Abstract
The steady, boundary layer flow and heat transfer on a stretching surface in rotating fluid has been examined. Using suitable similarity transformations, the partial differential equations governing the flow and heat transfer phenomenon convert to a system of non-linear ordinary differential equations. The obtained equations are solved by using the shooting technique with fifth order Runge–Kutta–Fehlberg method. The parameters involving in the problem are Casson fluid parameter \(\beta \), non-dimensional parameter \(\lambda \) that signifies the importance of rotation rate to stretching rate and Prandtl number \(Pr\). The effects of these parameters on physical quantities such as velocity and temperature profiles, skin frictions and Nusselt number are inspected with the aid of graphs and tables.
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References
Crane LJ (1977) Flow past a stretching slate. Z Angew Math Phys 21:645–647
Gupta PS, Gupta AS (1977) Heat and mass transfer on a stretching sheet with suction or blowing. Can J Chem Eng 55:744–746
Grubka J, Bobba KM (1985) Heat transfer characteristics of a continuous stretching surface with variable temperature. Trans ASME J Heat Transf 107:248–250
Banks WHH (1983) Similarity solutions of the boundary layer equation for a stretching wall. J Mech Theor Appl 2:375–392
Ali ME (1995) On thermal boundary layer on a power law stretched surface with suction or injection. Int J Heat Mass Flow 16:280–290
Elbashbeshy EMA (1998) Heat transfer over a stretching surface with variable heat flux. J Phys D Appl Phys 31:1951–1955
Sriramalu A, Kishan N, Anand RJ (2001) Steady flow and heat transfer of a viscous incompressible fluid flow through porous medium over a stretching sheet. J Energy Heat Mass Transf 23:483–495
Andersson HI (2002) Slip flow past a stretching surface. Acta Mech 158:121–125
Wang CY (2002) Flow due to a stretching boundary with partial slip-an exact solution of the Navier-Stokes equations. Chem Eng Sci 57:3745–3747
Mehmood A, Ali A, Shah T (2008) Unsteady boundary-layer viscous flow due to an impulsively started porous plate. Can J Phys 86:1079–1082
Mehmood A, Ali A (2008) Analytic solution of three-dimensional viscous flow and heat transfer over a stretching flat surface by homotopy analysis method. ASME J Heat Transf 130:121701–121707
Ali A, Mehmood A (2008) Homotopy analysis of unsteady boundary layer flow adjacent to permeable stretching surface in a porous medium. Commun Nonlinear Sci Numer Simul 13:340–349
Fang T, Zhang J, Yao S (2009) Slip MHD flow over a stretching sheet-an exact solution. Commun Nonlinear Sci Numer Simul 14:3731–3737
Mehmood A, Ali A (2010) Injection flow past a porous plate: solution to an unsolved problem. Int J Nonlinear Sci Numer Simul 11:511–518
Yao S, Fang T, Zhong Y (2011) Heat transfer of a generalized stretching/ shrinking wall problem with convective boundary conditions. Commun Nonlinear Sci Numer Simul 16:752–760
Deka RK, Gupta AS, Takhar HS, Soundalgekar VM (1999) Flow past an accelerated horizontal plate in a rotating fluid. Acta Mech 138:13–19
Wang CY (1988) Stretching a surface in a rotating fluid. Z Angew Math Phys 39:177–185
Takhar HS, Chamkha AJ, Nath G (2003) Flow and heat transfer on a stretching surface in a rotating fluid with a magnetic field. Int J Therm Sci 42:23–31
Rajeswari V, Nath G (2004) Unsteady flow over a stretching surface in a rotating fluid. Int J Eng Sci 30:121–128
Nazar R, Amin N, Pop I (2004) Unsteady boundary layer flow due to a stretching surface in a rotating fluid. Mech Res Commun 31:121–128
Abbas Z, Javed T, Sajid M, Ali N (2010) Unsteady MHD flow and heat transfer on a stretching sheet in a rotating fluid. J Taiwan Inst Chem Eng 41:644–650
Zaimi K, Ishak A, Pop I (2013) Stretching surface in rotating viscoelastic fluid. Appl Math Mech Engl Ed 34:945–952
Casson NA (1959) A flow equation for pigment oil suspension of printing ink type. In: Mill CC (ed) Rheology of dispersed system. Pergamon Press, Oxford
Eldabe NTM, Salwa MGE (1995) Heat transfer of MHD non-newtonian casson fluid flow between two rotating cylinders. J Phys Soc Jpn 64:41–64
Boyd J, Buick JM, Green S (2007) Analysis of the Casson and Carreau-Yasuda Non-Newtonian blood models in steady and oscillatory flow using the Lattice Boltzmann Method. Phys Fluids 19:93–103
Bhargava R, Takhar HS, Rawat S, Bèg TA, Bèg OA (2007) Finite element solutions for Non-Newtonian Pulsatile flow in a Non-Darician porous medium conduit. Nonlinear Anal Model Control 12:317–327
Attia HA, Ahmed MES (2010) Transient MHD couette flow of a Casson fluid between parallel plates with heat transfer. Ital J Pure Appl Math 27:19–38
Mukhopadhyay S (2013) Casson fluid flow and heat transfer over a nonlinearly stretching surface. Chin Phys B 27:074701–074705
Nandy SK (2013) Analytical solution of MHD stagnation-point flow and heat transfer of Casson fluid over a stretching sheet with partial slip. ISRN Thermodyn 2013:9. doi:10.1155/2013/108264 Article ID 108264
Mukhopadhyay S, Mondal IC, Chamkha AJ (2013) Casson fluid flow and heat transfer past a symmetric wedge. Heat Transf Asian Res 42:665–675
Tufail MN, Butt AS, Ali A (2014) Heat source/sink effects on Non-Newtonian MHD fluid flow and heat transfer over a permeable stretching surface: Lie group analysis. Indian J Phys 1:75–82
Qasim M, Noreen S (2014) Heat transfer in the boundary layer flow of a Casson fluid over a permeable shrinking sheet with viscous dissipation. Eur Phys J Plus 7:129–137
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Butt, A.S., Ali, A. & Mehmood, A. Study of Flow and Heat Transfer on a Stretching Surface in a Rotating Casson Fluid. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 85, 421–426 (2015). https://doi.org/10.1007/s40010-015-0217-1
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DOI: https://doi.org/10.1007/s40010-015-0217-1