Sains Malaysiana 47(5)(2018): 1069–1076

http://dx.doi.org/10.17576/jsm-2018-4705-25

 

Effects of Thermal Radiation on Mixed Convection Flow over a Permeable Vertical Shrinking Flat Plate in an Oldroyd-B Fluid

(Kesan Sinaran Terma pada Aliran Olakan Campuran terhadap Plat Rata Telap Menegak Mengecut dalam Bendalir Oldroyd-B)

 

KOHILAVANI NAGANTHRAN1*, ROSLINDA NAZAR1 & IOAN POP2

 

1School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

 

2Department of Mathematics, Babeş-Bolyai University, R-400084 Cluj-Napoca, Romania

 

Diserahkan: 14 September 2017/Diterima: 12 Disember 2017

 

 

ABSTRACT

This study offers the numerical solutions for the problem of mixed convection stagnation-point flow along a permeable vertical flat plate in an Oldroyd-B fluid. The present investigation considers the effects of thermal radiation and heat generation/absorption in the fluid flow. The similarity transformation simplifies the complex model and the bvp4c function generates the numerical solutions according to the variations in the governing parameters. A higher degree of shrinking hastens flow separations. The dual solutions are visible in the range of buoyancy opposing flow. The results from this study may be useful for the scientist to understand the behaviour of the dilute polymer solutions in the industrial applications, for example, the drag reduction in pipe flows.

 

Keywords: Mixed convection; Oldroyd-B fluid; stability analysis; shrinking plate; stagnation-point flow

 

ABSTRAK

Kajian ini memberikan penyelesaian berangka bagi masalah aliran titik genangan olakan campuran sepanjang plat rata telap menegak dalam bendalir Oldroyd-B. Kajian ini mempertimbangkan kesan sinaran terma dan penjanaan/penyerapan haba dalam aliran bendalir. Penjelmaan keserupaan mempermudahkan model kompleks dan fungsi bvp4c menghasilkan penyelesaian berangka mengikut variasi parameter menakluk. Darjah pengecutan yang lebih tinggi mempercepatkan pemisahan aliran. Penyelesaian dual boleh dilihat dalam julat aliran menentang apungan. Keputusan daripada kajian ini boleh digunakan oleh saintis untuk memahami tingkah laku larutan polimer cair dalam aplikasi perindustrian, contohnya pengurangan seretan dalam aliran paip.

 

Kata kunci: Aliran titik genangan; analisis kestabilan; bendalir Oldroyd-B; olakan campuran; plat mengecut

RUJUKAN

Acrivos, A. 1958. Combined laminar free- and forced-convection heat transfer in external flows. AIChE J. 4(3): 285-289.

Bhatnagar, R.K., Gupta, G. & Rajagopal, K.R. 1995. Flow of an Oldroyd-B fluid due to a stretching sheet in the presence of a free stream velocity. Int. J. Nonlinear Mech. 30(3): 391-405.

Bhattacharyya, K. & Layek, G.C. 2011. Effects of suction/ blowing on steady boundary layer stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation. Int. J. Heat Mass Trans. 54(1-3): 302-307.

Burdujan, I. 2011. The flow of a particular class of Oldroyd-B fluids. Annals of AOSR 3(1): 23-45.

Chen, C.H. 1998. Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heat Mass Transfer 33(5-6): 471-476.

Fetecau, C. & Fetecau, C. 2003. The first problem of stokes for an Oldroyd-B fluid. Int. J. Nonlinear Mech. 38(10): 1539-1544.

Fetecau, C. & Kannan, K. 2005. A note on an unsteady flow of an Oldroyd-B fluid. Int. J. Math. Math. Sci. 2005(19): 3185-3194.

Guillope, C. & Saut, J.C. 1990. Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type. ESAIM 24(3): 369-401.

Harris, S.D., Ingham, D.B. & Pop, I. 2009. Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transport Porous Med. 77(2): 267-285.

Hayat, T., Kiran, A., Imtiaz, M. & Alsaedi, A. 2017. Melting heat and thermal radiation effects on stretched flow of an Oldroyd-B fluid. Appl. Math. Mech.- Engl. Ed. 38(7): 957- 968.

Hayat, T., Muhammad, T., Shehzad, S.A. & Alsaedi, A. 2015a. Temperature and concentration stratification effects in mixed convection flow of an Oldroyd-B fluid with thermal radiation and chemical reaction. PLoS ONE 10(6): e0127646.

Hayat, T., Waqas, M., Shehzad, S.A. & Alsaedi, A. 2015b. MHD stagnation point flow of Jeffrey fluid by a radially stretching surface with viscous dissipation and Joule heating. J. Hydrol. Hydromech.63(4): 311-317.

Hayat, T., Hussain, Z., Farooq, M., Alsaedi, A. & Obaid, M. 2014. Thermally stratified stagnation point flow of an Oldroyd-B fluid. Int. J. Nonlinear Sci. Numer. Simul.15(1): 77-86.

Hayat, T., Shehzad, S.A., Alsaedi, A. & Alhothuali, M.S. 2013. Three-dimensional flow of Oldroyd-B fluid over surface with convective boundary conditions. Appl. Math. Mech.- Engl. Ed. 34(4): 489-500.

Karwe, M.V. & Jaluria, Y. 1988. Fluid flow and mixed convection transport from a moving plate in rolling and extrusion processes. J. Heat Transfer 110(3): 655-661.

Merkin, J.H. 1985. On dual solutions occurring in mixed convection in a porous medium. J. Eng. Math. 20(2): 171-179.

Miklavčič, M. & Wang, C.Y. 2006. Viscous flow due to a shrinking sheet. Quart. Appl. Math. 64(2): 283-290.

Oldroyd, J.G. 1958. Non-Newtonian effects in steady motion of some idealized elasto-viscous fluids. Proc. Royal Soc. Lond. A 245(1241): 278-297.

Oldroyd, J.G. 1950. On the formulation of rheological equations of state. Proc. Royal Soc. Lond. A 200(1063): 523-541.

Phan-Tien, N. 1984. Stagnation flows for the Oldroyd-B fluid. Rheol. Acta23(2): 172-176.

Pop, I. & Ingham, D.B. 2001. Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media. 1st ed. Oxford: Pergamon.

Rajagopal, K.R. & Bhatnagar, R.K. 1995. Exact solutions for some simple flows of an Oldroyd-B fluid. Acta Mech. 113(1- 4): 233-239.

Roşca, N.C. & Pop, I. 2013. Mixed convection stagnation point flow past a vertical flat plate with a second order slip: Heat flux case. Int. J. Heat Mass Transf. 65: 102-109.

Sajid, M., Ahmed, B. & Abbas, Z. 2015. Steady mixed convection stagnation point flow of MHD Oldroyd-B fluid over a stretching sheet. J. Egyptian Math. Soc. 23(2): 440-444.

Wang, C.Y. 2008. Stagnation flow towards a shrinking sheet. Int. J. NonLinear Mech. 43(5): 377-382.

Waters, N.D. & King, M.J. 1971. The unsteady flow of an elastic-viscous liquid in a straight pipe of circular cross section. J. Phys. D: Appl. Phys. 4(2): 204-211.

Weidman, P.D., Kubitschek, D.G. & Davis, A.M.J. 2006. The effects of transpiration on self-similar boundary layer flow over moving surfaces. Int. J. Eng. Sci. 44(11-12): 730-737.

 

 

*Pengarang untuk surat-menyurat; email: kohi_kk@yahoo.com

 

 

 

 

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