Dual Solutions for Heat and Mass Transfer in MHD Bio-Convective Flow over a Stretching/Shrinking Surface with Suction/Injection

Abstract:

The objective of the present study is to investigate the heat and mass transfer characteristics of the MHD stagnation-point flow of gyrotactic microorganisms contained nanofluid past a nonlinear stretching/shrinking sheet in presence of space and temperature dependent internal heat generation/absorption with suction/injection. The governing partial differential equations are transformed to system of ordinary differential equations by using similarity transformation and then solved numerically using Runge-Kutta based shooting technique. The influence of non-dimensional governing parameters on velocity, temperature, nanoparticle volume fraction and density of the motile microorganisms along with friction factor, local Nusselt number, local Sherwood number and the local density of the motile microorganisms was discussed and presented through graphs and tables. Dual solutions are presented for certain range of suction and injection parameters. The validity of the present results compared with the existed results.

• Periodical: International Journal of Engineering Research in Africa (Volume 21)
• Pages: 84-101
• DOI: https://doi.org/10.4028/www.scientific.net/JERA.21.84
• Online since: December 2015
• Authors: M. Satish Kumar, Naramgari Sandeep*, B. Rushi Kumar
• Keywords: Gyrotactic Microorganisms, Injection, Nanofluid, Non-Uniform Heat Source/Sink, Shrinking Sheet, Stagnation-Point Flow, Stretching Sheet, Suction

References

[1] M. Massoudi, M. Ramezan, Boundary layer heat transfer analysis of a viscoelastic fluid at a stagnation point, ASME Heat Transfer Division, 130, (1990) 81-86.

DOI: 10.1016/0093-6413(92)90037-b

[2] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, ASME Publication, 66, (1995) 99-105.

[3] N. Bachok, A. Ishak, I. Pop, Stagnation-point flow over a stretching/shrinking in a Nanofluid, Nano scale Research letters, 6, (2011) 623-631.

DOI: 10.1186/1556-276x-6-623

[4] S. Nadeem, C. Lee, Boundary layer flow of Nanofluid over an exponentially stretching surface, Nano scale Research Letters, 7, (2012) 94-101.

DOI: 10.1186/1556-276x-7-94

[5] W. Ibrahim, B. Shankar, M.M. Nandeppanavar, MHD stagnation point flow and heat transfer due to Nanofluid towards a stretching sheet, Int.J. Heat and mass transfer, 56, (2013) 1-9.

DOI: 10.1016/j.ijheatmasstransfer.2012.08.034

[6] N. Bachok, A. Ishak, R. Nazar, N. Senu, Stagnation-point flow over a permeable stretching/shrinking sheet in a copper-water Nanofluid. " Boundary value problems, 39, (2013) doi: 10. 1186/1687-2770-2013-39.

DOI: 10.1186/1687-2770-2013-39

[7] R. Nazar, M. Jaradat, M.A. Norihan, I. Pop, Stagnation-point flow past a shrinking sheet in a Nanofluid, Central European Journal of Physics, 9, (2011) 1195-1202.

DOI: 10.2478/s11534-011-0024-5

[8] S.S. Motsa, Y. Khan, S. Shateyi, A New numerical solution of Maxwell fluid over a shrinking sheet in the region of a stagnation point, Mathematical Problems in Engineering, 11, (2012) ID: 290615.

DOI: 10.1155/2012/290615

[9] M. Mustafa, T. Hayat, A. Alsaedi, Axisymmetric flow of a Nanofluid over a radially stretching sheet with convective boundary conditions, Current Nano science, 8, (2012) 328-334.

DOI: 10.2174/157341312800620241

[10] T. Hayat, S.A. Shehzad, A. Alsaedi, Soret and Dufour effects magneto hydrodynamic (MHD) flow of Casson fluid, Applied Mathematics and Mechanics, 33, (2012) 1301-1312.

DOI: 10.1007/s10483-012-1623-6

[11] S. Shateyi, O.D. Makinde, Hydromagnetic Stagnation-point flows towards a radially stretching convectively heated disk, Mathematical Problems in Engineering, (2013), ID 616947. http: /dx. doi. org/10. 1155/2013/616947.

DOI: 10.1155/2013/616947

[12] M. Shejkholeslami, S. Abelman, D.D. Ganji, Numerical simulation of MHD Nanofluid flow and heat transfer considering viscous dissipation, Int.J. Heat and Mass transfer, 79, (2014) 212-222.

DOI: 10.1016/j.ijheatmasstransfer.2014.08.004

[13] S.K. Nandy, T.R. Mahapatra, Effects of slip and heat generation/absorption on MHD stagnation flow of Nanofluid past a stretching/shrinking surface with convective boundary conditions, Int.J. Heat and Mass Transfer, 64, (2013) 1091-1100.

DOI: 10.1016/j.ijheatmasstransfer.2013.05.040

[14] N. Bachok, A. Ishak, I. Pop, Unsteady three-dimensional boundary layer flow due to a permeable shrinking sheet, Applied Mathematics and Mechanics, 31, (2010) 1421-1428.

DOI: 10.1007/s10483-010-1372-6

[15] S. Nadeem, R.U. Haq, Z.H. Khan, Numerical solution of non-Newtonian Nanofluid flow over a stretching sheet, Applied Nanoscience, 4, (2014) 625-631.

DOI: 10.1007/s13204-013-0235-8

[16] W. Ibrahim, O.D. Makinde, The effect of double stratification on boundary layer flow and heat transfer of Nanofluid over a vertical plate, Computers &Fluids, 86, (2013) 433-441.

DOI: 10.1016/j.compfluid.2013.07.029

[17] S. Nadeem, R.U. Haq, Z.H. Khan, Numerical study of MHD boundary layer flow of Maxwell fluid past a stretching sheet in the presence of nanoparticles, Journal of the Taiwan Institute of Chemical Engineers, 45, (2014) 121-126.

DOI: 10.1016/j.jtice.2013.04.006

[18] K. Bhattacharyya, S. Mukhopadhyay, G.C. Layek, Unsteady MHD boundary layer flow with diffusion and first-order chemical reaction over a permeable stretching sheet with suction or blowing, Chemical Engineering Communications, 200, (2013).

DOI: 10.1080/00986445.2012.712577

[19] S.V. Subhashini, R. Sumathi, E. Momoniat, Dual solutions of a mixed convection flow near the stagnation point region over an exponentially stretching/shrinking sheet in nanofluids, Meccanica, 49, (2014) 2467-2478.

DOI: 10.1007/s11012-014-0016-9

[20] N. Sandeep, V. Sugunamma, P. Mohan Krishna, Effects of Radiation on an Unsteady Natural Convective Flow of a EG Nimonic 80a Nanofluid past an Infinite Vertical Plate, Int. Journal of Advanced in Physics Theories Applications, 23, (2013) 36-43.

[21] C.R. Natalia, T. Grosan, I. Pop, Stagnation-point flow and mass transfer with chemical reaction past a permeable stretching/shrinking in a Nanofluid, Sains Malaysiana, 41, (2012) 1271-1279.

DOI: 10.17576/jsm-2019-4801-28

[22] A.V. Kuznetsov, The onset of Bio-convection in a suspension of Gyrotactic Microorganisms in a fluid layer of finite depth heated from below, Int. Commun. Heat Mass Transfer, 32, (2005) 574-582.

DOI: 10.1016/j.icheatmasstransfer.2004.10.021

[23] N. Sandeep, V. Sugunamma P. Mohan Krishna, Aligned Magnetic Field Radiation and Rotation Effects on Unsteady Hydro Magnetic Free Convection Flow Past an Impulsively Moving Vertical Plate in a Porous Medium, Int. Journal. Eng. Mathematics. (2014).

DOI: 10.1155/2014/565162

[24] P. Geng, A.V. Kuznetsov, Introducing the concept of effective diffusivity to evaluate the effect of Bio convection on small solid particles, Int. J. Transp. Phenom, 7, (2005a) 321-338.

[25] P. Geng, A.V. Kuznetsov, Settling of Bi-dispersed Small Solid Particles in a Dilute Suspension containing Gyrotactic Micro-organisms, Int.J. Eng. Sci, 43, (2005b) 992-1010.

DOI: 10.1016/j.ijengsci.2005.03.002

[26] A.V. Kuznetsov, D.A. Nield, Natural convective boundary-layer flow of a Nanofluid past a vertical plate, Int.J. Thermal. Sci, 49, (2010) 243-247.

DOI: 10.1016/j.ijthermalsci.2009.07.015

[27] A. Aziz, W.A. Khan, I. Pop, Free convective boundary layer flow past a horizontal flat plate embedded in porous medium filled by Nanofluid containing gyrotactic micro-organisms, Int.J. Thermal Sci., 56, (2012) 48-57.

DOI: 10.1016/j.ijthermalsci.2012.01.011

[28] K. Zaimi, A. Ishak, I. Pop, Stagnation point flow toward a stretching/shrinking sheet in a nanofluid containing both nano particles and gyrotactic micro-organisms, J. Heat transfer., 136, (2014) 041405-1-9.

DOI: 10.1115/1.4026011

[29] R. Sivaraj and B. Rushi Kumar, Unsteady MHD dusty viscoelastic fluid Couette flow in an irregular channel with varying mass diffusion, International Journal of Heat and Mass Transfer 55 (2012) 3076–3089.

DOI: 10.1016/j.ijheatmasstransfer.2012.01.049

[30] R. Sivaraj and B. Rushi Kumar, Viscoelastic fluid flow over a moving vertical cone and flat plate with variable electric conductivity, International Journal of Heat and Mass Transfer 61 (2013) 119–128.

DOI: 10.1016/j.ijheatmasstransfer.2013.01.060

[31] B. Rushi Kumar and 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

[32] B. Rushi Kumar and 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

[33] N. Sandeep, C. Sulochana, Dual solutions for unsteady mixed flow of MHD micro polar fluid over a stretching/shrinking sheet with non-uniform heat source/sink, Engineering Science and Technology an International. 18 (2015) 738-745.

DOI: 10.1016/j.jestch.2015.05.006

[34] N. Sandeep, C. Sulochana, C. S. K. Raju, M. Jayachandrababu, V. Sugunamma, Unsteady boundary layer flow of thermophoretic MHD nano fluid past a stretching sheet with space and time dependent internal heat source/sink, Applications & Applied Mathematics, 10(1) (2015).

DOI: 10.4028/www.scientific.net/ddf.388.14

[35] J.V. Ramana Reddy, V. Sugunamma, N. Sandeep, Thermo diffusion and hall current effects on an unsteady flow of a nanofluid under the influence of inclined magnetic field, Int.J. Eng. Resaech in Afrika , 20 (2016) 61-79.

DOI: 10.4028/www.scientific.net/jera.20.61

[36] C.S.K. Raju, N. Sandeep, Dual solutions for unsteady heat and mass transfer in bio-convection flow towards a rotating cone/plate in a rotating fluid, Int.J. Eng. Resaech in Afrika, 20 (2016)161-176.

DOI: 10.4028/www.scientific.net/jera.20.161