# THIN FILM FLOW OVER AN UNSTEADY STRETCHING SHEET WITH THERMOCAPILLARITY IN PRESENCE OF MAGNETIC FIELD

## Main Article Content

## Abstract

An analysis is carried out to study the effects of thermocapillarity on thin film flow over an unsteady stretching sheet in presence of uniform transverse magnetic field and internal heat source/sink. Using a similarity transformation the governing time dependent boundary layer equations are reduced to a set of coupled ordinary differential equations and then solved numerically for some representative values of non-dimensional parameters using Nachtsheim and Swigert shooting iteration technique together with Runge-Kutta sixth-order integration scheme. It is observed that the thermocapillary action reduces the rate of heat transfer at the surface while dealing with conducting fluid in presence of magnetic field.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2120>. Date accessed: 21 aug. 2017. doi: https://doi.org/10.2298/TSCI150221141D.

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Accepted 2017-03-13

Published 2017-03-13

## References

[2] Schlichting, H., Boundary-layer theory. New York: McGraw-Hill. 1955.

[3] Afzal, N., Varshney, I.S., The cooling of a low heat resistance stretching sheet moving through a fluid. Warme- und Stoffubertragung. 14 (1980), 2, pp. 289-293

[4] Ali, M.E., Heat transfer characteristics of a continuous stretching surface. Warme- und Stoffubertragung. 29(1994), 4, pp. 227-234

[5] Ishak, A., et al., Boundary layer flow and heat transfer over an unsteady stretching vertical surface. Meccanica. 44 (2009), 4, pp. 369-375

[6] Mabood, F., Khan, W.A., Ismail, A.I.Md., MHD stagnation point flow and heat transfer impinging on stretching sheet with chemical reaction and transpiration. Chemical Engineering Journal 273 (2015), 3, pp. 430–437.

[7] Mabood, F., Khan, W.A., Ismail, A.I.Md., MHD boundary layer flow and heat transfer of nanofluids over a nonlinear stretching sheet: A numerical Study. Journal of Magnetism and Magnetic Materials 374 (2015), 11, pp. 569–576.

[8] Wang, C.Y., Liquid film on an unsteady stretching surface. Quarterly of Applied Mathematics. 48 (1990), 3, pp. 601–610

[9] Roberts, S.M. , Shipman, J.S., Two Point Boundary Value Problems: Shooting Methods. New York: Elsevier. 1972.

[10] Andersson, H.I., et al., Heat transfer in a liquid film on an unsteady stretching surface. International Journal of Heat and Mass Transfer. 43 (2000), 1, pp. 69–74

[11] Wang, C., Analytic solutions for a liquid film on an unsteady stretching surface. Heat and Mass Transfer. 42 (2006), 8, pp. 759-766

[12] Aziz, R.C., et al., Thin film flow and heat transfer on an unsteady stretching sheet with internal heating. Meccanica. 46 (2011), 2, pp. 349-357

[13] Liu, I.C., Andersson, H.I., Heat transfer in a liquid film on an unsteady stretching sheet. International Journal of Thermal Sciences, 47 (2008), 6, pp. 766–772

[14] Usha, R., Sridharan, R., On the motion of a liquid film on an unsteady stretching surface. ASME Fluids Engineering. 150 (1993), 1, pp. 43-48

[15] Chen, C.H., Heat transfer in a power-law fluid film over an unsteady stretching sheet. Heat and Mass Transfer. 39 (2003), 8-9, pp. 791–796

[16] Chen, C.H., Marangoni effects on forced convection of power law liquids in a thin film over an unsteady stretching sheet. Physics Letters A. 370 (2007), 1, pp.51-57

[17] Dandapat, B.S., et al., Thermocapillarity in a liquid film on an unsteady stretching surface. International Journal of Heat and Mass Transfer 46 (2003), 16, pp. 3009-3015

[18] Dandapat, B.S., et al., The effects of variable fluid properties and thermocapillarity on the flow of a thin film on an unsteady stretching sheet. International Journal of Heat and Mass Transfer. 50 (2007), 5-6, pp. 991-996

[19] Abel, M.S., et al., Heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation in presence of external magnetic field. Applied Mathematical Modelling. 33 (2009), 8, pp. 3430-3441

[20] Noor, N.F.M., et al., MHD flow and heat transfer in a thin liquid film on an unsteady stretching by the homotopy analysis method. International Journal for Numerical Methods in Fluids. 63 (2010), 3, pp. 357–373

[21] Noor, N.F.M., Hashim, I., Thermocapillarity and magnetic field effects in a thin liquid on an unsteady stretching surface. International Journal of Heat and Mass Transfer. 53 (2010), 9-10, pp. 2044-2051

[22] Dandapat, B.S., Singh, S.K., Thin film flow over a heated nonlinear stretching sheet in presence of uniform transverse magnetic field. International Communications in Heat and mass Transfer. 38 (2011), 3, pp. 324-328

[23] Das K, Zheng L., Melting effects on the stagnation point flow of a Jeffrey fluid in the presence of magnetic field, Heat Transfer Research. 44 (2013), 6, pp. 493–506

[24] Das K., A mathematical model on magnetohydrodynamic slip flow and heat transfer over a non-linear stretching sheet, Thermal Science, 17 (2013), S2, pp. S475-S488

[25] Das K., Influence of chemical reaction and viscous dissipation on MHD mixed convection flow. Journal of Mechanical Science and Technology. 28 (2014), 5, pp.1881-1885

[26] Das K, Jana S, Kundu P.K., Thermophoretic MHD slip flow over a permeable surface with variable fluid properties, Alexandria Engineering Journal. 54 (2015), 1, pp. 35–44