Slip-Flow Constant-Wall-Temperature Nusselt Number in Circular Tubes in the Presence of Axial Heat Conduction

2001 ◽  
Author(s):  
Olga Simek ◽  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Conduction ◽  
Wall Temperature ◽  
Slip Flow ◽  
Small Scale ◽  
Constant Wall Temperature ◽  
Circular Tubes ◽  
Axial Heat ◽  
Axial Heat Conduction

Abstract We present an investigation of slip-flow constant-wall-temperature convective heat transfer in circular tubes under hydrodynamically and thermally fully developed conditions. Our analysis includes the contribution of axial heat conduction (finite Peclet number) which is important in small scale flows, and has not been included in previous investigations of slip-flow heat transfer. The Nusselt number is found to decrease with increasing Knudsen number for all Peclet numbers in the fully accommodating case, as expected. The effect of axial heat conduction is found to be most important at Kn = 0, and results in an increase in the Nusselt number of the order of 15%; as Kn increases, the effect of axial heat conduction decreases.

scholarly journals Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels1

2001 ◽  
Vol 124 (2) ◽  
pp. 356-364 ◽  
Author(s):  
Nicolas G. Hadjiconstantinou ◽  
Olga Simek
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Conduction ◽  
Flow Regime ◽  
Wall Temperature ◽  
Slip Flow ◽  
Constant Wall Temperature ◽  
Slip Flow Regime ◽  
Axial Heat ◽  
Axial Heat Conduction

We investigate the constant-wall-temperature convective heat-transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically and thermally fully developed conditions. Our investigation covers both the slip-flow regime 0⩽Kn⩽0.1, and most of the transition regime 0.1<Kn⩽10, where Kn, the Knudsen number, is defined as the ratio between the molecular mean free path and the channel height. We use slip-flow theory in the presence of axial heat conduction to calculate the Nusselt number in the range 0⩽Kn⩽0.2, and a stochastic molecular simulation technique known as the direct simulation Monte Carlo (DSMC) to calculate the Nusselt number in the range 0.02<Kn<2. Inclusion of the effects of axial heat conduction in the continuum model is necessary since small-scale internal flows are typically characterized by finite Peclet numbers. Our results show that the slip-flow prediction is in good agreement with the DSMC results for Kn⩽0.1, but also remains a good approximation beyond its expected range of applicability. We also show that the Nusselt number decreases monotonically with increasing Knudsen number in the fully accommodating case, both in the slip-flow and transition regimes. In the slip-flow regime, axial heat conduction is found to increase the Nusselt number; this effect is largest at Kn=0 and is of the order of 10 percent. Qualitatively similar results are obtained for slip-flow heat transfer in circular tubes.

Effects of Axial Heat Conduction in the Wall on Convection in Microtubes

2003 ◽  
Author(s):  
Zhi-Xin Li ◽  
Wei Wang ◽  
Zeng-Yuan Guo
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Conduction ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Convective Boundary Condition ◽  
Thermal Conductivity Ratio ◽  
Convective Boundary ◽  
Axial Heat ◽  
Axial Heat Conduction

Single-phase convective heat transfer in microtubes was numerically studied with consideration on the heat conduction in the tube wall. It indicates that the Nusselt numbers of the fully developed laminar convective heat transfer in microtubes with convective boundary condition outside the tube vary from 3.66 to 4.36, which represent the conventional results for isothermal and constant heat flux boundaries respectively. The Nusselt number depends on the parameters of thermal conductivity ratio (k*), diameter ratio (D*), and Biot number. One-dimensional thermal resistance model could underestimate the Nusselt number if the axial heat conduction in the wall can not be ignored. Discrepancies between the experimental results for the Nusselt number based on 1-D model and the standard values might be misunderstood as being caused by novel phenomena at microscales.

On the Convective Heat Transfer in a Tube of Elliptic Cross Section Maintained Under Constant Wall Temperature

1986 ◽  
Vol 108 (1) ◽  
pp. 33-39 ◽  
Author(s):  
M. A. Ebadian ◽  
H. C. Topakoglu ◽  
O. A. Arnas
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Convective Heat Transfer ◽  
Cross Section ◽  
Convective Heat ◽  
Wall Temperature ◽  
Elliptic Cross Section ◽  
Constant Wall Temperature ◽  
Elliptic Cross

The convective heat transfer problem along the portion of a tube of elliptic cross section maintained under a constant wall temperature where hydrodynamically and thermally fully developed flow conditions prevail is solved in this paper. The successive approximation method is used for the solution utilizing elliptic coordinates. Analytical expressions for temperature distribution and Nusselt number corresponding to the first cycle of approximation are obtained in terms of the ellipticity of the cross section. In the case of a circular section, the first cycle approximation of the Nusselt number is obtained as 3.7288 compared to the exact value of 3.6568. Representative temperature distribution curves are plotted and compared to those corresponding with constant wall heat flux conditions.

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