Non-Uniform Heat Source/Sink and Joule Heating Effects on Chemically Radiative MHD Mixed Convective Flow of Micropolar Fluid over a Stretching Sheet in Porous Medium

Abstract:

This article describes the effects of Joule heating and chemical reaction on unsteady MHD mixed convective micropolar fluid over a stretching sheet in presence of radiation, non-uniform heat source and porous medium. The arising non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations and then solved numerically by using the Runge– Kutta–Fehlberg fourth–fifth order method along shooting technique. The graphical and tabular results elucidate the influence of different non-dimensional governing parameters on the velocity, temperature and concentration fields along with the wall friction, local Nusselt and Sherwood numbers. We found the dual nature of the solutions for suction and injection cases. A good agreement of the present results has been observed by comparing with the existing literature results.

• Periodical: Defect and Diffusion Forum (Volume 388)
• Pages: 281-302
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.388.281
• Online since: October 2018
• Authors: G. Charan Kumar*, Konda Jayarami Reddy, Rama Krishna Konijeti, M. Narendradh Reddy
• Keywords: Joule Heating, MHD Flows, Non-Uniform Heat Source/Sink, Porous Medium, Suction/Injection

References

[1] A.C. Eringen, Theory of Micropolar Fluids, J. Math. Mech. 16 (1966) 1-18.

[2] A.C. Eringen. Simple microfluids. Int. J. Engg Sci., 1964, 2, 205–217.

[3] A.C. Eringen. Theory of micropolar fluids. J. Appl. Math. Mech., 1966, 16, 1–8.

[4] A.C. Eringen Micro continuum field theories I: foundations and solid, 1999 (Springer, New York) p.1–56.

[5] A.C. Eringen Micro continuum field theories II: fluent media, 2001 (Springer, New York) p.1–80.

[6] M.M. Khonsari, On the self-excited whirl orbits of a journal in a sleave bearing lubricated with micropolar fluids, Acta Mech. 81 (1990) 235-244.

DOI: 10.1007/bf01176991

[7] B. Hadimoto and T. Tokioka, Two-dimensional shear flows of linear micropolar fluids, Int. J. Eng. Sci., 7(1969)515-522.

[8] J. D. Lee and A. C. Eringen Boundary effects of orientation of numatic liquid crystals, J. Chem. Phys., 55(1971) 4509-4512.

[9] T. Ariman, M.A. Turk and N.D. Sylvester, Application of Microcontinuum fluid mechanics, Int. J. Eng. Sci., 12 (1974) 273-293.

DOI: 10.1016/0020-7225(74)90059-7

[10] F. Mabood, S. M. Ibrahim, M. M. Rashidi, M. S. Shadloo, and G. Lorenzini, Non-uniform heat source/sink and Soret effects on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation,, International Journal of Heat and Mass Transfer 93, 674–682 (2016).

DOI: 10.1016/j.ijheatmasstransfer.2015.10.014

[11] F. Mabood and S. M. Ibrahim, Effects of Soret and Non-Uniform Heat Source on MHD Non-Darcian Convective Flow over a Stretching Sheet in a Dissipative Micropolar Fluid with Radiation, Journal of Applied Fluid Mechanics, Vol. 9, No. 5, pp.2503-2513, (2016).

DOI: 10.18869/acadpub.jafm.68.236.24674

[12] K Singh., M Kumar, Effects of thermal radiation on mixed convection flow of a micropolar fluid from an unsteady stretching surface with viscous dissipation and heat generation/absorption, International Journal of Chemical Engineering, Vol 2016, (2016).

DOI: 10.1155/2016/8190234

[13] Z. Uddin, M. Kumar, and S. Harmand, Influence of thermal radiation and heat generation//absorption on MHD heat transfer flow of a micropolar fluid past a wedge with hall and ion slip currents,, Thermal Science, vol. 18, no. 2, pp. S489–S502, (2014).

DOI: 10.2298/tsci110712085u

[14] R. A. Mohamed and S. M. Abo-Dahab, Influence of chemical reaction and thermal radiation on the heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium with heat generation,, International Journal of Thermal Sciences, vol. 48, no. 9, p.1800–1813, (2009).

DOI: 10.1016/j.ijthermalsci.2009.01.019

[15] Z. Ziabakhsh, G. Domairry, and H. Bararnia, Analytical solution of non-Newtonian micropolar fluid flow with uniform suction/blowing and heat generation,, Journal of the Taiwan Institute of Chemical Engineers, vol. 40, no. 4, p.443–451, (2009).

DOI: 10.1016/j.jtice.2008.12.005

[16] M. A. A. Mahmoud and S. E. Waheed, MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity,, Journal of the Egyptian Mathematical Society, vol. 20, no. 1, p.20–27, 201.

DOI: 10.1016/j.joems.2011.12.009

[17] M.M. Rashidi, S. A. Mohimanian and S. Abbasbandy (2011). Analytic approximation solutions for heat transfer of a micropolar fluid through a porous medium with radiation. Communications in Non-linear Science and Numerical Simulation 16, 1874-1879.

DOI: 10.1016/j.cnsns.2010.08.016

[18] M. Naveed., Z Abbas., M Sajid, MHD flow of micropolar fluid due to a curved stretching sheet with thermal radiation, Journal of Applied Fluid Mechanics, Vol. 9, No. 1, pp.131-138, (2016).

DOI: 10.18869/acadpub.jafm.68.224.23967

[19] T. Hayat, and M. Qasim (2010). Effects of thermal radiation on unsteady magnetohydrodynamic flow of a micropolar fluid with heat and mass transfer. Naturforsch 65(a), 950-960.

DOI: 10.1515/zna-2010-1107

[20] H.A.M. El-Arabawy, Effect of suction/injection on the flow of a micropolar fluid past a continuously moving plate in the presence of radiation, Int. J. Heat Mass Transfer, 46 (2003), p.1471–1477.

DOI: 10.1016/s0017-9310(02)00320-4

[21] M.M. Rahman and M.A. Sattar, Transient convective flow of micropolar fluid past a continuously moving vertical porous plate in the presence of radiation, Int. Jour. Appl. Mechs. Engg., 12(2007), 497-513.

DOI: 10.1115/1.2136918

[22] M. Abd-El Aziz, and Cairo, (2006), Thermal radiation effects on magnetohydrodynamic mixed convection flow of a micropolar fluid past a continuously moving semi-infinite plate for high temperature differences, Acta Mechanica, Vol.187, p.113–127.

DOI: 10.1007/s00707-006-0377-9

[23] M.M. Rahman, and Sultana, T., (2008), Radiative Heat Transfer Flow of Micropolar Fluid with Variable Heat Flux in a Porous Medium, Nonlinear Analysis: Modelling and Control, Vol. 13, No. 1, p.71–87.

DOI: 10.15388/na.2008.13.1.14590

[24] D. Pal and S. Chatterjee, MHD mixed convection stagnation-point flow of a micropolar fluid in a porous medium towards a heated stretching sheet with thermal radiation,, Mathematical Modelling and Analysis, vol. 17, no. 4, p.498–518, (2012).

DOI: 10.3846/13926292.2012.706653

[25] M. Hussain, M. Ashraf, S. Nadeem, and M. Khan, Radiation effects on the thermal boundary layer flow of a micropolar fluid towards a permeable stretching sheet,, Journal of the Franklin Institute, vol. 350, no. 1, p.194–210, (2013).

DOI: 10.1016/j.jfranklin.2012.07.005

[26] D. Prakash and M. Muthtamilselvan, Effect of radiation on transient MHD flow of micropolar fluid between porous vertical channel with boundary conditions of the third kind,, Ain Shams Engineering Journal, vol. 5, no. 4, p.1277–1286, (2014).

DOI: 10.1016/j.asej.2014.05.004

[27] S.Y. Ibrahim and O.D. Makinde, chemically reacting Magnetohydrodynamics (MHD) boundary layer flow of heat and mass transfer past a low-heat-resistant sheet moving vertically downwards Sci. Res. Essays 6 4762-75, (2011).

DOI: 10.1007/s13369-011-0143-8

[28] K. Bhattacharyya, S. Mukhopadhyay and G. C. Layek (2013).

[29] F.S. Ibrahim, A.M. Elaiw and A.A. Bakr, Effect of the chemical reaction and radiation absorption on unsteady MHD mixed convection flow past a semi-infinite vertical permeable moving plate with heat source and suction, Commun. Nonlinear Sci. Numer. Simul., 13(2008).

DOI: 10.1016/j.cnsns.2006.09.007

[30] R. Ravindran, M. Ganapathirao, I. Pop, Effects of chemical reaction and heat generation/absorption on unsteady mixed convection MHD flow over a vertical cone with non-uniform slot mass transfer, Int.J.Heat & Mass Transfer 73 (2014) 743-751.

DOI: 10.1016/j.ijheatmasstransfer.2014.02.053

[31] B. Venkateswarlu, P.V. SatyaNarayana. Chemical reaction and radiation absorption effects on the flow and heat transfer of a nanofluid in a rotating system, Appl Nanosci, 5 (2015), pp.351-360.

DOI: 10.1007/s13204-014-0324-3

[32] B Talukdar, D Pal, Perturbation analysis of unsteady magneto hydrodynamic convective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction, CNSNS (2010), pp.1813-1830.

DOI: 10.1016/j.cnsns.2009.07.011

[33] E.M. Sparrow, R.D. Cess Effect of magnetic field on free convection heat transfer Int. J. Heat Mass Transfer, 3 (1961), p.267–274.

DOI: 10.1016/0017-9310(61)90042-4

[34] C. H. Chen, Combined effects of Joule heating and viscous dissipation on magnetohydrodynamic flow past a permeable, stretching surface with free convection and radiative heat transfer, ASME J. Heat Transfer 132 (2010) Article no.: 064503.

DOI: 10.1115/1.4000946

[35] D Pal, B Talukdar, Combined effects of Joule heating and chemical reaction on unsteady magnetohydrodynamic mixed convection of viscous dissipating fluid over a vertical plate in porous media with thermal radiation, Mathematical and Computer Modelling, Vol. 54 (11 – 12), 2011, 3016 – 3036.

DOI: 10.1016/j.mcm.2011.07.030

[36] Jayarami Reddy Konda, Madhusudhana N.P., Ramakrishna Konijeti, MHD mixed convection flow of radiating and chemically reactive Casson nanofluid over a nonlinear permeable stretching sheet with viscous dissipation and heat source, Multidiscipline Modeling in Materials and Structures, (2018).

DOI: 10.1108/MMMS-10-2017-0127

[37] N Sandeep., C.Sulochana. Dual solutions for unsteady mixed convection flow of MHD micropolar fluid over a stretching /shrinking sheet with non-uniform heat source/sink, Engineering Science and Technology, an International Journal, 18, (2015).

DOI: 10.1016/j.jestch.2015.05.006