Comparison of Selected Meshless Methods for Analysis of Steady, Fully-Developed, Laminar Flow of an Incompressible Newtonian Fluid in Internally Finned Tubes

Abstract:

Fluid flow in internally finned tubes is a very important problem from a practical point of view. In the literature there are many different numerical methods which were used for analysis this problem. However to the best knowledge of the authors of the present paper there are no so many papers in which meshless methods were applied for this purpose. The main advantages of these methods are: easy implementation, semi-analytical form of the approximate solution and no need for mesh generation. In the paper these meshless methods are compared in application for analysis of incompressible, fully-developed, Newtonian fluid flow in an internally finned tube.

• Periodical: Applied Mechanics and Materials (Volume 797)
• Pages: 274-281
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.797.274
• Online since: November 2015
• Authors: Jakub Krzysztof Grabski, Jan Adam Kołodziej
• Keywords: Collocation Method, Finned Tubes, Kansa Method, Method of Fundamental Solutions, Trefftz Method

References

[1] Y.A. Çengel, Heat transfer. A practical approach, McGraw-Hill, New York, (2003).

[2] J.P. Holman, Heat transfer, McGraw-Hill, Boston, (2002).

[3] J.H. Masliyah, K. Nandakumar, Heat transfer in internally finned tubes, J. Heat Transfer 98 (1976) 257-261.

DOI: 10.1115/1.3450528

[4] G. Fabbri, Heat transfer optimization in internally finned tubes under laminar flow, Int. J. Heat Mass Transfer 41 (1998) 1243-1253.

DOI: 10.1016/s0017-9310(97)00209-3

[5] G. Fabbri, Optimum profiles for asymmetrical longitudinal fins in cylindrical ducts, Int. J. Heat Mass Transfer 42 (1999) 511-523.

DOI: 10.1016/s0017-9310(98)00179-3

[6] H.M. Soliman, T.S. Chau, A.C. Trupp, Analysis of laminar heat transfer in internally finned tubes with uniform outside wall temperature, J. Heat Transfer 102 (1980) 598-604.

DOI: 10.1115/1.3244358

[7] I.M. Ruston, H.M. Soliman, Forced convection in the entrance region of tubes with longitudinal internal fins, J. Heat Transfer 110 (1988) 310-313.

DOI: 10.1115/1.3250485

[8] I.J. Kettner, D. Degani, G. Gutfinger, Numerical study of heat transfer in internally finned tubes, Num. Heat Transfer A-Appl. 20 (1991) 159-180.

DOI: 10.1080/10407789108944815

[9] G.A. Lendeza, A. Camp, Computation of the Nusselt number asymptotes for laminar convection flows in internally finned tubes, Int. Commun. Heat Mass Transfer 26 (1999) 399-409.

DOI: 10.1016/s0735-1933(99)00026-3

[10] O. Zeitoun, A.S. Hegazy, Heat transfer for laminar flow in internally finned pipes with different fin heights and uniform wall temperature, Heat Mass Transfer 40 (2004), 253-259.

DOI: 10.1007/s00231-003-0446-8

[11] A. Al-Sarkhi, E. Abu-Nada, Characteristics of forced convection heat transfer in vertical internally finned tube, Int. Commun. Heat Mass Transfer 32 (2005) 557-564.

DOI: 10.1016/j.icheatmasstransfer.2004.03.015

[12] E. Trefftz, Ein Gegenstück zum Ritzchen Verfahren, in: Proceedings of the 2nd International Congress of Applied Mechanics, Zurich, 1926, pp.131-137.

[13] J.A. Kołodziej, A.P. Zieliński, Boundary collocation techniques and their application in engineering, WITPress, Southampton, Boston, (2009).

[14] J.A. Kołodziej, A. Uściłowska, Trefftz-type procedure for Laplace equation on domains with circular holes, circular inclusions, corners, slits, and symmetry, Comput. Assisted Mech. Eng. Sci. 4 (1997) 507-519.

[15] J.A. Kołodziej, T. Stręk, Analytical approximations of the shape factors for conductive heat flow in circular and regular polygonal cross-sections, Int. J. Heat Mass Transfer 44 (2001) 999-1012.

DOI: 10.1016/s0017-9310(00)00162-9

[16] J.A. Kołodziej, A. Uściłowska, M. Ciałkowski, Semi-analytical approximations of the laminar friction coefficients for flow in conduits with polygonal cross-section, Acta Mech. 158 (2002) 127-144.

DOI: 10.1007/bf01176904

[17] J.A. Kołodziej, A. Fraska, Elastic torsion of bars possessing regular polygon in cross-section using BCM, Compt. Struct. 84 (2005) 78-91.

DOI: 10.1016/j.compstruc.2005.03.015

[18] V.D. Kupradze, M.A. Aleksidze, Approximate method of solving certain boundary-value problems, Soobshch Akad. Nauk Gruz. SSR 30 (1963) 529-536 (in Russian).

[19] V.D. Kupradze, M.A. Aleksidze, The method of fundamental equations for an approximate solution of certain boundary value problems, USSR Comput. Math. Comput. Phys. 4 (1964) 683-715.

DOI: 10.1016/0041-5553(64)90006-0

[20] G. Fairweather, A. Karageorghis, The method of fundamental solutions for elliptic boundary value problems, Adv. Comput. Math. 9 (1998) 69-95.

[21] G. Fairweather, A. Karageorghis, P.A. Martin, The method of fundamental solutions for scattering and radiation problems, Eng. Anal. Bound. Elem. 27 (2003) 759-769.

DOI: 10.1016/s0955-7997(03)00017-1

[22] M.A. Golberg, C.S. Chen, The method of fundamental solutions for potential, Helmholtz and diffusion problems, in: M.A. Golberg (ed. ), Boundary integral methods – numerical and mathematical aspects, Computational Mechanics Publications, Boston, 1998, pp.103-176.

[23] E.J. Kansa, Multiquadrics – A scattered data approximation scheme with applications to computational fluid-dynamics – I surface approximations and partial derivative estimates, Comput. Math. Appl. 19 (1990), 127-145.

DOI: 10.1016/0898-1221(90)90270-t

[24] E.J. Kansa, Multiquadrics – A scattered data approximation scheme with applications to computational fluid-dynamics – II solutions to parabolic, hyperbolic and elliptic partial differential equations, Comput. Math. Appl. 19 (1990), 147-161.

DOI: 10.1016/0898-1221(90)90271-k

[25] Y. -C. Hon, X.Z. Mao, An efficient numerical scheme for Burgers' equation, Appl. Math. Comput. 95 (1998) 155-165.

[26] M. Zerroukat, H. Power, C.S. Chen, A numerical method for heat transfer problems using collocation and radial basis functions, Int. J. Numer. Meth. Eng. 42 (1998) 1263-1278.

DOI: 10.1002/(sici)1097-0207(19980815)42:7<1263::aid-nme431>3.0.co;2-i

[27] W. Chen, L. Ye, H. Sun, Fractional diffusion equations by the Kansa method, Comput. Math. Appl. 59 (2010) 1614-1620.