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

Microchannel Heat Transfer with Slip Flow and Wall Effects

“…The temperature-jump parameter, Eq. (8), is r 1.667, which is a typical value for air [3]. The heating frequency is ω 1.0.…”

“…Here, F T is the thermal accommodation factor, γ is the specific heat ratio, and Pr is the Prandtl number of the fluid [3]. For Kn 0, the jump in wall temperature vanishes.…”

“…The effect of the axial conduction in the fluid becomes more pronounced as Pe decreases. The effect of axial conduction in the fluid on the heat transfer has been studied for both parallel-plate microchannel [1] and microtube [2,3] for boundary conditions defined by constant wall temperature [1,2] and constant wall heat flux [1,3].…”

Steady-periodic heating in parallel-plate microchannel flow with participating walls

“…Now replace this form of g into the expression for B 2 , evaluate the integral over y 2 with the sifting property of the Dirac delta function, and strip off the integral over x′ with the spatial-Fourier transform: (12) Then the interface temperature is given by (13) For the special case of spatially-uniform heat-flux introduced by the heater, quantity q h in x-space is given by (14) where q 0 is a constant. Substitute the spatial-Fourier transform of this heat flux into the above temperature expression, to find (15) This is the temperature at the fluid-solid interface (y 1 = 0) caused by a thin, uniform heater located on (0 < x < a).…”

“…There have been several thermal-entrance studies of microchannels with other velocity distributions, including Hartmann flow [10,11], porous-saturated flow [12], and slip flow [13]. Slip flow is important in a flowing gas when the mean-free-path λ cannot be neglected compared to the channel height L. Specifically, if the Knudsen number, defined by λ/L, is in the range (0.01,0.1), then slip flow is valid [14].…”