Analytical Solution for Slip Flow-Heat Transfer in Microtubes Including Viscous Dissipation and Axial Heat Conduction

Analytical Solution for Slip Flow-Heat Transfer in Microtubes Including Viscous Dissipation and Axial Heat Conduction

M. Mecili | E. Mezaache* 

Research Laboratory for Physics and Chemistry of Surfaces and Interfaces, Skikda University, 21000, Algeria

Corresponding Author Email: 
e_mezaache@yahoo.fr
Page: 
27-36
 |
DOI: 
https://doi.org/10.18280/ijht.310204
Received: 
N/A
| |
Accepted: 
N/A
| | Citation
31.2_04.pdf

OPEN ACCESS

Abstract: 

Heat transfer analysis of two-dimensional, incompressible, constant property, hydrodynamically fully developed, single phase laminar flow in microtube is performed for constant wall temperature thermal boundary condition subject to slip flow regime. The rarefaction effect which is important for slip flow is discussed trough the product Kn.βv. The viscous dissipation and the axial conduction within the fluid are included. The energy equation is solved analytically by using finite integral transform technique via Mathematica software. The effects of degree of rarefaction, jump temperature, axial conduction and viscous dissipation on heat transfer are discussed via the parameters (Kn.βv, β, Pe, Br). It is found that the heat transfer depends on the competition between the slip velocity and temperature jump. The length of thermal entrance region diminishes with increasing Br and β but increases with decreasing Pe.

1. Introduction
2. Slip Velocity and Temperature Jump
3. Analysis and Governing Equations
4. Analytical Solution
5. Results and Discussion
6. Conclusion
  References

[1] F. E. Larrodè, C. Housiadas and Y. Drossinos, Slip Flow Heat Transfer in Circular Tubes, Int. Journal of Heat and Mass Transfer, vol. 43, pp. 2669-2680, 2000. 

[2] W. Sun, S. Kakaç and A. G. Yazicioglu, A Numerical Study of Single-Phase Convective Heat Transfer in Microtubes for Slip Flow, Int. Journal of Thermal Sciences, vol. 46, pp. 1084-1094, 2007. 

[3] G. Tunc and Y. Bayazitoglu, Heat Transfer in Microtubes with Viscous Dissipation, Int. Journal of Heat and Mass Transfer, vol. 44, pp. 2395-2403, 2001. 

[4] B. Çetin, A. G. Yazicioglu and S. Kakaç, Fluid flow in microtubes with axial conduction including rarefaction and viscous dissipation, Int. Communication in Heat and Mass Transfer, vol. 35, pp. 535-544, 2008. 

[5] B. Çetin, A. G. Yazicioglu and S. Kakaç, Slip-Flow Heat Transfer in Microtubes with Axial Conduction and Viscous Dissipation–An Extended Graetz Problem, Int. Journal of Thermal Sciences, vol. 48, pp. 1673-1678, 2009. 

[6] O. Aydin, M. Avcı, Heat and Fluid Flow Characteristics of Gases in Micropipes, Int. Journal of Heat Mass and Transfer, vol. 49, pp. 1723-30, 2006. 

[7] A. K. Satapathy, Slip Flow Heat Transfer in an Infinite Microtube with Axial Conduction, Int. Journal of Thermal Sciences, vol. 49, pp. 153-160, 2010. 

[8] N. G Hadjiconstantinou, Dissipation in Small Scale Gaseous Flows, Journal of Heat Transfer, vol. 125, pp. 944-947, 2003. 

[9] N. Joeng and J. T. Joeng, Extended Graetz Problem Including Streamwise Conduction and Viscous Dissipation in Microchannel, Int. Journal of Heat and Mass Transfer, vol. 49, pp. 2151-2157, 2006. 

[10] C. H. Chen, Slip Flow Heat Transfer in Microchannel with Viscous Dissipation, Heat Mass Transfer, vol. 42, pp. 853-860, 2006. 

[11] L. Kuddusi, Prediction of Temperature Distribution and Nusselt Number in Rectangular Microchannels at Wall Slip Condition for all Versions of Constant Wall Temperature, Int. Journal of Thermal Sciences, vol. 46, pp. 998-1010, 2007. 

[12] M. Renksizbulut, H. Niazmand and G. Tercan, Slip-Flow and Heat Transfer in Rectangular Microchannels with Constant Wall Temperature, Int. Journal of Thermal Sciences, vol. 45, pp. 870-881, 2006. 

[13] L. Kuddusi, E. Cetegen, Prediction of Temperature Distribution and Nusselt Number in Rectangular Microchannels at Wall Slip Condition for all Versions of Constant Heat Flux, Int. Journal of Heat and Fluid Flow, vol. 28, pp. 777-786, 2007. 

[14] Aydin O, Avcı M. Laminar Forced Convection Slip-Flow in a Micro-Annulus Between Two Concentric Cylinders, Int. Journal of Heat and Mass Transfer, vol. 51, pp. 3460-3467, 2008. 

[15] M. I. Char and B. C. Tai, Effects of Viscous Dissipation on Slip-Flow Heat Transfer in a Micro Annulus, Int. Journal of Heat and Mass Transfer, vol. 53, pp. 1402-1408, 2010. 

[16] N. Xiao, J. Elsnab and T. Ameel, Microtube Gas Flows with Second-Order Slip Flow and Temperature Jump Boundary Conditions, Int. Journal of Thermal Sciences, vol. 48, pp. 243-251, 2009. 

[17] J. Van Rij, T. Haman and T. Ameel, The Effect of Creep Flow on Two-Dimensional Isoflux Microchannels, Int. Journal of Thermal Sciences, vol. 46, pp.1095-1103, 2007. 

[18] R. S. Myong, D. A. Lockerby and J. M. Reese, The Effect of Gaseous Slip on Microscale Heat Transfer: An Extended Graetz Problem, Int. Journal of Heat and Mass Transfer, vol. 49, pp. 2502-2513, 2006. 

[19] S. Chen, Z. Tian, Simulation of Thermal Micro-Flow using Lattice Boltzmann Method with Langmuir Slip Model, Int. Journal of Heat and Fluid Flow, vol. 31, pp. 227-235, 2010. 

[20] M. Mecili, E. Mezaache, Analytical Prediction for Slip Flow-Heat Transfer in Microtube and Parallel Plate Microchannel Including Viscous Dissipation, Int. Journal of Heat and Technology, vol. 29, pp. 79-86, 2011. 

[21] B. Cetin, H. Yuncu and S. Kakac, Gaseous Flow in Microconduits with Viscous Dissipation, Int. Journal of Trans. Phenomen., vol. 8, pp. 297-315, 2006.

Please sign up to receive notifications on new issues and newsletters from IIETA

Select Journal/Journals:

 

Copyright © 2024 IIETA. All Rights Reserved.