Magnetohydrodynamic Maxwell Nanofluids Flow over a Stretching Surface through a Porous Medium: Effects of Non-Linear Thermal Radiation, Convective Boundary Conditions and Heat Generation/Absorption

Authors: Sameh E. Ahmed, Ramadan A. Mohamed, Abd Elraheem M. Aly, Mahmoud S. Soliman

Abstract:

In this paper, an enhancement of the heat transfer using non-Newtonian nanofluids by magnetohydrodynamic (MHD) mixed convection along stretching sheets embedded in an isotropic porous medium is investigated. Case of the Maxwell nanofluids is studied using the two phase mathematical model of nanofluids and the Darcy model is applied for the porous medium. Important effects are taken into account, namely, non-linear thermal radiation, convective boundary conditions, electromagnetic force and presence of the heat source/sink. Suitable similarity transformations are used to convert the governing equations to a system of ordinary differential equations then it is solved numerically using a fourth order Runge-Kutta method with shooting technique. The main results of the study revealed that the velocity profiles are decreasing functions of the Darcy number, the Deborah number and the magnetic field parameter. Also, the increase in the non-linear radiation parameters causes an enhancement in the local Nusselt number.

Keywords: MHD, nanofluids, stretching surface, non-linear thermal radiation, convective condition.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3299901

References:

[1] Ch. Vittal, T. Vijayalaxmi, and C. K. Reddy. MHD Stagnation Point Flow and Convective Heat Transfer of Tangent Hyperbolic Nanofluid Over a Stretching Sheet with Zero Normal Flux of Nanoparticles . J. Nanofluids 7, 844–852 (2018).
[2] Shravani, D. Ramya, and S. Joga. Heat and Mass Transfer in Stagnation Point Flow over a Stretching Sheet with Chemical Reaction and Suction/Injection in viscoelastic Nanofluids. J. Nanofluids 7, 862–869 (2018)
[3] R. Cortell. Fluid flow and radiative nonlinear heat transfer. Journal of King Saud University - Science, 26 , 161-167 (2014).
[4] K. Das, P. R. Duari, P. K. Kundu. Nanofluid flow over an unsteady stretching surface. Alexandria Engineering Journal, Volume 53, Issue 3, September 2014, Pages 5 , 53, 737-745 (2014).
[5] S. Srinivas, T. Malathy, A. S. Reddy. A note on thermal-diffusion and chemical reaction effects on MHD. Journal of King Saud University - Engineering Sciences, 28, 213-221 , (2016).
[6] H. Dessie, N. Kishan. MHD effects on heat transfer over stretching sheet. Ain Shams Engineering Journal, 5, 967-977 (2014).
[7] G. M. Pavithra, B. J. Gireesha. Unsteady flow and heat transfer of a fluid. Ain Shams Engineering Journal, 5, 613-624 (2014).
[8] N. S. Akbar, S. N., Rizwan U. Haq, Z.H. Khan. Radiation effects on MHD stagnation point flow of nano fluid. Chinese Journal of Aeronautics, 26, 1389-1397 (2013).
[9] S. Mukhopadhyay, K. Bhattacharyya. Unsteady flow of a Maxwell fluid over a stretching surface. Journal of the Egyptian Mathematical Society, 20, 229-234 (2012).
[10] K. Das. Radiation and melting effects on MHD boundary layer flow. Ain Shams Engineering Journal, 5, 1207-1214 (2014).
[11] G.K. Ramesh, B.J. Gireesha, T. Hayat, A. Alsaedi. Stagnation point flow of Maxwell fluid towards a permeable surface. Alexandria Engineering Journal, 55, 857-865 (2016).
[12] S. Manjunatha, B.J. Gireesha. Effects of variable viscosity and thermal conductivity on MHD flow. Ain Shams Engineering Journal, 7, 505-515 (2016).
[13] Y. S. Daniel, S. K. Daniel. Effects of buoyancy and thermal radiation on MHD flow over a stretching porous sheet. Alexandria Engineering Journal, 54, 705-712 (2015).
[14] M.C. Raju, N. Ananda Reddy, S.V.K. Varma. Analytical study of MHD free convective, dissipative boundary layer flow. Ain Shams Engineering 5, 1361-1369 (2014).
[15] K. Das, P. R. Duari, P. K. Kundu. Numerical simulation of nanofluid flow with convective boundary condition. Journal of the Egyptian Mathematical Society, 23,435-439 (2015).
[16] N.S. Akbar, S. Nadeem, R. U. Haq, S. Ye. MHD stagnation point flow of Carreau fluid toward a permeable shrinking sheet. Ain Shams Engineering Journal, 5, 1233-1239 (2014).
[17] K. Das. Flow and heat transfer characteristics of nanofluids in a rotating frame. Alexandria Engineering Journal, 53, 757-766 (2014).
[18] M. M. Rashidi, B. Rostami, N. Freidoonimehr, S. Abbasbandy. Free convective heat and mass transfer for MHD fluid flow over a permeable vertical stretching sheet. Ain Shams Engineering Journal, 5, 901-912 (2014).
[19] T. E. Akinbobola, S. S. Okoya. The flow of second grade fluid over a stretching sheet with variable thermal conductivity and viscosity. Journal of the Nigerian Mathematical Society, 34, 331-342 (2015).
[20] N. Haroun, S. Mondal, P. Sibanda. Unsteady Natural Convective Boundary-layer Flow of MHD Nanofluid over a Stretching Surfaces. Procedia Engineering, 127, 18-24(2015).
[21] T. Salahuddin, M.Y. Malik, A. Hussain, M. Awais, Imad Khan, Mair Khan. Analysis of tangent hyperbolic nanofluid impinging on a stretching cylinder. Results in Physics, 7,426-434 (2017).
[22] T. Hayat, M. Ijaz Khan, M. Waqas, A. Alsaedi. Newtonian heating effect in nanofluid flow. Results in Physics, 7, 256-262 (2017).
[23] S. F. Ahmmed, R. Biswas, and M. Afikuzzaman. Unsteady Magnetohydrodynamic Free Convection Flow of Nanofluid Through an Exponentially Accelerated Inclined Plate Embedded in a Porous Medium with Variable Thermal Conductivity in the Presence of Radiation. J. Nanofluids 7, 891–901 (2018).
[24] H. N. Ismail, A. A. Megahed, M. S. Abdel-Wahed, and M. Omama. Thermal Radiative Effects on MHD Casson Nanofluid Boundary Layer Over a Moving Surface. J. Nanofluids 7, 910–916 (2018)
[25] C. Haritha, B. C. Shekar, and N. Kishan. MHD Natural Convection Heat Transfer in a Porous Square Cavity Filled by Nanofluids with Viscous Dissipation. J. Nanofluids 7, 928–938 (2018).
[26] S. Mondal, S. K. Nandy, and P. Sibanda. MHD Flow and Heat Transfer of Maxwell Nanofluid Over an Unsteady Permeable Shrinking Sheet with Convective Boundary Conditions. J. Nanofluids 7, 995–1003 (2018).
[27] P. H. Nirmala, A. Saila Kumari, and C. S. K. Raju . An Integral Vonkarman Treatment of Magnetohydrodynamic Natural Convection on Heat and Mass Transfer Along a Radiating Vertical Surface in a Saturated Porous. J. Nanofluids 7, 626–634 (2018).
[28] M. M. Nandeppanavar, B. C. Prasannakumara, and J. M. Shilpa. Three-Dimensional Flow, Heat and Mass Transfer of MHD Non-Newtonian Nanofluid Due to Stretching Sheet. J. Nanofluids 7, 635–645 (2018).
[29] M. K. Nayak, Sachin Shaw, and Ali J. Chamkha. Free Convective 3D Stretched Radiative Flow of Nanofluid in Presence of Variable Magnetic Field and Internal Heating. J. Nanofluids 7, 646–656 (2018(.
[30] P. Rajendar and L. A. Babu. MHD Stagnation Point Flow of Williamson Nanofluid Over an Exponentially Inclined Stretching Surface with Thermal Radiation and Viscous Dissipation. J. Nanofluids 7, 683–693 (2018).
[31] A. Mahdy, E. Ahmed Sameh, Unsteady MHD Convective Flow of Non-Newtonian Casson Fluid in the Stagnation Region of an Impulsively Rotating Sphere, Journal of Aerospace Engineering, 30(5), 04017036 (2017).
[32] A.M. Rashad, M.M. Rashidi, G. Lorenzini, S.E. Ahmed, A.M. Aly, Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium saturated with Cu–water nanofluid, International Journal of Heat and Mass Transfer, 104, 878-889 (2017).
[33] S.E. Ahmed, Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature, Applied Mathematics and Mechanics, 38(8), 1171-1180 (2017).
[34] S. Hussain, S.E. Ahmed, T. Akbar, Entropy generation analysis in MHD mixed convection of hybrid nanofluid in an open cavity with a horizontal channel containing an adiabatic obstacle, International Journal of Heat and Mass Transfer, 114, 1054-1066 (2017).
[35] S.E. Ahmed, S.S. Mohamed, M.A. Mansour, A. Mahdy, Heat transfer and entropy generation due to a nanofluid over stretching cylinder effects of thermal stratification, Computational Thermal Sciences: An International Journal 9(1), 29-47 (2017).
[36] S.E. Ahmed, Z.A.S. Raizah, A.M. Aly, Entropy generation due to mixed convection over vertical permeable cylinders using nanofluids, Journal of King Saud University - Science, (2017).
[37] A.M. Rashad, R.S.R. Gorla, M.A. Mansour, S.E. Ahmed, Magnetohydrodynamic effect on natural convection in a cavity filled with a porous medium saturated with nanofluid, Journal of Porous Media, 20(4), 363-379 (2017).
[38] A. Mahdy, M.A. Mansour, S.E. Ahmed, S.S. Mohamed, Entropy generation of cu-water nanofluids through non-Darcy porous medium over a cone with convective boundary condition and viscous dissipation effects, Special Topics & Reviews in Porous Media: An International Journal, 8(1), 59-72 (2017).
[39] S.E. Ahmed, H.M. Elshehabey, Buoyancy-driven flow of nanofluids in an inclined enclosure containing an adiabatic obstacle with heat generation/absorption: Effects of periodic thermal conditions, International Journal of Heat and Mass Transfer, 124, 58-73 (2018).
[40] Z.A.S. Raizah, A.M. Aly, S.E. Ahmed, Natural convection flow of a power-law non-Newtonian nanofluid in inclined open shallow cavities filled with porous media, International Journal of Mechanical Sciences, 140, 376-393 (2018).