Heat Transfer with Viscous Dissipation in Couette-Poiseuille Flow under Asymmetric Wall Heat Fluxes

Affiliation(s)

Faculty of Engineering, Multimedia University, Cyberjaya, Malaysia.

School of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore City, Singapore.

Faculty of Engineering & Technology, Multimedia University, Jalan Ayer Keroh Lama, Melaka, Malaysia.

Faculty of Engineering, Multimedia University, Cyberjaya, Malaysia.

School of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore City, Singapore.

Faculty of Engineering & Technology, Multimedia University, Jalan Ayer Keroh Lama, Melaka, Malaysia.

ABSTRACT

Analytical solutions of temperature distributions and the Nusselt numbers in forced convection are reported for flow through infinitely long parallel plates, where the upper plate moves in the flow direction with constant velocity and the lower plate is kept stationary. The flow is assumed to be laminar, both hydro-dynamically and thermally fully developed, taking into account the effect of viscous dissipation of the flowing fluid. Both the plates being kept at specified and at different constant heat fluxes are considered as thermal boundary conditions. The solutions obtained from energy equation are in terms of Brinkman number, dimensionless velocity and heat flux ratio. These parameters greatly influence and give complete understanding on heat transfer rates that has potentials for designing and analyzing energy equipment and processes.

Analytical solutions of temperature distributions and the Nusselt numbers in forced convection are reported for flow through infinitely long parallel plates, where the upper plate moves in the flow direction with constant velocity and the lower plate is kept stationary. The flow is assumed to be laminar, both hydro-dynamically and thermally fully developed, taking into account the effect of viscous dissipation of the flowing fluid. Both the plates being kept at specified and at different constant heat fluxes are considered as thermal boundary conditions. The solutions obtained from energy equation are in terms of Brinkman number, dimensionless velocity and heat flux ratio. These parameters greatly influence and give complete understanding on heat transfer rates that has potentials for designing and analyzing energy equipment and processes.

Cite this paper

J. Sheela-Francisca, C. Tso and D. Rilling, "Heat Transfer with Viscous Dissipation in Couette-Poiseuille Flow under Asymmetric Wall Heat Fluxes,"*Open Journal of Fluid Dynamics*, Vol. 2 No. 4, 2012, pp. 111-119. doi: 10.4236/ojfd.2012.24011.

J. Sheela-Francisca, C. Tso and D. Rilling, "Heat Transfer with Viscous Dissipation in Couette-Poiseuille Flow under Asymmetric Wall Heat Fluxes,"

References

[1] J. Sheela-Francisca and C. P. Tso, “Viscous Dissiption Effects on Parallel Plates with Constant Heat Flux Boundary Conditions,” International Communcations in Heat Mass Transfer, Vol. 36, No. 3, 2009, pp. 249-254. doi:10.1016/j.icheatmasstransfer.2008.11.003

[2] O. Aydin and M. Avci, “Viscous-Dissipation Effects on the Heat Transfer in a Poiseuille Flow,” Applied Energy, Vol. 83, No. 5, 2006, pp. 495-512. doi:10.1016/j.apenergy.2005.03.003

[3] J. W. Ou and K. C. Cheng, “Effects of Pressure Work and Viscous Dissipation on Graetz Problem for Gas Flows in Parallel Plate Channels,” Warmeund Stoffubertraggung, Vol. 6, No. 4, 1973, pp. 191-198. doi:10.1007/BF02575264

[4] C. P. Tso, J. Sheela Francisca and Y.-M. Hung, “Viscous Dissipation Effects of Power-Law Fluid within Parallel Plates with Constant Heat Flues,” Journal of Non-Newtonian Fluid Mechanics, Vol. 165, No. 11-12, 2010, pp. 625-630. doi:10.1016/j.jnnfm.2010.02.023

[5] D. E. Gray, “The Motion of Viscous Fluids,” Amercan Institute of Physics Handbook, 3rd Edition, Section 3c-2, American Institute of Physics, McGraw-Hill, New York, 1972.

[6] D. A. Nield, A. V. Kuznetsov and M. Xiong, “Thermally Developing Forced Convection in a Porous Medium: Parallel Plate Channel with Walls at Uniform Temperature, with Axial Conduction and Viscous Dissipation Effects,” International Journal Heat and Mass Transfer, Vol. 46, No. 4, 2003, pp. 643-651. doi:10.1016/S0017-9310(02)00327-7

[7] Y. M. Hung and C. P. Tso, “Effects of Viscous Disspation on Fully Developed Forced Convection in Porous Media,” International Communications in Heat Mass Transfer, Vol. 36, No. 6, 2009, pp. 597-603. doi:10.1016/j.icheatmasstransfer.2009.03.008

[8] M. M. Salah El-Din, “Effect of Viscous Dissipation on Fully Developed Combined Convection in a Horizontal Double-Passage Channel,” Heat Mass Transfer, Vol. 38, No. 7-8, 2002, pp. 673-677. doi:10.1007/s002310100255

[9] O. Aydin, “Effects of Viscous Dissipation on the Heat Transfer in Forced Pipe Flow. Part 1: Both Hydro-Dynamically and Thermally Fully Developed Flow,” Energy Conversion Management, Vol. 46, 2005, pp. 757-769.

[10] O. Aydin, “Effects of Viscous Dissipation on the Heat Transfer in a Forced Pipe Flow. Part 2: Thermally Developing Flow,” Energy Conversion Management, Vol. 46, No. 18-19, 2005, pp. 3091-3102. doi:10.1016/j.enconman.2005.03.011

[11] S. H. Hashemabadi, S. Gh. Etemad and J. Thibault, “Forced Convection Heat Transfer of Couette-Poiseuille Flow of Nonlinear Visco-Elastic Fluids between Parallel Plates,” International Journal of Heat and Mass Transfer, Vol. 47, No. 17-18, 2004, pp. 3985-3991. doi:10.1016/j.ijheatmasstransfer.2004.03.026

[12] F. T. Pinho and P. J. Oliveira, “Analysis of Forced Convection in Pipes And Channels with the Simplified Phan-Thien-Tanner Fluid,” International Journal of Heat and Mass Transfer, Vol. 43, No. 13, 2000, pp. 2273-2287. doi:10.1016/S0017-9310(99)00303-8

[13] S. H. Hashemabadi, S. Gh. Etemad and J. Thibault, “Mathematical Modeling of Laminar Forced Convection of Simplified Phan-Thien-Tanner (SPTT) Fluid between Moving Parallel Plates,” International Communications in Heat Mass Transfer, Vol. 30, No. 2, 2003, pp. 197-205. doi:10.1016/S0735-1933(03)00030-7

[14] G. Davaa, T. Shigechi and S. Momoki, “Effect of Viscous Dissipation on Fully Developed Heat Transfer of Non-Newtonian Fluids in Plane Laminar Poiseuille-Couette Flow,” International Communications in Heat Mass Transfer, Vol. 31, No. 5, 2004, pp. 663-672. doi:10.1016/S0735-1933(04)00053-3

[15] O. Aydin and M. Avci, “Laminar Forced Convection with Viscous Dissipation in a Couette-Poiseuille Flow between Parallel Plates,” Applied Energy, Vol. 83, No. 8, 2006, pp. 856-867. doi:10.1016/j.apenergy.2005.08.005

[16] S. Gh. Etemad, A. S. Majumdar and B. Huang, “Viscous Dissipation Effects in Entrance Region Heat Transfer for a Power Law Fluid Flowing between Parallel Plates,” International Journal of Heat and Fluid Flow, Vol. 15, No. 2, 1994, pp. 122-131. doi:10.1016/0142-727X(94)90066-3

[17] M. Lewandowska and L. Malinowski, “An Analytcal Solution of the Hyperbolic Heat Conduction Equation for the Case of a Finite Medium Symmetrically Heated on Both Sides,” International Communications in Heat Mass Transfer, Vol. 33, No. 1, 2006, pp. 61-69. doi:10.1016/j.icheatmasstransfer.2005.08.004

[18] A. Pantokratoras, “Effect of Viscous Dissipation and Pressure Stress Work in Natural Convection along a Vertical Isothermal Plate. New Results,” International Journal of Heat and Mass Transfer, Vol. 46, No. 25, 2003, pp. 4979-4983. doi:10.1016/S0017-9310(03)00321-1

[19] Y.-L. Chen and K.-Q. Zhu, “Couette-Poiseuille Flow of Bingham Fluids between Two Porous Parallel Plates with Slip Conditions,” Journal of Non-Newtonian Fluid Mechanics, Vol. 153, No. 1, 2008, pp. 1-11. doi:10.1016/j.jnnfm.2007.11.004

[20] O. Jambal, T. Shigechi, G. Davaa and S. Momoki, “Effects of Viscous Dissipation and Fluid Axial Heat Conduction on Heat Transfer for Non-Newtonian Fluids in Ducts with Uniform Wall Temperature Part I: Parallel Plates and Circular Ducts,” International Communications in Heat Mass Transfer, Vol. 32, No. 9, 2005, pp. 1165-1173. doi:10.1016/j.icheatmasstransfer.2005.07.002

[21] K. C. Cheng and R. S. Wu, “Viscous Dissipation Effects on Convective Instability and Heat Transfer in Plane Poiseuille Flow Heated from Below,” Applied Science Research, Vol. 32, No. 4, 1976, pp. 327-346.

[22] B. Li, L. Zheng and X. Zhang, “Heat Transfer in Pseudo-Plastic Non-Newtonian Fluids with Variable Thermal Conductivity,” Energy Conversion Management, Vol. 52, No. 1, 2011, pp. 355-358. doi:10.1016/j.enconman.2010.07.008

[23] W. M. Kays, “Convective Heat and Mass Transfer,” 4th Edition, McGraw-Hill, New York, 1966, p. 104.

[1] J. Sheela-Francisca and C. P. Tso, “Viscous Dissiption Effects on Parallel Plates with Constant Heat Flux Boundary Conditions,” International Communcations in Heat Mass Transfer, Vol. 36, No. 3, 2009, pp. 249-254. doi:10.1016/j.icheatmasstransfer.2008.11.003

[2] O. Aydin and M. Avci, “Viscous-Dissipation Effects on the Heat Transfer in a Poiseuille Flow,” Applied Energy, Vol. 83, No. 5, 2006, pp. 495-512. doi:10.1016/j.apenergy.2005.03.003

[3] J. W. Ou and K. C. Cheng, “Effects of Pressure Work and Viscous Dissipation on Graetz Problem for Gas Flows in Parallel Plate Channels,” Warmeund Stoffubertraggung, Vol. 6, No. 4, 1973, pp. 191-198. doi:10.1007/BF02575264

[4] C. P. Tso, J. Sheela Francisca and Y.-M. Hung, “Viscous Dissipation Effects of Power-Law Fluid within Parallel Plates with Constant Heat Flues,” Journal of Non-Newtonian Fluid Mechanics, Vol. 165, No. 11-12, 2010, pp. 625-630. doi:10.1016/j.jnnfm.2010.02.023

[5] D. E. Gray, “The Motion of Viscous Fluids,” Amercan Institute of Physics Handbook, 3rd Edition, Section 3c-2, American Institute of Physics, McGraw-Hill, New York, 1972.

[6] D. A. Nield, A. V. Kuznetsov and M. Xiong, “Thermally Developing Forced Convection in a Porous Medium: Parallel Plate Channel with Walls at Uniform Temperature, with Axial Conduction and Viscous Dissipation Effects,” International Journal Heat and Mass Transfer, Vol. 46, No. 4, 2003, pp. 643-651. doi:10.1016/S0017-9310(02)00327-7

[7] Y. M. Hung and C. P. Tso, “Effects of Viscous Disspation on Fully Developed Forced Convection in Porous Media,” International Communications in Heat Mass Transfer, Vol. 36, No. 6, 2009, pp. 597-603. doi:10.1016/j.icheatmasstransfer.2009.03.008

[8] M. M. Salah El-Din, “Effect of Viscous Dissipation on Fully Developed Combined Convection in a Horizontal Double-Passage Channel,” Heat Mass Transfer, Vol. 38, No. 7-8, 2002, pp. 673-677. doi:10.1007/s002310100255

[9] O. Aydin, “Effects of Viscous Dissipation on the Heat Transfer in Forced Pipe Flow. Part 1: Both Hydro-Dynamically and Thermally Fully Developed Flow,” Energy Conversion Management, Vol. 46, 2005, pp. 757-769.

[10] O. Aydin, “Effects of Viscous Dissipation on the Heat Transfer in a Forced Pipe Flow. Part 2: Thermally Developing Flow,” Energy Conversion Management, Vol. 46, No. 18-19, 2005, pp. 3091-3102. doi:10.1016/j.enconman.2005.03.011

[11] S. H. Hashemabadi, S. Gh. Etemad and J. Thibault, “Forced Convection Heat Transfer of Couette-Poiseuille Flow of Nonlinear Visco-Elastic Fluids between Parallel Plates,” International Journal of Heat and Mass Transfer, Vol. 47, No. 17-18, 2004, pp. 3985-3991. doi:10.1016/j.ijheatmasstransfer.2004.03.026

[12] F. T. Pinho and P. J. Oliveira, “Analysis of Forced Convection in Pipes And Channels with the Simplified Phan-Thien-Tanner Fluid,” International Journal of Heat and Mass Transfer, Vol. 43, No. 13, 2000, pp. 2273-2287. doi:10.1016/S0017-9310(99)00303-8

[13] S. H. Hashemabadi, S. Gh. Etemad and J. Thibault, “Mathematical Modeling of Laminar Forced Convection of Simplified Phan-Thien-Tanner (SPTT) Fluid between Moving Parallel Plates,” International Communications in Heat Mass Transfer, Vol. 30, No. 2, 2003, pp. 197-205. doi:10.1016/S0735-1933(03)00030-7

[14] G. Davaa, T. Shigechi and S. Momoki, “Effect of Viscous Dissipation on Fully Developed Heat Transfer of Non-Newtonian Fluids in Plane Laminar Poiseuille-Couette Flow,” International Communications in Heat Mass Transfer, Vol. 31, No. 5, 2004, pp. 663-672. doi:10.1016/S0735-1933(04)00053-3

[15] O. Aydin and M. Avci, “Laminar Forced Convection with Viscous Dissipation in a Couette-Poiseuille Flow between Parallel Plates,” Applied Energy, Vol. 83, No. 8, 2006, pp. 856-867. doi:10.1016/j.apenergy.2005.08.005

[16] S. Gh. Etemad, A. S. Majumdar and B. Huang, “Viscous Dissipation Effects in Entrance Region Heat Transfer for a Power Law Fluid Flowing between Parallel Plates,” International Journal of Heat and Fluid Flow, Vol. 15, No. 2, 1994, pp. 122-131. doi:10.1016/0142-727X(94)90066-3

[17] M. Lewandowska and L. Malinowski, “An Analytcal Solution of the Hyperbolic Heat Conduction Equation for the Case of a Finite Medium Symmetrically Heated on Both Sides,” International Communications in Heat Mass Transfer, Vol. 33, No. 1, 2006, pp. 61-69. doi:10.1016/j.icheatmasstransfer.2005.08.004

[18] A. Pantokratoras, “Effect of Viscous Dissipation and Pressure Stress Work in Natural Convection along a Vertical Isothermal Plate. New Results,” International Journal of Heat and Mass Transfer, Vol. 46, No. 25, 2003, pp. 4979-4983. doi:10.1016/S0017-9310(03)00321-1

[19] Y.-L. Chen and K.-Q. Zhu, “Couette-Poiseuille Flow of Bingham Fluids between Two Porous Parallel Plates with Slip Conditions,” Journal of Non-Newtonian Fluid Mechanics, Vol. 153, No. 1, 2008, pp. 1-11. doi:10.1016/j.jnnfm.2007.11.004

[20] O. Jambal, T. Shigechi, G. Davaa and S. Momoki, “Effects of Viscous Dissipation and Fluid Axial Heat Conduction on Heat Transfer for Non-Newtonian Fluids in Ducts with Uniform Wall Temperature Part I: Parallel Plates and Circular Ducts,” International Communications in Heat Mass Transfer, Vol. 32, No. 9, 2005, pp. 1165-1173. doi:10.1016/j.icheatmasstransfer.2005.07.002

[21] K. C. Cheng and R. S. Wu, “Viscous Dissipation Effects on Convective Instability and Heat Transfer in Plane Poiseuille Flow Heated from Below,” Applied Science Research, Vol. 32, No. 4, 1976, pp. 327-346.

[22] B. Li, L. Zheng and X. Zhang, “Heat Transfer in Pseudo-Plastic Non-Newtonian Fluids with Variable Thermal Conductivity,” Energy Conversion Management, Vol. 52, No. 1, 2011, pp. 355-358. doi:10.1016/j.enconman.2010.07.008

[23] W. M. Kays, “Convective Heat and Mass Transfer,” 4th Edition, McGraw-Hill, New York, 1966, p. 104.