Extended Graetz Problem Including Axial Conduction and Viscous Dissipation in Microtube

Slip flow heat transfer in an infinite microtube with axial conduction

“…7, the fullydeveloped Nusselt number attains the asymptotic value of 5.411 for all values of Pe. A similar trend of results is also reported by Jeong and Jeong [2,12] for slip-flow heat transfer in a channel with parabolic velocity profile. In both Figs.…”

“…(17) and (18) by operating Eqs. (12) and (13) with R 1 0 rJ 0 ðl m rÞdr. Although the resultant equations for E mn and F m so obtained are seemingly different from Eq.…”

“…The Graetz problem has subsequently been extended by many investigators so as to include axial conduction and viscous dissipation in tube/channel geometries. The extended Graetz problem in the slip-flow regime has also been investigated by several researchers in microchannels [2][3][4][5][6][7] and in microtubes [8][9][10][11][12][13][14]. The analytical methods commonly adopted are separation of variables, integral transform technique and direct simulation Monte-Carlo (DSMC) technique.…”

“…Using the method of separation of variables, the effect of axial conduction together with viscous dissipation for thermally developing flow was studied by Jeong and Jeong [2] in a microchannel and by Jeong and Jeong [12] in a microtube. Hadjiconstantinou and Simek [3] solved the constant-wall-temperature heat transfer characteristics of a model gaseous flow in micro and nano channels by the DSMC technique.…”

Slug flow heat transfer in a semi‐infinite microtube with temperature jump wall condition

“…Jeong and Jeong studied the effect of axial conduction together with viscous dissipation in a microchannel [2] and in a microtube [11] for thermally developing flow, by the method of separation of variables. Yu and Ameel [3] applied a modified generalized integral transform technique to solve the energy equation for the slip-flow regime in a rectangular microchannel.…”