. The exact form of second-order slip condition and precise values of secondorder slip coefficients are not described in literature.…”

Comprehensive Analysis of Convective Heat Transfer in Parallel Plate Microchannel with Viscous Dissipation and Constant Heat Flux Boundary Conditions

“…While, the fully developed Nusselt number does not vary significantly with the change in the thermophysical properties in the analysis [34,35]. Efforts have been made to study the effect of second order boundary conditions and asymmetric heat flux boundary conditions on the heat transfer characteristics of various geometries such as: parallel plate microchannels and micropipe [36][37][38]. It is observed that the asymmetric heat flux condition significantly alters the temperature profile and singularities in Nusselt number are obtained for various values of Knudsen number [18][19][20].…”

“…It is reported that velocity slip and temperature jump affect the heat transfer performance in opposite ways [15]. Also, the studies report the deviation in heat transfer performance by considering the first and second order slip models [36][37][38]. The effect of asymmetric heat flux ratio on the heat transfer ratio and the heat transfer performance has also been reported [9,[18][19][20].…”