A mathematical model is presented for the magneto-hydrodynamic flow and heat transfer in an electro-conductive Casson viscoplastic non-Newtonian fluid external to a vertical penetrable vertical cone under radial magnetic field and convective heating. The boundary layer conservation equations are parabolic in nature which can be transformed into a non-dimensional form via appropriate non-similarity variables and the emerging boundary value problem is solved computationally with the second order accurate implicit Keller-box finite-difference scheme. The influences of the emerging parameters, i.e. Magnetic parameter (M), Casson fluid parameter (β), Convective heating ( ), and Prandtl number (Pr) on velocity and temperature distributions are illustrated graphically. Validation of solutions with earlier published work is included.

Thermal Convection, Convective Boundary Condition, Keller-box Numerical Method, Cone, Casson Viscoplastic Model.
How to Cite this Article?
Amanulla,Ch., Nagendra,N., and Reddy,M.S.N. (2017). Heat Transfer In MHD Viscoplastic Fluid Flow from a Vertical Permeable Cone with Convective Heating. i-manager’s Journal on Mathematics, 6(1), 35-42.
[1]. S. Livescu, (2012). “Mathematical modeling of thixotropic drilling mud and crude oil flow in wells and pipelines - A review”. J. Petroleum Science and Engineering, Vol.98, No.99, pp.174–184.
[2]. J. Hron, J. Málek, P. Pustejovská, and K.R. Rajagopal, (2010). “On the modeling of the synovial fluid”. Advances in Tribology, Article ID 104957
[3]. F. Loix, L. Orgéas, C. Geindreau, P. Badel, P. Boisse, and J.F. Bloch, (2009). “Flow of non-Newtonian liquid polymers through deformed composites reinforcements”. Composites Science and Technology, Vol.69, No.5, pp.612–619.
[4]. V. Kechichian, G.P. Crivellari, J.A.W. Gut, and C.C. Tadini, (2012). “Modeling of continuous thermal processing of a non- Newtonian liquid food under diffusive laminar flow in a tubular system”. Int. J. Heat and Mass Transfer, Vol.55, No.21-22, pp.5783–5792 .
[5]. M. Ghannam, and N. Esmail, (2002). “Flow behavior of enhanced oil recovery Alcoflood polymers”. J. Applied Polymer Science, Vol.85, No.14, pp.2896 - 2904.
[6]. N. Casson, (1959). “A Flow Equation for Pigment oil-Suspensions of the Printing Ink Type”. In: C.C. Mill, Ed., Rheology of Disperse Systems, Pergamon Press, Oxford, pp.84-104.
[7]. R.B. Bird, G.C. Dai, and B.J. Yarusso, (1983). “The Rheology and Flow of Viscoplastic Materials”. Rev. Chem. Eng, Vol.1, No.1, pp.36-69.
[8]. S.G. Mohiddin, V.R. Prasad, S.V.K. Varma, and O.A. Bég, (2010). “Numerical study of unsteady free convective heat and mass transfer in a Walters-B viscoelastic flow along a vertical cone”. Int. J. of Appl. Math. and Mech., Vol..6, No.15, pp.88- 114.
[9]. N. Nagendra, M.V.S. Reddy, and B. Jayaraj, (2008). “Peristaltic motion of a power law fluid in an asymmetric vertical channel”. Journal of Interdisciplinary Mathematics, Vol.11, No.4, pp.505-519.
[10]. A. Noghrehabadi, A. Behseresht, and M. Ghalambaz, (2013). “Natural convection flow of nanofluids over a vertical cone embedded in non-Darcy porous media”. J. Thermophys. Heat Transf., Vol.27, No.2, pp.334–341.
[11]. I. Pop, and T.Y. Na, (1999). “Natural convection over a vertical wavy frustum of a cone”. Int. J. Non Linear Mech., Vol.34, No.5, pp.925–934.
[12]. C.Y. Cheng, (2011). “Natural convection boundary layer flow of a micropolar fluid over a vertical permeable cone with variable temperature”. Int. Commun. Heat Mass Transf., Vol.38, No.4, pp.429–433.
[13]. S. Nadeem, and S. Saleem, (2015). “Analytical study of third grade fluid over a rotating vertical cone in the presence of nanoparticles”. Int. J. Heat Mass Transf., Vol.85, pp.1041–1048.
[14]. A. Subba Rao, V.R. Prasad, N.B. Reddy, and O.A. Bég, (2015). “Modelling Laminar Transport Phenomena in a Casson Rheological Fluid from an Isothermal Sphere with Partial Slip”. Thermal Science, Vol.19, No.5, pp.1507-1519.
[15]. A. Subba Rao, V.R. Prasad, N. Nagendra, N.B. Reddy, and O.A. Bég, (2016). “Non-similar computational solution for boundary layer flows of non-Newtonian fluid from an inclined plate with thermal slip”. J. Appl. Fluid Mech., Vol.9, No.2, pp.795–807
[16]. A. Subba Rao, V.R. Prasad, K. Harshavalli, and O.A. Bég, (2016). “Thermal radiation effects on non-Newtonian fluid in a variable porosity regime with partial slip”. J. Porous Media, Vol.19, No.4, pp.313-329.
[17]. A. Subba Rao, V.R. Prasad, N.B. Reddy, and O.A. Bég, (2015). “Heat Transfer in a Casson Rheological Fluid from a Semiinfinite Vertical Plate with Partial Slip”. Heat Transfer-Asian Research, Vol.44, No.3, pp.272-291.
[18]. A. Subba Rao, CH. Amanulla, N. Nagendra, O.A. Bég, and A. Kadir, (2017). “Hydromagnetic Flow and Heat Transfer in a Williamson Non-Newtonian Fluid from a Horizontal Circular Cylinder with Newtonian Heating”. Int. J. Appl. Comput. Math., pp.1-21.
[19]. M.M. Alam, M.A. Alim, and M.M.K. Chowdhury, (2007). “Free Convection from a Vertical Permeable Circular Cone with Pressure Work and Non-Uniform Surface Temperature”. Nonlinear Analysis: Modelling and Control, Vol.12, No.1, pp.21–32.
[20]. T. Cebeci, and P. Bradshaw, (1984). Physical and Computational Aspects of Convective Heat Transfer. Springer, New York.
[21]. H.B. Keller, (1970). “A New Difference Method for Parabolic Problems”. In J. Bramble, Ed., Numerical Methods for Partial Differential Equations, Academic Press, New York, USA, pp.327-350.
[22]. A. Subba Rao, N. Nagendra, and V.R. Prasad, (2015). “Heat Transfer in a Non-Newtonian Jeffrey's Fluid over a Non- Isothermal Wedge”. Procedia Engineering, Vol.127, pp.775-782.
[23]. A. Subba Rao, and N. Nagendra, (2015). “Thermal radiation effects on oldroyd-b nano fluid from a stretching sheet in a non- darcy porous medium”. Global Journal of Pure and Applied Mathematics, Vol.11, No.2, pp.45-49.
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