Document Type: Research Paper

Authors

1 India

2 VIT, Vellore

Abstract

This article explores the heat and mass transfer behaviour of magnetohydrodynamic free convective flow past a permeable vertical rotating cone and a plate filled with gyrotactic microorganisms in the presence of nonlinear thermal radiation, thermo diffusion and diffusion thermo effects. We presented dual solutions for the flow over a rotating cone and a rotating flat plate cases. Similarity variables are employed to convert the nonlinear partial differential equations into ordinary differential equations. Comparisons with previously published work are performed and results are found to be in excellent agreement. The resultant non-dimensional governing equations along with associated boundary conditions are solved numerically using Runge–Kutta and Newton’s methods. The impact of pertinent parameters on velocity, temperature, concentration and density of the motile microorganisms along with the friction factor, local Nusselt, Sherwood numbers and the local density of the motile microorganisms was determined and analyzed with the help of graphs and tables. Results proved that there is a significant variation of heat and mass transfer in the flow over a rotating cone and a plate. It is also found that the heat and mass transfer performance of the flow over a rotating cone is significantly high when compared with the flow over a rotating plate.

Graphical Abstract

Keywords

Main Subjects

[1]          M. AboeldahabEmad, “Radiation effect on heat transfer in electrically conducting fluid at a stretching surface with uniform free stream”, J. Phys D App. Phys., Vol. 33, No. 24, pp. 3180–3185, (2000).

[2]          M. Gnaneswara Reddy, “Influence of magnetohydrodynamic and thermal radiation boundary layer flow of a nanofluid past a stretching sheet”, Journal of Scientific Research, Vol. 6,No.2, pp. 257-272 (2014).

[3]          E. M. Abo-Eldahab, and M. S. Elgendy, “Radiation effect on convective heat transfer in an electrically conducting fluid at a stretching surface with variable viscosity and uniform free stream”, Physica Scripta, Vol. 62, No. , pp. 321-325, (2000).

[4]          A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition”,Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 4, pp. 1064-068, (2009).

[5]           R. Cortell, “Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition”, Applied Mathematics and Computation, Vol. 206, No.1, pp. 832-840, (2008).

[6]          A. Ishak, “Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition”, Appl Math Comput, Vol. 217, No. 2, pp. 837-842, (2010).

[7]          S. Yao, T. Fang and Y. Zhong, “Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions”, Comm Nonlinear SciNumSimul, Vol. 16,  No. 2, pp. 752-760, (2011).

[8]          A. Alsaedi, Z. Iqbal, M.  Mustafa, T.  Hayat, “Exact solutions for the magnetohydrodynamic flow of a Jeffrey fluid with convective boundary conditions and chemical reaction”, Z Naturforsch, Vol. 67a, No. 1, pp. 517- 524, (2012).

[9]          O. D. Makinde, and A. Aziz, “Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition”, Int. J. Therm Sci., Vol. 50, No.7, pp. 1326-1332, (2011).

[10]      M. Gnaneswara Reddy, “Thermal radiation and chemical reaction effects on MHD mixed convective boundary layer                                                           slip flow in a porous medium with heat source and Ohmic heating”,Eur. Phys. J. Plus, Vol. 129, No. 41, pp.1-17,  (2014).

[11]      M. Gnaneswara Reddy,  “Effects of Thermophoresis, viscous dissipation and Joule heating on steady MHD flow over an inclined radiative isothermal permeable surface with variable thermal conductivity”,Journal of Applied Fluid Mechanics, Vol. 7, No. 1, pp. 51-61, (2014).

[12]      A. Bejan, Convection Heat Transfer, 3rd edn. Wiley, New York (2013)

[13]      A. Bejan, and R. K.  Khair, “Heat and mass transfer by natural convection in a porous medium”, Int. J. Heat Mass Transfer, Vol. 28, pp. 909–918, (1985).

[14]      D. A. Nield, and A. Bejan, Convection in Porous Media, 4th edn. Springer, New York (2013)

[15]      I. Pop, and D. B. Ingham, Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media, Pergamon, Oxford (2001)

[16]      D. B. Ingham, and I. Pop, Transport Phenomena in Porous Media II, Pergamon, Oxford (2002)

[17]      E.M. Sparrow, and J. L. Gregg, “Mass transfer, flow and heat transfer about a rotating disk”, Trans. Am. Sot. Mech. Eng. Ser. C J. Heat Transfer, Vol. 82, No. 4, pp. 294–302, (1960).

[18]      R. G. Hering, and R. J. Grosh, “Laminar free convection from a non-isothermal cone at low Prandtl number”, Int. J. Heat Mass Transfer, Vol. 8, No. 10, pp. 1333–1337, (1965).

[19]      F. Kreith, “Convective heat transfer in rotating systems “, In: Irvine, T.F., Hamett, J.P. (eds.) Advances in Heat Transfer, Vol. 5, pp. 129–251, (1968).

[20]      K. Himasekhar, P.K. Sarma, and K.  Janardhan, “Laminar mixed convection from a vertical rotating cone”, Int. Commun. Heat Mass Transfer, Vol. 16, No. 1, pp. 99–106, (1989).

[21]      A.J. Chamkha, “Combined convection heat transfer from a rotating cone embedded in a power-law fluid saturated porous medium”, Fluid/Particle Separat. J., Vol. 13, No. 1, pp. 12–29, (2000).

[22]      H.S. Takhar, A.J.  Chamkha, and G. Nath, “Unsteady mixed convection flow from a rotating vertical cone with a magnetic field”, Heat Mass Transfer, Vol. 39, No. 4, pp. 297–304, (2003)

[23]      S. Roy, and D. Anil kumar, “Unsteady mixed convection from a rotating cone in a rotating fluid due to the combined effects of thermal and mass diffusion”, Int. J. Heat Mass Transfer, Vol. 47, No. 8,  pp. 1673–1684, (2004).

[24]      M. Gnaneswara Reddy ,and N. Bhaskar Reddy, “Mass Transfer and heat generation effects on MHD free convection flow past an inclined vertical surface in a porous medium”, Journal of Applied Fluid Mechanics, Vol. 4, No. 2, pp. 7-11, ( 2011). 

[25]      R. Bhuvanavijaya, and B. Mallikarjuna,” Effect of variable thermal conductivity on convective heat and mass transfer over a vertical plate in a rotating system with variable porosity regime”, J. Naval Architect. Mar. Eng., Vol. 11, pp. 83–92, (2014).

[26]       M. Gnaneswara Reddy,   “Lie group analysis of heat and mass transfer effects on steady MHD free convection dissipative fluid flow past an inclined porous surface with heat generation”, Theoret. Appl. Mech., Vol. 39, No. 3, pp. 233–254, (2012).

[27]      B. Mallikarjuna, A. M. Rashad, Ali J. Chamkha, and S. Hariprasad Raju, “Chemical reaction effects on MHD convective heat and mass transfer flow past a rotating vertical cone embedded in a variable porosity regime”, AfrikaMathematika,  Vol. 27,  pp. 645-665, (2016).

[28]      G. Awad, P. Sibanda, S.S. Mosta, and O.D. Makinde, “Convection from an inverted cone in a porous medium with cross-diffusion effects”, Comp. Maths. Apps. , Vol. 61, No. 5, pp. 1431–1441, (2011).

[29]       N. Sandeep, B. Rushi Kumar and M. S. Jagadeesh Kumar, “A comparative study on convective heat and mass transfer in non-Newtonian nano fluid flow past a permeable stretching sheet”, J. Mol. Liq. Vol. 212, pp. 585-591, (2015).

[30]      C.S.K. Raju, and N. Sandeep, Heat and mass transfer in MHD non-Newtonian bio-convection flow over a rotating cone/plate with cross diffusion, Journal of Molecular Liquids, Vol. 215, pp. 115-126, (2016).

[31]      M. Gnaneswara Reddy, and N. Sandeep, “Heat and mass transfer in radiative MHD Carreau fluid with cross diffusion”, Ain Shams Engineering Journal, )2016( (Article in Press).

 

CAPTCHA Image