Unsteady heat transfer for a fully developed laminar flow inside a parallel-plate channel and circular duct that are subjected to a periodically varying inlet temperature is studied. The thermal capacitance of the duct wall and the boundary condition that accounts for external convection are considered. An exact solution is presented for this extended Graetz problem as the result of using a new methodology based on a variational method. The quasi-steady approach that employs a heat transfer coefficient at the liquid–solid interface is also investigated, and the results are compared with the variational solution. The damping and phase lag coefficients as functions of the inlet temperature frequency are presented in graphical form.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Kakaç and Y. Yener, Exact solution of transient forced convection energy equation for timewise variation of inlet temperature, Int. J. Heat Mass Transfer, 16, 2205–2214 (1973).
S. Kakaç and Y. Yener, Frequency response analysis of transient turbulent forced convection for timewise variation of inlet temperature, in: S. Kakaç and D. B. Spalding (Eds), Turbulent Forced Convection in Channels and Bundles, Hemisphere Publishing Corporation, New York (1979), pp. 865–880.
R. M. Cotta and M. N. Ozisik, Laminar forced convection inside ducts with periodic variation of inlet temperature, Int. J. Heat Mass Transfer, 29, 1445–1501 (1986).
W. S. Kim and M. N. Ozisik, Turbulent forced convection inside a parallel-plate channel with periodic variation of inlet temperature, Trans. ASME, J. Heat Transfer, 111, 882–888 (1989).
M. Arik, C. A. C. Santos, and S. Kakaç, Turbulent forced convection with sinusoidal variation of inlet temperature between two parallel plates, Int. Commun. Heat Mass Transfer, 23, 1121–1132 (1996).
M. Unsal, A solution for the complex eigenvalues and eigenfunctions of the periodic Graetz problem, Int. Commun. Heat Mass Transfer, 25, No. 4, 585–592 (1998).
E. M. Sparrow and F. N. De Farias, Unsteady heat transfer in ducts with time varying inlet temperature and participating walls, Int. J. Heat Mass Transfer, 11, 837–853 (1968).
R. M. Cotta, M. D. Mikhailov, and M. N. Ozisik, Transient conjugated forced convection in ducts with periodically varying inlet temperature, Int. J. Heat Mass Transfer, 30, 2073–2082 (1987).
W. S. Kim and M. N. Ozisik, Conjugated laminar forced convection in ducts with periodic variation of inlet temperature, Int. J. Heat Fluid Flow, 11, 311–320 (1990).
J. S. Travelho and F. N. Santos, Solution for transient conjugated forced convection in the thermal entrance region of a duct with periodically varying inlet temperature, Trans. ASME, J. Heat Transfer, 113, 558–562 (1991).
J. S. Travelho and F. N. Santos, Unsteady conjugate heat transfer in a circular duct with convection from the ambient and periodically varying inlet temperature, Trans. ASME, J. Heat Transfer, 120, 506–510 (1998).
S. Kakaç and W. Li, Unsteady turbulent forced convection in a parallel-plate channel with timewise variation of inlet temperature, Int. J. Heat Mass Transfer, 37, 447–456 (1994).
W. Li and S. Kakaç, Unsteady thermal entrance heat transfer in laminar flow with a periodic variation of inlet temperature, Int. J. Heat Mass Transfer, 34, 2581–2592 (1991).
B. Fourcher and K. Mansouri, An approximate analytical solution to the Graetz problem with periodic inlet temperature, Int. J. Heat Fluid Flow, 18, 229–235 (1997).
K. Mansouri and B. Fourcher, The effects of inlet temperature frequency on the quasi-steady approach of periodic conjugated heat transfer problem, Int. J. Eng. Sci., 42, 825–839 (2004).
R. O. C. Guedes and R. M. Cotta, Periodic laminar forced convection within ducts including wall heat conduction effects, Int. J. Eng. Sci., 29, 535–547 (1991).
R. O. C. Guedes, M. N. Ozisik, and R. M. Cotta, Conjugated periodic turbulent forced convection in a parallel-plate channel, Trans. ASME, J. Heat Transfer, 116, 40–46 (1994).
K. Mansouri and A. Hadiouche, On the solution of a periodic internal laminar flow, in: Proc. CHT-08 Int. Symp. on Advances in Computational Heat Transfer, Morocco, May 11–16, 2008, Begell House (2008).
G. D. Ngoma and F. Erchiqui, Heat transfer and slip effects on liquid flow in a micro-channel, Int. J. Thermal Sci., 46, 1076–1083 (2007).
W. Sun, S. Kakaç, and A. G. Yazicioglu, A numerical study of single phase convective heat transfer in microtubes for slip flow, Int. J. Thermal Sci., 46, 2581–2592 (2007).
J. Peixinho, C. Desaubry, and M. Lebouché, Heat transfer of non-Newtonian fluid (Carbopol aqueous solution) in transitional pipe flow, Int. J. Heat Mass Transfer, 51, 195–209 (2008).
F. Tamisli, Laminar flow of a non-Newtonian fluid in channels with wall suction or injection, Int. J. Eng. Sci., 44, 650–661 (2006).
O. Jambal, T. Shigechi, G. Davaa, and S. Momki, Effects of viscous dissipation and fluid axial heat convection on heat transfer for non-Newtonian fluids in ducts with uniform wall temperature, Int. Comm. Heat Mass Transfer, 32, 1165–1173 (2005).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 2, pp. 357–368, March–April, 2010.
Rights and permissions
About this article
Cite this article
Hadiouche, A., Mansouri, K. Analysis of the effects of inlet temperature frequency in fully developed laminar duct flows. J Eng Phys Thermophy 83, 380–392 (2010). https://doi.org/10.1007/s10891-010-0355-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-010-0355-x