On a Two-Fluid Inclined Film Flow with Evaporation

References

• F. Abergel and J.L. Bona . A mathematical theory for viscous free-surface flows over a perturbed plane . Arch. Ration. Mech. Anal ., 118 : 71 – 93 , 1992 . http://dx.doi.org/10.1007/BF00375692
   Web of Science ®Google Scholar
• J.P. Burelbach , S.G. Bankhoff and S.H. Davis . Nonlinear stability of evaporating condensing liquid films . J. Fluid Mech ., 195 : 463 – 494 , 1988 . http://dx.doi.org/10.1017/S0022112088002484 .
   Web of Science ®Google Scholar
• C. Cuvelier and J.M. Driessen Thermocapillary free boundaries in crystal growth . J. Fluid Mech 169 : 1 – 26 , 1986 . http://dx.doi.org/10.1017/S0022112086000526
   Web of Science ®Google Scholar
• I.V. Denisova and Š . Nečasova . Oberbeck–Boussinesq approximation for the motion of two incompressible fluids J. Math. Sci ., 159 4 : 436 – 451 , 2009 . http://dx.doi.org/10.1007/s10958-009-9455-6 .
   Google Scholar
• P. Ehrhard and S.H. Davis Non-isothermal spreading of liquid drops on horizontal plates J. Fluid Mech ., 229 : 365 – 388 , 1991 . http://dx.doi.org/10.1017/S0022112091003063 .
   Web of Science ®Google Scholar
• Erunova , I.B. and Rivkind , V.Ya. 1991 . Investigation of the problem of liquid evaporation . Vestnik St. Petersburg Univ. Math. , 24 : 25 – 30 .
   Google Scholar
• M.V. Lagunova . On the solvability of the plane problem of thermocapillary convection . Probl. Mat. Anal. – Lin. and Nonlin. BVPs Spectr. Theory 10 : 33 – 47 , 1986 . (In Russian)
   Google Scholar
• I.N. Larina , V.A. Rykov and E.M. Shakov . Evaporation from a surface and vapor flow through a plane channel into a vacuum . Fluid Dynam ., 31 : 127 – 133 , 1996 . http://dx.doi.org/10.1007/BF02230757
   Google Scholar
• Nazarov , S.A. and Pileckas , K. 1993 . On noncompact free boundary problems for the plane stationary Navier–Stokes equations . J. Reine Angew. Math. , 438 : 103 – 141 .
   Web of Science ®Google Scholar
• P. Neittaanmäki and V.Ya. Rivkind . Mathematical modelling of liquid drops evaporation . In Jyväskylä-St. Petersburg Seminar on Partial Differential Equations and Numerical Methods, Ber. Univ. Jyväskylä Math. Inst ., 56 , pp. 89 – 100 , 1993
   Google Scholar
• Pileckas , K. and Socolowsky , J. 2002 . Analysis of two linearized problems modeling viscous two-layer flows . Math. Nachr. , 245 : 129 – 166 .
   Web of Science ®Google Scholar
• K . Pileckas and J . Socolowsky . Viscous two-fluid flows in perturbed unbounded domains . Math. Nachr 278 5 : 589 – 623 , 2005 . http://dx.doi.org/10.1002/mana.200310260 .
   Google Scholar
• V.V. Pukhnachov . Free boundary problems in the theory of thermo-capillary convection . In A. Bossavit , A. Damlamian and M. Fremond (Eds.), Free boundary problems in the theory of thermo-capillary convection Free Boundary Problems: Applications and Theory, vol. I, volume 121 of Res. Notes Math , pp. 405 – 415 . Pitman Advanced Publishing program , Boston, London, Melbourne , 1985
   Google Scholar
• V.Ya . Rivkind . Numerical solution of coupled Navier–Stokes and Stefan equations . In P . Neittaanmäki Proceedings of the Conference on Numerical Methods for Free Boundary Problems , pp. 57 – 67 . Birkhäuser Verlag , Basel , 1991 .
   Google Scholar
• V.Ya. Rivkind and A.V. Ilin . On a numerical method for solving the nonisothermal flow problem of a liquid layer . Numer. Methods , 15 : 98 – 104 , 1988 . (In Russian)
   Google Scholar
• P.A. Sackinger , R.A. Brown and J.J. Derby . A finite element method for analysis of fluid flow, heat transfer and free interfaces in Czochralski crystal growth . Internat. J. Numer. Methods Fluids , 9 : 453 – 492 , 1989 . http://dx.doi.org/10.1002/fld.1650090406
   Web of Science ®Google Scholar
• G.R. Schmidt , T.J. Chung and A. Nadarajah . Thermocapillary flow with evaporation and condensation at low gravity. Part I: Non-deforming surface, and Part II: Deformable surface . J. Fluid Mech ., 294 : 323 – 347 , 349–366 , 1995 .
   Web of Science ®Google Scholar
• Y. Shen , G.P. Neitzel , D.F. Jankowski and H.D. Mittelmann . Energy stability of thermocapillary convection in a model of the float-zone crystal-growth process . J. Fluid Mech ., 217 : 639 – 660 , 1990 . http://dx.doi.org/10.1017/S002211209000088X .
   Web of Science ®Google Scholar
• J. Socolowsky Existence and uniqueness of the solution to a free boundary value problem with thermocapillary convection in an unbounded domain . Acta Appl. Math ., 37 : 181 – 194 , 1994 . http://dx.doi.org/10.1007/BF00995140 .
   Web of Science ®Google Scholar
• Socolowsky J . On the numerical solution of heat-conducting multiple-layer coating flows . Lithuanian Math. J ., 38 1 : 98 – 115 , 1998 . http://dx.doi.org/10.1007/BF02465548 .
   Google Scholar
• J. Socolowsky . The analysis of a coating flow with evaporation . In P . Neittaanmäki and L . Rivkind (Eds.), Analysis and Approximation of Boundary Value Problems, volume No. A 2/2000 of Reports of the Department of Mathematical Information Technology Series A. Collections , pp. 209 – 225 . University of Jyväskylä , Finland , 2000 .
   Google Scholar
• J. Socolowsky . On the Nusselt solution of a nonisothermal two-fluid inclined film flow . Int. J. Math. Math. Sci. (IJMMS) , p. 8 , 2009 . http://dx.doi.org/10.1155/2009/981983. Electronic Journal
   Google Scholar
• V.A. Solonnikov . On the Stokes equation in domains with nonsmooth boundaries and on a viscous incompressible flow with a free surface . In Nonlinear Partial Diff. Equations and Their Applications , 3 , pp. 340 – 423 . College de France Seminar , 1980
   Google Scholar
• Solonnikov , V.A. 1989 . Solvability of the problem on the effluence of a viscous incompressible fluid into an open bassin . Proc. Math. Inst. Steklov , 179 ( 2 ) : 193 – 226 .
   Google Scholar
• B.W. van de Fliert . A free boundary problem for evaporating layers . Nonlinear Anal ., 47 3 : 1785 – 1796 , 2001 . http://dx.doi.org/10.1016/S0362-546X(01)00310-8
   Google Scholar