Exact solutions for unsteady free convection flow of Casson fluid over an oscillating vertical plate with constant wall temperature. (English) Zbl 1356.35179

Khalid, Asma; Khan, Ilyas; Shafie, Sharidan

Abstr. Appl. Anal. 2015, Article ID 946350, 8 p. (2015).

Summary: The unsteady free flow of a Casson fluid past an oscillating vertical plate with constant wall temperature has been studied. The Casson fluid model is used to distinguish the non-Newtonian fluid behaviour. The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. Laplace transform method is used to find the exact solutions of these equations. Expressions for shear stress in terms of skin friction and the rate of heat transfer in terms of Nusselt number are also obtained. Numerical results of velocity and temperature profiles with various values of embedded flow parameters are shown graphically and their effects are discussed in detail.

MSC:

35Q35	PDEs in connection with fluid mechanics
76A05	Non-Newtonian fluids
76T20	Suspensions
35C05	Solutions to PDEs in closed form
44A10	Laplace transform
76R10	Free convection
34A30	Linear ordinary differential equations and systems

Keywords:

Casson fluid; non-Newtonian fluid; linear ordinary differential equations; Laplace transform; Nusselt number

References:

[1]	Sajid, M.; Pop, I.; Hayat, T., Fully developed mixed convection flow of a viscoelastic fluid between permeable parallel vertical plates, Computers & Mathematics with Applications, 59, 1, 493-498 (2010) · Zbl 1189.76058
[2]	Khan, I.; Fakhar, K.; Sharidan, S., Magnetohydrodynamic rotating flow of a generalized Burgers’ fluid in a porous medium with Hall current, Transport in Porous Media, 91, 1, 49-58 (2012)
[3]	Anwar, M. I.; Khan, I.; Shafie, S.; Salleh, M. Z., Conjugate effects of heat and mass transfer of nano fluids over a non-linear stretching sheet, International Journal of Physical Sciences, 7, 26, 4081-4092 (2012)
[4]	Khan, M.; Nadeem, S.; Hayat, T.; Siddiqui, A. M., Unsteady motions of a generalized second-grade fluid, Mathematical and Computer Modelling, 41, 6-7, 629-637 (2005) · Zbl 1080.76007
[5]	Ali, N.; Hayat, T.; Asghar, S., Peristaltic flow of a Maxwell fluid in a channel with compliant walls, Chaos, Solitons and Fractals, 39, 1, 407-416 (2009) · Zbl 1197.76017
[6]	Khan, I.; Fakhar, K.; Anwar, M., Hydromagnetic rotating flows of an oldroyd-B fluid in a porous medium, Special Topics and Reviews in Porous Media, 3, 1, 89-95 (2012)
[7]	Hayat, T.; Awais, M.; Alsaedi, A., Newtonian heating and magnetohydrodynamic effects in flow of a Jeffery fluid over a radially stretching surface, International Journal of Physical Sciences, 7, 2838-2844 (2012)
[8]	Ali, F.; Khan, I.; Ul Haq, S.; Shafie, S., Influence of thermal radiation on unsteady free convection MHD flow of Brinkman type fluid in a porous medium with Newtonian heating, Mathematical Problems in Engineering, 2013 (2013) · Zbl 1299.76297
[9]	Fetecau, C.; Vieru, D.; Fetecau, C., A note on the second problem of Stokes for Newtonian fluids, International Journal of Non-Linear Mechanics, 43, 5, 451-457 (2008) · Zbl 1203.76011
[10]	Erdogan, M. E., A note on an unsteady flow of a viscous fluid due to an oscillating plane wall, International Journal of Non-Linear Mechanics, 35, 1, 1-6 (2000) · Zbl 1006.76028
[11]	Khan, W. A.; Aziz, A., Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux, International Journal of Thermal Sciences, 50, 7, 1207-1214 (2011)
[12]	Fetecau, C.; Rana, M., General solutions for the unsteady flow of second-grade fluids over an infinite plate that applies arbitrary shear to the fluid, Zeitschrift für Naturforschung A: A Journal of Physical Science, 66, 12, 753-759 (2011)
[13]	Casson, N., A flow equation for the pigment oil suspensions of the printing ink type, Rheology of Disperse Systems, 84-102 (1959), New York, NY, USA: Pergamon, New York, NY, USA
[14]	Hayat, T.; Awais, M.; Sajid, M., Mass transfer effects on the unsteady flow of UCM fluid over a stretching sheet, International Journal of Modern Physics B, 25, 21, 2863-2878 (2011) · Zbl 1333.76011
[15]	Dash, R. K.; Mehta, K. N.; Jayaraman, G., Casson fluid flow in a pipe filled with a homogeneous porous medium, International Journal of Engineering Science, 34, 10, 1145-1156 (1996) · Zbl 0900.76022
[16]	Fung, Y. C., Biodynamics Circulation (1984), New York, NY, USA: Springer, New York, NY, USA
[17]	Fredrickson, A. G., Principles and Applications of Rheology (1964), Englewood Cliffs, NJ, USA: Prentice-Hall, Englewood Cliffs, NJ, USA
[18]	Boyd, J.; Buick, J. M.; Green, S., Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method, Physics of Fluids, 19, 9 (2007) · Zbl 1182.76081
[19]	Mernone, A. V.; Mazumdar, J. N.; Lucas, S. K., A mathematical study of peristaltic transport of a Casson fluid, Mathematical and Computer Modelling, 35, 7-8, 895-912 (2002) · Zbl 1022.76058
[20]	Mustafa, M.; Hayat, T.; Pop, I.; Aziz, A., Unsteady boundary layer flow of a Casson fluid due to an impulsively started moving flat plate, Heat Transfer—Asian Research, 40, 6, 563-576 (2011)
[21]	Hayat, T.; Shehzad, S. A.; Alsaedi, A.; Alhothuali, M. S., Mixed convection stagnation point flow of casson fluid with convective boundary conditions, Chinese Physics Letters, 29, 11 (2012) · Zbl 1266.76006
[22]	Mukhopadhyay, S., Effects of thermal radiation on Casson fluid flow and heat transfer over an unsteady stretching surface subjected to suction/blowing, Chinese Physics B, 22, 11 (2013)
[23]	Mukhopadhyay, S.; De, P. R.; Bhattacharyya, K.; Layek, G. C., Casson fluid flow over an unsteady stretching surface, Ain Shams Engineering Journal, 4, 4, 933-938 (2013)
[24]	Bhattacharyya, K., Boundary layer stagnation-point flow of casson fluid and heat transfer towards a shrinking/stretching sheet, Frontiers in Heat and Mass Transfer, 4, 2 (2013)
[25]	Pramanik, S., Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation, Ain Shams Engineering Journal, 5, 1, 205-212 (2014)
[26]	Kim, S., Study of non-Newtonian viscosity and yield stress of blood in a scanning capillary-tube rheometer (A) [Ph.D. thesis] (2002), Mechanical Engineering and Mechanics