Numerical Exploration of Cattaneo-Christov Heat Flux and Mass Transfer in Magnetohydrodynamic Flow over Various Geometries

Abstract:

The flow geometry plays a major role in heat and mass transfer processes of many engineering and industrial applications.In the present paper, we examined the combined effects of Cattaneo-Christov heat flux, external magnetic field, chemical reaction, heat source and buoyancy forces on the flow of an incompressible electrically conducting fluid with heat and mass transfer over three different geometries (cone, wedge and a plate). The nonlinear governing equations are obtained and tackled numerically using shooting technique with Runge-Kutta-Felhberg integration scheme. Numerical results are presented graphically and discussed quantitatively. It is found that the thermal boundary layer is highly effective on the flow over a wedge when compared with the other two geometries (plate and a cone).

• Periodical: Defect and Diffusion Forum (Volume 374)
• Pages: 67-82
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.374.67
• Online since: April 2017
• Authors: Oluwole Daniel Makinde*, Naramgari Sandeep, Isaac Lare Animasaun, M.S. Tshehla
• Keywords: Buoyancy Force, Cattaneo-Christov Heat Flux, Chemical Reaction, Magnetohydrodynamics, Variable Heat Source

References

[1] J. B. J. Fourier, Theorie analytique De La chaleur, Paris, (1822).

[2] A. Fick, On liquid diffusion, Poggendorffs Annalen. 94 (1855) 59.

[3] C. Cattaneo, Sulla conduzione del calore, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 3 (1948) 83–101.

[4] C. I. Christov, On frame indifferent formulation of the Maxwell-Cattaneo model of finite speed heat conduction, Mech. Res. Commun. 36 (2009) 481–486.

DOI: 10.1016/j.mechrescom.2008.11.003

[5] G. Ramanaiah, V. Kumaran, Darcy-Brickman free convection about a wedge and a cone subjected to a mixed thermal boundary condition, Int.J. Math. and Math. Sci., 15 (1992) 789–794.

DOI: 10.1155/s0161171292001029

[6] K. Vajravelu, J. Nayfeh, Hydromagnetic convection at a cone and a wedge, International Communications in Heat and Mass Transfer. 19 (1992) 701–710.

DOI: 10.1016/0735-1933(92)90052-j

[7] M.M. Rahman, A. Faghri, Transport in a thin liquid film on the outer surface of a wedge or cone embedded in a porous medium part II: Computation and comparison of results, International Communications in Heat and Mass Transfer. 20 (1993) 29–42.

DOI: 10.1016/0735-1933(93)90004-f

[8] T. Watanabe, I. Pop, Magnetohydrodynamic free convection flow over a wedge in the presence of a transverse magnetic field, International Communications in Heat and Mass Transfer. 20 (1993) 871–881.

DOI: 10.1016/0735-1933(93)90040-3

[9] A.J. Chamkha, Non-Darcy hydromagnetic free convection from a cone and a wedge in porous media, Int. Comm. Heat and Mass Transfer 23 (1996) 875–887.

DOI: 10.1016/0735-1933(96)00070-x

[10] H.S. Takhar, R.S.R. Gorla, V.M. Soundalgekar, Radiation effects on MHD free convection flow of a gas past a semi-infinite vertical plate, International Journal of Numerical Methods for Heat and Fluid Flow. 6 (1996) 77–83.

DOI: 10.1108/09615539610113118

[11] K. Yih, Effect of radiation on natural convection about a truncated cone, International Journal of Heat and Mass Transfer. 42 (1999) 4299–4305.

DOI: 10.1016/s0017-9310(99)00092-7

[12] A. Hossain, S. Munir, D.A.S. Rees, Flow of viscous incompressible fluid with temperature dependent viscosity and thermal conductivity past a permeable wedge with uniform surface heat flux, Int. J. Therm. Sci. 39 (2000) 635–644.

DOI: 10.1016/s1290-0729(00)00227-1

[13] S.P. Anjalidevi, R. Kandasamy, Effects of heat and mass transfer on MHD laminar boundary layer flow over a wedge with suction or injection, J. Energy, Heat and Mass Transfer 23 (2001) 167-178.

DOI: 10.1016/s0735-1933(02)00389-5

[14] Y.J. Kim, Heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium, Transport in Porous Media. 56 (2004) 17–37.

DOI: 10.1023/b:tipm.0000018420.72016.9d

[15] R. Kandasamy, W. Abd, A. Khamis, Effects of chemical reaction, heat and mass transfer on boundary layer flow over a porous wedge with heat radiation in the presence of suction or injection, Theoretical and Applied Mechanics 33 (2006) 123–148.

DOI: 10.2298/tam0602123k

[16] S. M. M. El-Kabeir, M.M.M. Abdou, Chemical reaction, heat and mass transfer on MHD flow over a vertical isothermal cone surface in micropolar fluids with heat generation/absorption, Applied Mathematical Sciences, 1(34) (2007) 1663–1674.

[17] K. Atalık, Ü. Sönmezler, Heat transfer enhancement for boundary layer flow over a wedge by the use of electric fields, Applied Mathematical Modelling. 35 (2011) 4516–4525.

DOI: 10.1016/j.apm.2011.03.023

[18] B. Rushi Kumar, R. Sivaraj, Heat and mass transfer in MHD viscoelastic fluid flow over a vertical cone and flat plate with variable viscosity, International Journal of Heat and Mass Transfer 56 (2013) 370–379.

DOI: 10.1016/j.ijheatmasstransfer.2012.09.001

[19] B. Rushi Kumar, R. Sivaraj, MHD viscoelastic fluid non-Darcy flow over a vertical cone and a flat plate, International Communications in Heat and Mass Transfer 40 (2013) 1–6.

DOI: 10.1016/j.icheatmasstransfer.2012.10.025

[20] J. Benazir, R. Sivaraj, O.D. Makinde, unsteady magnetohydrodynamic Casson fluid flow over a vertical cone and flat plate with non-uniform heat source/sink", International Journal of Engineering Research in Africa, 21 (2016) 69-83.

DOI: 10.4028/www.scientific.net/jera.21.69

[21] M. Mustafa, Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper- convected Maxwell fluid, AIP Advances, 5 (2015) 047109.

DOI: 10.1063/1.4917306

[22] T. Hayat, M. Farooq, A. Alsaedi, F. Al-Solamy, Impact of Cattaneo-Christov heat flux in the flow over a stretching sheet with variable thickness, AIP Advances, 5 (8) (2015) 087159.

DOI: 10.1063/1.4929523

[23] M. Waqas, T. Hayat, M. Farooq, S.A. Shehzad, A. Alsaedi, Cattaneo-Christov heat flux model for flow of variable thermal conductivity generalized Burgers fluid, Journal of Molecular Liquids. 220 (2016) 642–648.

DOI: 10.1016/j.molliq.2016.04.086

[24] W. Ibrahim, O.D. Makinde, Magnetohydrodynamic stagnation point flow of a power-law nanofluid towards a convectively heated stretching sheet with slip. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 230(5) (2016).

DOI: 10.1177/0954408914550357

[25] M. Gnaneswara Reddy, O. D. Makinde, Magnetohydrodynamic peristaltic transport of Jeffery nanofluid in an asymmetric channel. Journal of Molecular Liquids, 223 (2016) 1242-1248.

DOI: 10.1016/j.molliq.2016.09.080

[26] W. A. Khan, O. D. Makinde, Z. H. Khan, Non-aligned MHD stagnation point flow of variable viscosity nanofluids past a stretching sheet with radiative heat. International Journal of Heat and Mass Transfer, 96, (2016) 525-534.

DOI: 10.1016/j.ijheatmasstransfer.2016.01.052

[27] D. Mythili, R. Sivaraj, M.M. Rashidi, Heat generating/absorbing and chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium, International Journal of Numerical Methods for Heat and Fluid Flow 27 (2017).

DOI: 10.1108/hff-08-2015-0318

[28] C.S.K. Raju, N. Sandeep, A. Malvandi, Free convective heat and mass transfer of MHD non-Newtonian nanofluids over a cone in the presence of non-uniform heat source/sink, Journal of Molecular Liquids. 221 (2016) 108–115.

DOI: 10.1016/j.molliq.2016.05.078

[29] C.S.K. Raju, N. Sandeep, Opposing and assisting flow characteristics of radiative Casson fluid due to cone in the presence of induced magnetic field, International Journal of Advanced Science and Technology, 88 (2016) 43–62.

DOI: 10.14257/ijast.2016.88.05

[30] W. A. Khan, J. R. Culham, O.D. Makinde, Combined heat and mass transfer of third‐grade nanofluids over a convectively‐heated stretching permeable surface. The Canadian Journal of Chemical Engineering, Vol. 93(10), (2015) 1880-1888.

DOI: 10.1002/cjce.22283

[31] W.A. Khan, O. D. Makinde, MHD nanofluidbioconvection due to gyrotactic microorganisms over a convectively heat stretching sheet. International Journal of Thermal Sciences 81 (2014) 118-124.

DOI: 10.1016/j.ijthermalsci.2014.03.009

[32] I. L. Animasaun, N. Sandeep, Buoyancy induced model for theflow of 36 nm alumina-water nanofluidalong upper horizontal surface of a paraboloid of revolution with variablethermal conductivity and viscosity, Powder Technology. 301 (2016) 858 – 867.

DOI: 10.1016/j.powtec.2016.07.023

[33] O.D. Makinde, I. L. Animasaun, Bioconvection in MHD nanofluidflow with nonlinear thermalradiation and quartic autocatalysis chemical reaction past an uppersurface of a paraboloid of revolution, International Journal of Thermal Sciences. 109 (2016).

DOI: 10.1016/j.ijthermalsci.2016.06.003

[34] O.D. Makinde, I. L. Animasaun, Thermophoresis and Brownian motion effects on MHD bioconvection ofnanofluid with nonlinear thermal radiation and quartic chemicalreaction past an upper horizontal surface of a paraboloid of revolution. Journal of Molecular Liquids. 221 (2016).

DOI: 10.1016/j.molliq.2016.06.047

[35] O.A. Abegunrin, S.O. Okhuevbie, I.L. Animasaun, Comparison between the flow of two non-Newtonianfluids over an upper horizontal surface of paraboloid of revolution: Boundary layer analysis. Alexandria Engineering Journal 55(3) (2016).

DOI: 10.1016/j.aej.2016.08.002