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Hermite-Padé approach to thermal radiation effect on inherent irreversibility in a variable viscosity channel flow. (English) Zbl 1189.76078
Summary: This present work examines the effect of thermal radiation on inherent irreversibility in the flow of a variable viscosity optically thin fluid through a channel with isothermal walls. First and Second Laws of thermodynamics are employed in order to analyze the problem. The simplified governing non-linear equations are solved analytically using a perturbation method coupled with a special type of Hermite-Padé semi-analytical technique. Expressions for dimensionless velocity and temperature, thermal criticality conditions and entropy generation number are obtained. Both numerical and graphical results are presented and discussed quantitatively with respect to various parameters embedded in the problem.

MSC:
76B10Jets and cavities, cavitation, free-streamline theory, water-entry problems, etc.
65N99Numerical methods for BVP of PDE
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References:
[1] Arpaci, V. S.; Selamet, A.; Kao, S. H.: Introduction to heat transfer, (2000)
[2] Makinde, O. D.: Entropy-generation analysis for variable-viscosity channel flow with non-uniform wall temperature, Appl. energy 85, 384-393 (2008)
[3] Sahin, A. Z.: Effect of variable viscosity on the entropy generation and pumping power in a laminar fluid flow through a duct subjected to constant heat flux, Heat mass transfer 35, 499 (1999)
[4] Chang, L. C.; Yang, K. T.; Lloyd, J. R.: Radiation--natural convection interaction in two-dimensional complex enclosure, J. heat transfer 105, 89-95 (1983)
[5] Lauriat, G.: Combined radiation--convection in gray fluids enclosed in vertical cavities, J. heat transfer 104, 609-615 (1982)
[6] Cogley, A. C. L.; Vincenti, W. G.; Gilles, E. S.: Differential approximation for radiative heat transfer in a nonlinear equations-grey gas near equilibrium, Am. inst. Aeronaut. astronaut. J. 6, 551-553 (1968)
[7] Akiyama, M.; Chong, Q. P.: Numerical analysis of natural convection with surface radiation in a square enclosure, Numer. heat transfer part A 32, 419-433 (1997)
[8] Chawla, T. C.; Chan, S. H.: Combined radiation and convection in thermally developing Poiseuille flow with scattering, J. heat transfer 102, 297-302 (1980)
[9] Tabanfar, S.; Modest, M. F.: Combined radiation and convection in absorbing, emitting, nongray gas--particulate tube flow, J. heat transfer 109, 478-484 (1987)
[10] Bejan, A.: Entropy generation minimization, (1996) · Zbl 0864.76001
[11] Bejan, A.: A study of entropy generation in fundamental convective heat transfer, J. heat transfer 101, 718-725 (1979)
[12] Bejan, A.: Second-law analysis in heat transfer and thermal design, Adv. heat transfer 15, 1-58 (1982)
[13] Bejan, A.; Tsatsaronis, G.; Moran, M.: Thermal design and optimization, (1996) · Zbl 0883.76001
[14] Arpaci, V. S.: Radiative entropy production--heat lost to entropy, Adv. heat transfer 21, 239-276 (1991)
[15] Makinde, O. D.: Irreversibility analysis for gravity driven non-Newtonian liquid film along an inclined isothermal plate, Phys. scr. 74, 642-645 (2006) · Zbl 05651719
[16] Vainberg, M. M.; Trenogin, V. A.: Theory of branching of solutions of nonlinear equations, (1974) · Zbl 0274.47033
[17] Makinde, O. D.: Thermal ignition in a reactive viscous flow through a channel filled with a porous medium, ASME, J. Heat transfer 128, 601-604 (2006)
[18] Tourigny, Y.; Drazin, P. G.: The asymptotic behaviour of algebraic approximants, Proc. R. Soc. lond. A 456, 1117-1137 (2000) · Zbl 0971.41007 · doi:10.1098/rspa.2000.0554
[19] He, J. H.: Variational iteration method, A kind of nonlinear analytical technique, some examples, Int. J. Nonlinear mech. 34, No. 4, 699-708 (1999) · Zbl 05137891
[20] He, J. H.: Variational iteration method--some recent results and new interpretations, J. comp. Appl. math. 207, 3-17 (2007) · Zbl 1119.65049 · doi:10.1016/j.cam.2006.07.009
[21] He, J. H.: Homotopy perturbation method -- a new nonlinear analytical technique, Appl. math. Comput. 135, 73-79 (2000) · Zbl 1030.34013 · doi:10.1016/S0096-3003(01)00312-5
[22] Adomian, G.: Solving frontier problems of physics: the decomposition method, (1994) · Zbl 0802.65122
[23] http://maplesoft.com/products/maple/technical.aspx