Numerical Study of Viscous Dissipation and Roughness Effects on Fluid Flow and Heat Transfer in Microchannels using Perturbation Method
Authors
Abstract
In this paper, viscous dissipation and roughness effects on heat transfer and fluid flow are investigated in microchannels using perturbation method in slip flow regime. The flow is considered to be laminar, developing thermally and hydrodynamically, two-dimensional, incompressible and steady-state. The working fluid is air, flowing between two parallel plates. The equations obtained from developing Navier-Stokes and energy equations are solved numerically according to different orders of Knudsen number, with second-order velocity slip and temperature jump boundary conditions. The effects of thermal creep has been ignored. Tempreture and velocity fields are obtained and estimated for both constatnt heat flux and constant wall tempreture. The effects of roughness height, space between roughness elements, roughness elements length, Re number and Kn number on slip behavior of gas flow are investigated.The results indicate considerable effect of viscous dissipation and roughness on fluid flow and heat transfer in microchannel.
Keywords
1. Dorin, L., and Adrianl E. C., “The Viscous Disspation Effect on Heat Transfer and Fluid Flow in Micro-Tubes”, Heat and Mass Transfer, Vol. 37, pp. 128-1214, 2010.
2. Milton V. D., “Perturbation Mehods in Fluid Mechanics”, Stanford, California, 1975.
3. Koo, J., and Kleinstreuer, C., “Viscous Dissipation Effects in Microtubes and Microchannels”, International Journal of Heat and Mass Transfer, Vol. 47, pp. 3159-3169, 2004.
4. Celata, G. P., Morini,G. L., Marconi, V., McPhail, S. J., and Zummo, G., “Using Viscous Heating to Determine the Friction Factor in Microchannels an Experimental Validation”, Experimental Thermal and Fluid Science, Vol. 30, pp. 725-731, 2006.
5. Rands, C., Webb, B. W., and Maynes, D., “Characterization of Transition to Turbulence In microchannels”, International Journal of Heat and Mass Transfer, Vol. 49, pp. 2924-2930, 2006.
6. Nonino, C., Giudice, S. D., and Savino, S., “Temperature- Dependent Viscosity and Viscous Dissipation Effects in Simultaneously Developing Flows in Micro Channels with Convective Boundary Conditions”, Journal of Heat Transfer, Vol. 129, pp. 1187-1194, 2007.
7. Hung, Y. M., “A Comparative Study of Viscous Dissipation Effect on Entropy Generation in Single-Phase Liquid Flow in Micro Channels”, International Journal of Thermal Sciences, Vol. 48, pp. 1026-1035, 2009.
8. Van Rij, J., Ameel, T., and Harman, T., “The Effect of Viscous Dissipation and Rarefaction on Rectangular Micro Channel Convective Heat Transfer”, International Journal of Thermal Sciences, Vol. 48, pp. 271-281, 2009.
9. Arici, M. E., and Aydin, O., “Conjugate Heat Transfer in Thermally Developing Laminar Flow with Viscous Dissipation Effects”, International Journal of Heat and Mass Transfer, Vol. 45. pp. 1199-1203, 2009.
10. Bing-Yang, C., Min, C., and Guo, Z. Y., “Rarefied Gas Flow in Rough Micro Channels by Molecular Dynamics Simulation”, Chinese Physics Letters, Vol. 9, No. 21, pp. 1777-1779, 2004.
11. Croce, G., and D’Agaro, P. “Numerical Simulation of Roughness Effect on Micro Channel Heat Transfer and Pressure Drop in Laminar Flow”, Physics, Vol. 38, pp. 1518-1530, 2005.
12. Shen, S., Xu, J. L., Zhou, J. J., and Chen, Y., “Flow and Heat Transfer in Micro Channnels with Rough wall Surface”, Energy Conversion and Management, Vol. 47, pp.1311-1325., 2005.
13. Ji, Y., Yuan, K., and Chung, J. N., “Numerical Simulation of Wall Roughness on Gaseous Flow and Heat Transfer in a Micro Channel”, International Journal of Heat and Mass Transfer, Vol. 49, pp. 1329-1339, 2006.
14. Hakak, K., M., Shams., M., and Hossaninpour, S., “Effects of Rarefaction and Compressibility on Fluid Flow at Slip Flow Regime by Direct Simulation of Roughness”, International Journal of Aerospace and Mechanical Engineering, Vol. 3, pp. 204-210, 2009.
15. Turgay, M. B., and Yazicioglu, A. G., “Effect of Surface Roughness in Parallel-Plate Microchannels on Heat Transfer”, Numerical Heat Transfer, Part A: Applications, Vol. 56, pp. 497-514, 2009.
16. Zhang, C., Chen, Y., and Shi, M., “Effects of Roughness Elements on Laminar Flow and Heat Transfer in Micro Channels”, Chemical Engineering and Processing, Vol. 49, pp. 1188-1192, 2010.
17. Karniadakis, G., Beskok, A., and Aluru, N., “Micro flows and Nano flows Fundamentals and Simulations”, Springer, 2004.
18. Cropper W., H., “The Life and Times of Leading Physicists from Galileo to Hawking”, Great Physicists, Oxford University Press, 2004.
19. Jeong, H., and Jeong, J., “Extended Graetz Problem Including Stream Wise Conduction and Viscous Dissipation in Micro Channel”, International Journal of Heat and Mass Transfer, Vol. 49, pp. 2151-2157, 2006.
20. Kakac, S., Vasiliev., L. L., Bayzitoglu, Y., and Yener, Y., “Micro Scale Heat Transfer Fundamentals and Applications”, Springer, Cesme-lzmir, Turkey, 2004.
2. Milton V. D., “Perturbation Mehods in Fluid Mechanics”, Stanford, California, 1975.
3. Koo, J., and Kleinstreuer, C., “Viscous Dissipation Effects in Microtubes and Microchannels”, International Journal of Heat and Mass Transfer, Vol. 47, pp. 3159-3169, 2004.
4. Celata, G. P., Morini,G. L., Marconi, V., McPhail, S. J., and Zummo, G., “Using Viscous Heating to Determine the Friction Factor in Microchannels an Experimental Validation”, Experimental Thermal and Fluid Science, Vol. 30, pp. 725-731, 2006.
5. Rands, C., Webb, B. W., and Maynes, D., “Characterization of Transition to Turbulence In microchannels”, International Journal of Heat and Mass Transfer, Vol. 49, pp. 2924-2930, 2006.
6. Nonino, C., Giudice, S. D., and Savino, S., “Temperature- Dependent Viscosity and Viscous Dissipation Effects in Simultaneously Developing Flows in Micro Channels with Convective Boundary Conditions”, Journal of Heat Transfer, Vol. 129, pp. 1187-1194, 2007.
7. Hung, Y. M., “A Comparative Study of Viscous Dissipation Effect on Entropy Generation in Single-Phase Liquid Flow in Micro Channels”, International Journal of Thermal Sciences, Vol. 48, pp. 1026-1035, 2009.
8. Van Rij, J., Ameel, T., and Harman, T., “The Effect of Viscous Dissipation and Rarefaction on Rectangular Micro Channel Convective Heat Transfer”, International Journal of Thermal Sciences, Vol. 48, pp. 271-281, 2009.
9. Arici, M. E., and Aydin, O., “Conjugate Heat Transfer in Thermally Developing Laminar Flow with Viscous Dissipation Effects”, International Journal of Heat and Mass Transfer, Vol. 45. pp. 1199-1203, 2009.
10. Bing-Yang, C., Min, C., and Guo, Z. Y., “Rarefied Gas Flow in Rough Micro Channels by Molecular Dynamics Simulation”, Chinese Physics Letters, Vol. 9, No. 21, pp. 1777-1779, 2004.
11. Croce, G., and D’Agaro, P. “Numerical Simulation of Roughness Effect on Micro Channel Heat Transfer and Pressure Drop in Laminar Flow”, Physics, Vol. 38, pp. 1518-1530, 2005.
12. Shen, S., Xu, J. L., Zhou, J. J., and Chen, Y., “Flow and Heat Transfer in Micro Channnels with Rough wall Surface”, Energy Conversion and Management, Vol. 47, pp.1311-1325., 2005.
13. Ji, Y., Yuan, K., and Chung, J. N., “Numerical Simulation of Wall Roughness on Gaseous Flow and Heat Transfer in a Micro Channel”, International Journal of Heat and Mass Transfer, Vol. 49, pp. 1329-1339, 2006.
14. Hakak, K., M., Shams., M., and Hossaninpour, S., “Effects of Rarefaction and Compressibility on Fluid Flow at Slip Flow Regime by Direct Simulation of Roughness”, International Journal of Aerospace and Mechanical Engineering, Vol. 3, pp. 204-210, 2009.
15. Turgay, M. B., and Yazicioglu, A. G., “Effect of Surface Roughness in Parallel-Plate Microchannels on Heat Transfer”, Numerical Heat Transfer, Part A: Applications, Vol. 56, pp. 497-514, 2009.
16. Zhang, C., Chen, Y., and Shi, M., “Effects of Roughness Elements on Laminar Flow and Heat Transfer in Micro Channels”, Chemical Engineering and Processing, Vol. 49, pp. 1188-1192, 2010.
17. Karniadakis, G., Beskok, A., and Aluru, N., “Micro flows and Nano flows Fundamentals and Simulations”, Springer, 2004.
18. Cropper W., H., “The Life and Times of Leading Physicists from Galileo to Hawking”, Great Physicists, Oxford University Press, 2004.
19. Jeong, H., and Jeong, J., “Extended Graetz Problem Including Stream Wise Conduction and Viscous Dissipation in Micro Channel”, International Journal of Heat and Mass Transfer, Vol. 49, pp. 2151-2157, 2006.
20. Kakac, S., Vasiliev., L. L., Bayzitoglu, Y., and Yener, Y., “Micro Scale Heat Transfer Fundamentals and Applications”, Springer, Cesme-lzmir, Turkey, 2004.
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