We studied the thin film flow for lifting and drainage problems using an incompressible, nonisothermal modified second grade fluid. We developed nonlinear differential equations from momentum and energy equations, respectively. Series solutions for both lifting and drainage problems are obtained. Expressions for the velocity profile, temperature distribution, volume flux, average film velocity, and shear stress on cylinder for both cases are obtained. Effects of different parameters on the flow problems are presented graphically.
References
A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Some exact solutions for the thin film flow of a PTT fluid,” Physics Letters A, vol. 356, no. 4-5, pp. 353–356, 2006. 1160.76317 10.1016/j.physleta.2006.03.071 A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Some exact solutions for the thin film flow of a PTT fluid,” Physics Letters A, vol. 356, no. 4-5, pp. 353–356, 2006. 1160.76317 10.1016/j.physleta.2006.03.071
A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder,” Physics Letters A, vol. 352, no. 4-5, pp. 404–410, 2006. 1187.76622 10.1016/j.physleta.2005.12.033 A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder,” Physics Letters A, vol. 352, no. 4-5, pp. 404–410, 2006. 1187.76622 10.1016/j.physleta.2005.12.033
A. M. Siddiqui, M. Ahmed, and Q. K. Ghori, “Thin film flow of non-Newtonian fluids on a moving belt,” Chaos, Solitons & Fractals, vol. 33, no. 3, pp. 1006–1016, 2007. MR2319627 1129.76009 A. M. Siddiqui, M. Ahmed, and Q. K. Ghori, “Thin film flow of non-Newtonian fluids on a moving belt,” Chaos, Solitons & Fractals, vol. 33, no. 3, pp. 1006–1016, 2007. MR2319627 1129.76009
A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane,” Chaos, Solitons & Fractals, vol. 35, no. 1, pp. 140–147, 2008. MR2355243 1135.76006 A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane,” Chaos, Solitons & Fractals, vol. 35, no. 1, pp. 140–147, 2008. MR2355243 1135.76006
S. Nadeem and M. Awais, “Thin film ow of an unsteady shrinking sheet through porous medium with variable viscosity,” Physics Letters A, vol. 372, pp. 4965–4972, 2008. 1221.76233 10.1016/j.physleta.2008.05.048 S. Nadeem and M. Awais, “Thin film ow of an unsteady shrinking sheet through porous medium with variable viscosity,” Physics Letters A, vol. 372, pp. 4965–4972, 2008. 1221.76233 10.1016/j.physleta.2008.05.048
M. Sajid, N. Ali, and T. Hayat, “On exact solutions for thin film flows of a micropolar fluid,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 451–461, 2009. MR2458822 1221.76038 10.1016/j.cnsns.2007.09.003 M. Sajid, N. Ali, and T. Hayat, “On exact solutions for thin film flows of a micropolar fluid,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 451–461, 2009. MR2458822 1221.76038 10.1016/j.cnsns.2007.09.003
V. Marinca, N. Herisanu, and I. Nemes, “Optimal homotopy asymptotic method with application to thin film flow,” Central European Journal of Physics, vol. 6, no. 3, pp. 648–653, 2008. V. Marinca, N. Herisanu, and I. Nemes, “Optimal homotopy asymptotic method with application to thin film flow,” Central European Journal of Physics, vol. 6, no. 3, pp. 648–653, 2008.
J. E. Dunn and K. R. Rajagopal, “Fluids of differential type: critical review and thermodynamic analysis,” International Journal of Engineering Science, vol. 33, no. 5, pp. 689–729, 1995. MR1321925 10.1016/0020-7225(94)00078-X 0899.76062 J. E. Dunn and K. R. Rajagopal, “Fluids of differential type: critical review and thermodynamic analysis,” International Journal of Engineering Science, vol. 33, no. 5, pp. 689–729, 1995. MR1321925 10.1016/0020-7225(94)00078-X 0899.76062
C. Truesdell and W. Noll, “The non-linear field theories of mechanics,” in Handbuch der Physik, HI/3, Springer, Berlin, Germany, 1965. MR0193816 0779.73004 C. Truesdell and W. Noll, “The non-linear field theories of mechanics,” in Handbuch der Physik, HI/3, Springer, Berlin, Germany, 1965. MR0193816 0779.73004
M. Khan, S. Nadeem, T. Hayat, and A. M. Siddiqui, “Unsteady motions of a generalized second grade fluid,” Mathematical and Computer Modelling, vol. 41, no. 6-7, pp. 629–637, 2005. MR2138588 1080.76007 10.1016/j.mcm.2005.01.029 M. Khan, S. Nadeem, T. Hayat, and A. M. Siddiqui, “Unsteady motions of a generalized second grade fluid,” Mathematical and Computer Modelling, vol. 41, no. 6-7, pp. 629–637, 2005. MR2138588 1080.76007 10.1016/j.mcm.2005.01.029
T. Hayat and M. Khan, “Homotopy solutions for a generalized second-grade fluid past a porous plate,” Nonlinear Dynamics, vol. 42, no. 4, pp. 395–405, 2005. MR2190665 1094.76005 10.1007/s11071-005-7346-z T. Hayat and M. Khan, “Homotopy solutions for a generalized second-grade fluid past a porous plate,” Nonlinear Dynamics, vol. 42, no. 4, pp. 395–405, 2005. MR2190665 1094.76005 10.1007/s11071-005-7346-z
M. Khan, Hashim, and C. Feteacu, “On the exact solutions for oscillating ow of an MHD second grade uid through porous media,” Special Topics and Reviews in Porous Media, vol. 3, no. 1, pp. 13–22, 2012. M. Khan, Hashim, and C. Feteacu, “On the exact solutions for oscillating ow of an MHD second grade uid through porous media,” Special Topics and Reviews in Porous Media, vol. 3, no. 1, pp. 13–22, 2012.
M. Khan, T. Safdar, and M. Azram, “Starting solution for some oscillatory rotating ows of MHD second grade uid through porous space,” Journal of Porous Media, vol. 14, no. 8, pp. 723–734, 2011. M. Khan, T. Safdar, and M. Azram, “Starting solution for some oscillatory rotating ows of MHD second grade uid through porous space,” Journal of Porous Media, vol. 14, no. 8, pp. 723–734, 2011.
H. I. Andersson and D. Y. Shang, “An extended study of the hydrodynamics of gravity-driven film flow of power-law fluids,” Fluid Dynamics Research, vol. 22, pp. 345–357, 1998. H. I. Andersson and D. Y. Shang, “An extended study of the hydrodynamics of gravity-driven film flow of power-law fluids,” Fluid Dynamics Research, vol. 22, pp. 345–357, 1998.
D. Y. Shang and H. I. Andersson, “Heat transfer in gravity-driven film flow of power-law fluids,” International Journal of Heat and Mass Transfer, vol. 42, pp. 2085–2099, 1999. 0955.76007 10.1016/S0017-9310(98)00301-9 D. Y. Shang and H. I. Andersson, “Heat transfer in gravity-driven film flow of power-law fluids,” International Journal of Heat and Mass Transfer, vol. 42, pp. 2085–2099, 1999. 0955.76007 10.1016/S0017-9310(98)00301-9
N. V. Lavrik, C. A. Tipple, M. J. Sepaniak, and D. Datskos, “Gold nano-structures for transduction of biomolecular interactions into micrometer scale movements,” Biomedical Microdevices, vol. 3, no. 1, pp. 35–44, 2001. N. V. Lavrik, C. A. Tipple, M. J. Sepaniak, and D. Datskos, “Gold nano-structures for transduction of biomolecular interactions into micrometer scale movements,” Biomedical Microdevices, vol. 3, no. 1, pp. 35–44, 2001.
M. Massoudi and T. X. Phuoc, “Flow of a generalized second grade non-Newtonian fluid with variable viscosity,” Continuum Mechanics and Thermodynamics, vol. 16, no. 6, pp. 529–538, 2004. MR2099279 1158.76304 10.1007/s00161-004-0178-0 M. Massoudi and T. X. Phuoc, “Flow of a generalized second grade non-Newtonian fluid with variable viscosity,” Continuum Mechanics and Thermodynamics, vol. 16, no. 6, pp. 529–538, 2004. MR2099279 1158.76304 10.1007/s00161-004-0178-0
C. Wang and I. Pop, “Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method,” Journal of Non-Newtonian Fluid Mechanics, vol. 138, pp. 161–172, 2006. \endinput 1195.76132 10.1016/j.jnnfm.2006.05.011 C. Wang and I. Pop, “Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method,” Journal of Non-Newtonian Fluid Mechanics, vol. 138, pp. 161–172, 2006. \endinput 1195.76132 10.1016/j.jnnfm.2006.05.011
