Effects of nonlinear velocity slip and temperature jump on pseudo-plastic power-law fluid over moving permeable surface in presence of magnetic field

doi:10.1007/s10483-017-2178-8

Abstract

Abstract:

Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions, the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud (Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228-1237 (2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.

Key words: variable mass, nonholonomic system, Gibbs-Appell’s equation, integral variational principle, quasi-velocity, magnetohydrodynamic (MHD), power-law fluid, slip velocity, temperature jump, varying thermal conductivity

2010 MSC Number:

O357.1

Xinhui SI, Haozhe LI, Yanan SHEN, Liancun ZHENG. Effects of nonlinear velocity slip and temperature jump on pseudo-plastic power-law fluid over moving permeable surface in presence of magnetic field. Applied Mathematics and Mechanics (English Edition), 2017, 38(3): 333-342.

TrendMD

References

[1] Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228-1237(2011)
[2] Soundalgekar, V. M. and Ramana Murty, T. V. Heat transfer past a continuous moving plate with variable temperature. Warme-und Stoffubertragung, 14, 91-93(1980)
[3] Howell, T. G., Jengand, D. R., and De Witt. K. J. Momentum and heat transfer on a continuous moving surface in a power-law fluid. International Journal of Heat and Mass Transfer, 40, 1853-1861(1997)
[4] Kumari, M. and Nath, G. MHD boundary-layer flow of a non-Newtonian fluid over a continuously moving surface with a parallel free stream. Acta Mechanica, 146, 139-150(2001)
[5] Salama, F. A. Effect of thermal conductivity on heat transfer for a power-law non-Newtonian fluid over a continuous stretched surface with various injection parameters. Applied Mathematics and Mechanics (English Edition), 31, 963-968(2010) DOI 10.1007/s10483-010-1331-z
[6] Djordje, S., Bozidar, D., and Vujanovic, D. A variational principle for the two-dimensional boundary-layer flow of non-Newtonian power-law fluids. Rheologica Acta, 14, 881-890(1975)
[7] Huang, M. J. and Lin, B. L. Forced convective flow over a flat plate in non-Newtonian power-law fluids. Warme-und Stoffiibertragung, 27, 399-404(1992)
[8] Mahmoud, M. A. A. and Megahed, A. M. Effects of viscous dissipation and heat generation (absorption) in a thermal boundary layer of a non-Newtonian fluid over a continuously moving permeable flat plate. Journal of Applied Mechanics and Technical Physics, 5, 819-825(2009)
[9] Sui, J. Z., Zheng, L. C., Zhang, X. X., and Chen, G. Mixed convection heat transfer in power-law fluids over a moving conveyor along an inclined plate. International Journal of Heat and Mass Transfer, 85, 1023-1033(2015)
[10] Afify, A. A., Uddin, M. J., and Ferdows, M. Scaling group transformation for MHD boundary layer flow over permeable stretching sheet in presence of slip flow with Newtonian heating effects. Applied Mathematics and Mechanics (English Edition), 35, 1375-1386(2014) DOI 10.1007/s10483-014-1873-7
[11] Zhu, J. L., Zheng, C., and Zhang, Z. G. Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet. Applied Mathematics and Mechanics (English Edition), 31, 439-448(2010) DOI 10.1007/s10483-010-1331-z
[12] Shojaeian, M. and Kosar, A. Convective heat transfer and entropy generation analysis on Newtonian and non-Newtonian fluid flows between parallel-plates under slip boundary conditions. International Journal of Heat and Mass Transfer, 70, 664-673(2014)
[13] Roux, C. L. Existence and uniqueness of the flow of second-grade fluids with slip boundary conditions. Archive for Rational Mechanics and Analysis, 148, 309-356(1999)
[14] Hayata, T., Imtiaza, M., Alsaedib, A., and Kutbi, M. A. MHD three-dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation. Journal of Magnetism and Magnetic Materials, 396, 31-37(2015)
[15] Zheng, L. C., Niu, J. J., Zhang, X. X., and Gao, Y. T. MHD flow and heat transfer over a porous shrinking surface with velocity slip and temperature jump. Mathematical and Computer Modelling, 56, 133-144(2012)
[16] Khaleda, A. R. A. and Vafai, K. The effect of the slip condition on Stokes and Couette flows due to an oscillating wall:exact solutions. International Journal of Non-Linear Mechanics, 39, 795-809(2004)
[17] Zahmatkesh, I., Alishahi, M. M., and Emdad, H. New velocity-slip and temperature-jump boundary conditions for Navier-Stokes computation of gas mixture flows in microgeometries. Mechanics Research Communications, 38, 417-424(2011)
[18] Nejad, M. M., Javaherdeh, K., and Moslemi, M. MHD mixed convection flow of power-law nonNewtonian fluids over an isothermal vertical wavy plate. Journal of Magnetism and Magnetic Materials, 389, 66-72(2015)
[19] Rajput, G. R., Krishna Prasad, J. S. V. R., and Timol, M. G. Similarity flow solution of MHD boundary layer model for non-Newtonian power-law fluids over a continuous moving surface. General Mathematics Notes, 24, 97-102(2014)
[20] Naikoti, K. and Borra, S. R. Quasi-linearization approach to MHD effects on boundary layer flow of power-law fluids past a semi-infinite flat plate with thermal dispersion. International Journal of Non-Linear Mechanics, 11, 301-311(2011)
[21] Lin, Y. H., Zheng, L. C., and Zhang, X. X. MHD Marangoni boundary layer flow and heat transfer of pseudo-plastic nanofluids over a porous medium with a modified model. Mechanics of Time-Dependent Materials, 19, 519-536(2015)
[22] Shampine L. F., Kierzenka, J., and Reichelt, M. W. Solving boundary value problems for ordinary diffierential equations in MATLAB with bvp4c. Tutorial Notes, 2000, 1-27(2000)
[23] Corless, R. M. and Fillion, N. Numerical Solutions of Boundary Value Problems, Springer, New York, 695-727(2013)
[24] Auzinger, W., Kneisl, G., Koch, O., and Weinmuller, E. A collocation code for singular boundary value problems in ordinary differential equations. Numerical Algorithms, 33, 27-39(2003)