Convection at the Entrance of Micropipes With Sudden Wall Temperature Change

Abstract

Transient heat convection in a circular microchannel for hydrodynamically fully developed and thermally developing flow conditions is analytically solved by the integral transform and the Laplace transform techniques. A prescribed wall temperature boundary condition is assumed. The effects of velocity slip, temperature jump, and viscous heating are investigated. The results confirm that the viscous heating effects increase the Nusselt number for the specified conditions.

Slip-flow heat transfer in microtubes with axial conduction and viscous dissipation – An extended Graetz problem

“…For the Kn number varying between 0.01 and 0.1 (which corresponds to the flow of the air at standard atmospheric conditions through the channel that has the characteristic length of 1-10 mm), the regime is known as the slip-flow regime and the continuum modeling together with the slip-velocity and the temperature-jump boundary conditions (the rarefaction effect) are valid [5]. More recently, the Graetz problem has also been extended to study the microscale flows by including the rarefaction effect both analytically [6][7][8][9][10][11][12] and numerically [13][14][15].…”

Analytical Heat and Fluid Flow in Microchannels and Microsystems

“…For this purpose, a more flexible hybrid numerical-analytical approach was employed, based on the ideas of the Generalized Integral Transform Technique, GITT (Cotta 1990(Cotta , 1993(Cotta , 1998Cotta and Mikhailov 1997, thus avoiding more involved analysis in relation to the eigenvalue problem. Nevertheless, only in Tunc and Bayazitoglu (2002b), an approximate analytical solution was first presented for transient convection in microchannels with slip flow, for a step change on wall temperature, based on a previously proposed hybrid approach that combines the Laplace and Integral transforms concepts (Cotta and Ozisik 1986). Nevertheless, the analysis of unsteady phenomena in applications with microsystems is relevant and in many situations is required (Jiang et al 2000;Castellões et al 2007).…”

The effect of creep flow on two-dimensional isoflux microchannels

“…(3) and (4), and the boundary conditions suggested by Karniadakis and Beskok [17] are given in Eqs. (5) and (6).…”

“…This study will analytically and numerically evaluate twodimensional microchannel flows with constant wall heat flux using the continuum conservation equations and the various forms of the slip boundary condition models presented in Eqs. (1)- (6). The effects of Knudsen number, accommodation coefficients, and creep flow on microchannel friction losses and convective heat transfer will be evaluated numerically through the Poiseuille number, Po, and the Nusselt number, Nu.…”

“…The majority of these studies have been analytical [1][2][3][4][5][6][7][8], although there are also several numerical studies based on either direct simulation Monte Carlo, DSMC [9][10][11], or on continuum methods with slip boundary conditions [12,13]. Nearly all of these studies have used the following simplifying assumptions: laminar, steady state, hydrodynamically fully developed, constant properties, no creep flow, and first-order accurate slip velocity and temperature jump boundary conditions with perfectly accommodating walls.…”