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Variation of parameters method for a three-dimensional problem of condensation film on an inclined rotating disk

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Języki publikacji
EN
Abstrakty
EN
In this paper, the steady three-dimensional problem of condensation film on an inclined rotating disk is considered. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equations system by a similarity transform. The equation system is solved by the variation of parameters method (VPM) which is rather used to solve nonhomogeneous linear differential equations but can also be used to solve nonlinear differential equations. This method has not previously been used to solve a nonlinear condensation problem. The dimensionless velocity and temperature profiles are shown, and the influence of Prandtl number and rotation ratio on the flow field and the Nusselt number are discussed in detail. In order to assess the accuracy of the solutions obtained by this method, the problem is also solved numerically using the Matlab bvp4c solver. The validity of our solutions is verified by the numerical results.
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EN
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15--28
Opis fizyczny
Bibliogr. 21 poz., rys., tab
Twórcy
autor
• Faculty of Engineering, Ataturk University Erzurum, Turkey
autor
• Faculty of Engineering, Ataturk University Erzurum, Turkey
Bibliografia
• [1] Nusselt, W. (1916). Die Oberffachenkondensation des Wasserdampfes. Z Vereines Deutsch Ing., 60, 541-546, 569-575.
• [2] Koh, J.C.Y., Sparrow, E.M., & Hartnett, J.P. (1961). The two phase boundary layer in laminar film condensation. Int. J. Heat and Mass Transf., 2, 69-82.
• [3] Sparrow, E,M., & Gregg, J.L. (1959). A boundary layer treatment of laminer film condensation. J. Heat Transfer, 81, 13-18.
• [4] Von Karman, T. (1921). Uber laminare und turbulente reibung. Zeitschrift fur Angewandte Mathematik und Mechanik, 1, 233-52.
• [5] Beckett, P.M., Hudson, P.C., & Poots, G. (1963). Laminar film condensation due to a rotating disk. Journal of Engineering Mathematics, 7, 63-73.
• [6] Chary, S.P., & Sarma, P.K. (1976). Condensation on a rotating disk with constant axial suction. Journal of Heat Transfer, 98, 682-84.
• [7] Wang, C.Y. (2007). Condensation film on an inclined rotating disk. App. Math. Modelling, 31, 1582-1593.
• [8] Rashidi, M.M., & Dinarvand, S. (2009). Purely analytic approximate solutions for steady threedimensional problem of condensation film on inclined rotating disk by homotopy analysis method. Nonlinear Analysis:Real World Applications, 10, 2346-2356.
• [9] Sheikholeslami, M., Ashorynejad, H.R., Ganji, D.D., & Yıldırım, A. (2012). Homotopy perturbation method for three-dimensional problem of condensation film on inclined rotating disk. Scientia Iranica B, 19, 437-442.
• [10] Rashidi, M.M., & Mohimanianpour, S.A. (2010). Analytic solution of steady three-dimensional problem of condensation film on inclined rotating disk by differential transform method. Mathematical Problems in Engineering, 1-15.
• [11] Hassan H.N., & Rashidi, M.M., (2013). Analytical solution for three-dimensional steady flow of condensation film on inclined rotating disk by optimal homotopy analysis method. Walailak Journal of Science and Technology, 10, 479-498.
• [12] Ullah H., Islami S., & Fiza M., (2016) Analytical solution for three-dimensional problem of condensation film on inclined rotating disk by extended asymptotic optimal homotopy method. Iran J. Sci. Technol. Trans. Mech. Eng. 40, 265-273.
• [13] Berkan, S., Hoseini, S.R., & Ganji D.D. (2017) Analytical investigation of steady three dimensional problem of condensation film on inclined rotating disk by Akbari-Ganji's method. Propulsion and Power Research, 6, 277-284.
• [14] Mohyud-Din, S.T., Noor, M.A., & Waheed, A. (2010). Variation of parameters method for initial and boundary value problems. World Applied Sciences Journal, 11, 622-39.
• [15] Rahmatullah., & Mohyud-Din, S.T. (2013). Variation of parameters method for nonlinear diffusion equations. International Journal of Modern Applied Physics, 3, 48-56.
• [16] Keckic, J. (1976). Additions to Kamkes treatise VII: variation of parameters for nonlinear second order differential equations. Publikacije Elektrotehnickog fakulteta, Serija Matematika i fizika, 544, 31-36.
• [17] Bogdanova, M.P. (1962). On a generalization of the method of variation of parameters. Doklady Akademii nauk BSSR, 6, 285-87.
• [18] Moore, T.J. (2014). Application of variation of parameters to solve nonlinear multimode heat transfer problems. Ph. D Thesis, Brigham Young University.
• [19] Moore, T.J., & Jones, M.R. (2014). Analysis of the conduction-radiation problem in absorbing, emitting, non-gray planar media using an exact method. Int. J. Heat and Mass Transf., 73, 804-809.
• [20] Moore, T.J., & Jones, M.R. (2015). Solving nonlinear heat transfer problems using variation of parameters method. Int. J. Therm. Sci., 93, 29-35.
• [21] Dawkins, P. (2011). Differential Equations (Vol. 503). Lamar University Press
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia