Abstract
A theoretical analysis of heat transfer characteristics is presented for the fully developed laminar flow of the incompressible gas in the triangular microchannels heated unsymmetrically with constant axial heat flux. Through solving the energy equation with temperature jump boundary conditions in slip flow regime by virtue of a computation-oriented method of the orthonormal function analysis, the dimensionless temperature profiles and the average Nusselt number for various thermal boundary conditions are obtained. The effects of Knudsen number, aspect ratio, and thermal boundary conditions on the heat transfer are discussed. The calculated results show that the orthonormal function method can be used to study the heat transfer characteristics of the unsymmetrically heated triangular microchannels. The average Nusselt number in triangular microchannels is lower for slip flow than for no-slip flow, and decreases with increasing Knudsen number. The aspect ratios and thermal boundary conditions of triangular microchannels have significant influences on the change of average Nusselt numbers with the increase in the Knudsen number. For the equilateral triangular microchannels, the decrease of the Nusselt number ratio due to temperature jump is smaller at large Knudsen number and larger at small Knudsen number on the boundary condition of bottom wall heated alone as compared with the one on the boundary condition of two heated hypotenuse walls. The correlations of the average Nusselt number with the Knudsen number for equilateral triangular microchannels are obtained.
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References
Tuckerman, D. B., Pease, R. F. W., High-performance heat sinking for VLSL, IEEE Electronic Device Letters, 1981, EDL-2(5): 126–129.
Choi, S. B., Barron, R. F., Warrington, R. O., Fluid flow and heat transfer in microtubes, Micromechanical Sensors, Actuators, and System, New York: ASME, 1991, DSC32: 123–134.
Yu, D., Warrington, R. O., Barron, R. F. et al., An experimental and theoretical investigation of fluid flow and heat transfer in microtubes, Proc. ASME/JSME Thermal Engineering Conference, Hawaii, 1994, 1: 523–530.
Adams, T. M., Abdel-khalik, S. I., Jeter, S. M. et al., An experimental investigation of single-phase forced convection in microchannels, Int. J. Heat Transfer, 1998, 41(6–7): 851–857.
Wu, P., Little, W. A., Measurement of the heat transfer characteristics of gas flow in fine channel heat exchangers used for microminiature refrigerators. Cryogenics, 1983, 8: 415–420.
Rujano, J. R., Rahman, M. M., Analysis and computation of conjugate heat transfer in trapezoidal microchannel heat sinks in a silicon substrate, 1995 National Heat Transfer Conference-Volume 3, ASME, 1995, HTD305: 175–185.
Kavehpour, H. P., Faghri, M., Asako, Y., Effects of compressibility and rarefaction on gaseous flow in microchannel, Numerical Heat Transfer, 1997, 32(A): 677–696.
Barron, R. F., Wang, X. M., Ameel, T. A., The Graetz problem extended to slip-flow, Int. J. Heat Transfer, 1997, 40(8): 1817–1823.
Yu, S. P., Ameel, T. A., A universal entrance Nusselt number for internal slip flow, Int. Commun. Heat Mass Transfer, 2001, 28(7): 905–910.
Zhu, X., Xin, M. D., Laminar flow and heat transfer in micro-annular channel in slip flow regime, J. of Engineering Thermophysics, 2001, 22(2): 203–206.
Zhu, X., Xin, M. D., Liao, Q., An analysis for heat transfer between two unsymmetrically heated parallel plates with micro space in slip flow regime, Microscale Thermophysical Engineering, 2002, 6(4): 287–302.
Zhu, X., Xin, M. D., Liao, Q., Analysis of gas slip flow in triangular microchannels, J. of Thermal Science and Technology, 2002, 1 (2): 141–145.
Kakac, S., Ramesh, K. S., Win, A., Handbook of Single-Phase Convective Heat Transfer, New York: Wiley, 1987.
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Zhu, X., Liao, Q. & Xin, M. Analysis of the heat transfer in unsymmetrically heated triangular microchannels in slip flow regime. Sci. China Ser. E-Technol. Sci. 47, 436–446 (2004). https://doi.org/10.1360/03ye0174
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DOI: https://doi.org/10.1360/03ye0174