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Research Papers: Forced Convection

Laminar Forced Convection in Transversely Corrugated Microtubes

[+] Author and Article Information
F. Talay Akyildiz

Department of Mathematics and Statistics,
Al-Imam University,
Riyadh, Saudi Arabia

Dennis A. Siginer

Life Fellow ASME
Departamento de Ingeniería Mecánica,
Centro de Investigación en Creatividad y
Educación Superior,
Universidad de Santiago de Chile,
Santiago, Chile;
Department of Mathematics and
Statistical Sciences,
Botswana International University of
Science and Technology,
Palapye, Botswana;
Department of Mechanical,
Energy and Industrial Engineering,
Botswana International University of
Science and Technology,
Palapye, Botswana
e-mails: siginerd@biust.ac.bw;
dennis.siginer@usach.cl

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 3, 2018; final manuscript received December 16, 2018; published online February 4, 2019. Assoc. Editor: Yuwen Zhang.

J. Heat Transfer 141(3), 031702 (Feb 04, 2019) (10 pages) Paper No: HT-18-1127; doi: 10.1115/1.4042331 History: Received March 03, 2018; Revised December 16, 2018

Forced convection heat transfer in fully developed laminar flow in transversely corrugated tubes is investigated for nonuniform but constant wall heat flux as well as for constant wall temperature. Epitrochoid conformal mapping is used to map the flow domain onto the unit circle in the computational domain. The governing equations are solved in the computational domain analytically. An exact analytical solution for the temperature field is derived together with closed form expressions for bulk temperature and Nusselt number for the case of the constant heat flux at the wall. A variable coefficient Helmholtz eigenvalue problem governs the case of the constant wall temperature. A novel semi-analytical solution based on the spectral Galerkin method is introduced to solve the Helmholtz equation. The solution in both constant wall heat flux and constant wall temperature case is shown to collapse onto the well-known results for the circular straight tube for zero waviness.

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References

Niu, J. L. , and Zhang, L. Z. , 2002, “ Heat Transfer and Friction Coefficient in Corrugated Ducts Confined by Sinusoidal and Arc Curves,” Int. J. Heat Mass Transfer, 45(3), pp. 571–578. [CrossRef]
Saunders, E. A. D. , 1998, Heat Exchangers: Selection, Design and Construction, Longman, Harlow, UK.
Walker, G. , 1990, Industrial Heat Exchangers, Hemisphere, New York.
Shah, R. K. , and London, A. L. , 1978, “ Laminar Flow Forced Convection in Ducts, Supplement 1,” Advances in Heat Transfer, Academic, New York.
Shah, R. K. , and Bhatti, M. S. , 1987, “ Laminar Convective Heat Transfer in Ducts,” Handbook of Single-Phase Convective Heat Transfer, S. Kakac , R. K. Shah , and W. Aung , eds., Wiley, New York, Chap. 3.
Turian, R. M. , and Kessler, F. D. , 2000, “ Capillary Flow in a Non-Circular Tube,” AIChE J., 46(4), pp. 695–706. [CrossRef]
Duan, Z. , and Muzychka, Y. , 2008, “ Effect of Corrugated Roughness on the Developed Laminar Flow in Microtubes,” ASME J. Fluids Eng., 130(3), p. 031102. [CrossRef]
Akyildiz, F. T. , and Siginer, D. A. , 2011, “ Fully Developed Laminar Slip and No-Slip Flow in Rough Microtubes,” J. Appl. Math. Phys. (ZAMP), 62(4), pp. 741–748. [CrossRef]
Akyildiz, F. T. , and Siginer, D. A. , 2012, “ Discussion on “Effects of Corrugated Roughness on Developed Laminar Flow in Microtubes,” ASME J. Fluids Eng., 134(8), p. 084502. [CrossRef]
Hooman, K. , 2007, “ Entropy Generation for Microscale Forced Convection: Effects of Different Thermal Boundary Conditions, Velocity Slip, Temperature Jump, Viscous Dissipation and Duct Geometry,” Int. Commun. Heat Mass Transfer, 34(8), pp. 945–957. [CrossRef]
Tamayol, A. , and Hooman, K. , 2011, “ Slip-Flow in Microchannels of Non-Circular Cross-Sections,” ASME J. Fluids Eng., 133(9), pp. 091201–091208. [CrossRef]
Akyildiz, F. T. , Siginer, D. A. , and Khezzar, L. , 2011, “ Energy Losses and Heat Transfer Enhancement in Transversally Corrugated Pipes,” Int. J. Heat Mass Transfer, 54(15–16), pp. 3801–3806. [CrossRef]
Muskhelishvili, N. I. , 1953, Some Basic Problems of the Mathematical Theory of Elasticity, Dordrecht, The Netherlands, p. XXXI (English Translation of the 3rd Russian Edition of 1949).
Aydin, O. , 2005, “ Effects of Viscous Dissipation on the Heat Transfer in Forced Pipe Flow—Part 1: Both Hydrodynamically and Thermally Fully Developed Flow,” Energy Convers. Manage., 46(5), pp. 757–769. [CrossRef]
Avcı, M. , and Aydın, O. , 2006, “ Laminar Forced Convection with Viscous Dissipation in a Concentric Annular Duct,” C. R. Méc., 334(3), pp. 164–169. [CrossRef]
Gilbarg, D. , and Trudinger, N. S. , 1983, Elliptic Partial Differential Equations of Second Order (Grundlehren Der Mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics), 2nd. ed., Vol. 224, Springer, Springer, Berlin.
Orszag, S. A. , and Patera, A. T. , 1983, “ Secondary Instability of Wall-Bounded Shear Flows,” J. Fluid Mech., 128(1), pp. 347–385. [CrossRef]
Shen, J. , 1997, “ Efficient Spectral-Galerkin Method III: Polar and Cylindrical Geometries,” SIAM J. Sci Comput., 18(6), pp. 1583–1604. [CrossRef]
Keys, W. M. , and Crawford, M. E. , 1993, Convection Heat and Mass Transfer, 3rd ed., McGraw Hill, New York.

Figures

Grahic Jump Location
Fig. 1

Epitrochoid conformal mapping for n=6 and ε=0.13

Grahic Jump Location
Fig. 2

Examples of tube cross section for three sets of values of the wave number n and the amplitude ε: (a) n =10, ε = 0.099, (b) n =100, ε = 0.0099, and (c) n =200, ε = 0.0049

Grahic Jump Location
Fig. 3

Coefficient of ε2 in Eq. (2.40)

Grahic Jump Location
Fig. 4

Constant wall heat flux: effect of the wave number n and corrugation amplitude ε on the bulk temperature θm

Grahic Jump Location
Fig. 5

Dimensionless temperature distributions for ε=0.15,n=10,contours=9/10,3/4,1/2,1/4,1/16:(a) fixed wall heat flux and (b) constant wall temperature

Grahic Jump Location
Fig. 6

Constant wall heat flux: effect of the wave number n on the Nusselt number Nu for the corrugation amplitude ε=0.05

Grahic Jump Location
Fig. 7

Constant wall heat flux: effect of the wave number n on the Nusselt number Nu for a fixed value of the amplitude ε=0.1

Grahic Jump Location
Fig. 8

Constant wall heat flux: effect of the wave number n on the Nusselt number Nu for a fixed value of the amplitude ε=0.15

Grahic Jump Location
Fig. 9

Constant wall heat flux: effect of the corrugation amplitude ε on the Nusselt number Nu for the wave number n =3

Grahic Jump Location
Fig. 10

Constant wall heat flux: effect of the corrugation amplitude ε on the Nusselt number Nu for the wave number n =5

Grahic Jump Location
Fig. 11

Constant wall temperature: effect of the wave number n and corrugation amplitude ε on the bulk temperature θm; Lozenge (n=1) and star (n=4)

Grahic Jump Location
Fig. 12

Constant wall temperature: effect of the wave number n on the Nusselt number Nu for a fixed value of the amplitude ε=0.1, dashed line (n=1), dashed dot line (n=3) and solid line (n=6)

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