Entropy Generation of Variable Viscosity and Thermal Radiation on Magneto Nanofluid Flow with Dusty Fluid

Document Type : Research Paper


1 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01 Scottsville, 3209, South Africa

2 Amity Institute of Information Technology, Amity University, NewTown, Kolkata, West Bengal 700135, India

3 Deptartment of Mathematics, Jadavpur University, West Bengal, Kolkata 700032, India


The present work illustrates the variable viscosity of dust nanofluid runs over a permeable stretched sheet with thermal radiation. The problem has been modelled mathematically introducing the mixed convective condition and magnetic effect. Additionally analysis of entropy generation and Bejan number provides the fine points of the flow. The of model equations are transformed into non-linear ordinary differential equations which are then transformed into linear form using the spectral quasi-linearization method (SQLM) for direct Taylor series expansions that can be applied to non-linear terms in order to linearize them. The spectral collocation approach is then applied to solve the resulting linearized system of equations. The validity of our model is established using relative entropy generation analysis. A convergence schematic was obtained graphically. Consequence of various parameters on flow features have been delivered via graphs. Some important findings reported in this study that entropy generation analysis have significant impact in controlling the rate of heat transfer in the boundary layer region. The paper acquires realistic numerical explanations for rapidly convergent solutions using the Spectral quasi-linearization method. Convergence of the numerical solutions was monitored using the convergence graph. The initial guess values are automatically satisfied the boundary conditions. The resulting equations are then integrated using the Spectral quasi-linearization methods. The influence of radiation, heat and mass parameters on the flow are made appropriately via graphs. The effects of varying certain physical parameters of interest are examined and presented.


Main Subjects

[1] O.D. Makinde, A. Aziz, Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, International Journal of Thermal Sciences, 50, 2011, 1326-1332.
[2] X.Q. Wang and A.S. Mujumdar, A review on nanofluids - part ii: Experiments and applications, Brazilian Journal of Chemical Engineering, 25, 2008, 631-648.
[3] S. Kakac, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, International Journal of Heat and Mass Transfer, 52, 2009, 3187-3196.
[4] D. Pal, H. Mondal, Soret-Dufour effects on hydromagnetic non-Darcy convective-radiative heat and mass transfer over a stretching sheet in porous medium with viscous dissipation and Ohmic heating, Journal of Applied Fluid Mechanics, 7(3), 2014, 513–523.
[5] D. Pal, H. Mondal, MHD non-Darcy mixed convective diffusion of species over a stretching sheet embedded in a porous medium with non-uniform heat source/sink, variable viscosity and Soret effects. Communications in Nonlinear Science and Numerical Simulation, 17, 2012, 672-684.
[6] M.M. Rashidi, E. Momoniat, B. Rostami, Analytic approximate solutions for the MHD boundary layer viscoelastic fluid flow over continuously moving stretched surface by homotopy analysis method with two auxiliary parameters, Journal of Applied Mathematics, 2012, Article ID: 780415.
[7] M.M. Rashidi, E. Erfani, Analytical method for solving steady MHD and convective flow due to a rotating disk with viscous dissipation and ohmic heating, Engineering Computations, 29, 2012, 562–579.
[8] D. Pal, S. Chatterjee, Heat and mass transfer in mhd non-darcian flow of a micropolar fluid over a stretching sheet embedded in a porous media with non-uniform heat source and thermal radiation, Communications in Nonlinear Science and Numerical Simulation, 15(7), 2010, 1843-1857.
[9] R. Kandasamy, K. Periasamy, K.S. Prabhu, Effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection, International Journal of Heat and Mass Transfer, 48(7), 2005, 1388-1394.
[10] R. Kandasamy, I. Muhaimin, A.B. Khamis, Thermophoresis and variable viscosity effects on mhd mixed convective heat and mass transfer past a porous wedge in the presence of chemical reaction, Heat and Mass Transfer, 45(6), 2009, 703-712.
[11] D. Pal, H. Mondal, Hydromagnetic convective diffusion of species in Darcy–Forchheimer porous medium with non-uniform heat source/sink and variable viscosity, International Communications in Heat and Mass Transfer, 39, 2012, 913-917
[12] S. Manjunatha, B.J. Gireesha, Effects of variable viscosity and thermal conductivity on MHD flow and heat transfer of a dusty fluid, Ain Shams Engineering Journal, 7, 2016, 505-515.
[13] A. Pantokratoras, Further results on the variable viscosity on the flow and heat transfer to a continuous moving flat plate, International Journal of Engineering Science, 42, 2004, 1891-1896.
[14] S. Mukhopadhyay, G.C. Layek, Effect of thermal radiation and variable fluid viscosity on free convective and heat transfer past a porous stretching surface, International Journal of Heat and Mass Transfer, 21, 2008, 2167-78.
[15] M.S. Abel, P.G. Siddheshwar, M.M. Nandeppanawar, Heat transfer in a viscoelastic boundary layer flow over a stretching sheet with viscous dissipation and non-uniform heat source, International Journal of Heat and Mass Transfer, 50, 2007, 960-966.
[16] A. Noghrehabadi, M.R. Saffarian, R. Pourrajab, M. Ghalambaz, Entropy analysis for nanofluid flow over a stretching sheet in the presence of heat generation/absorption and partial slip. Journal of Mechanical Science and Technology, 27(3), 2013, 927-37.
[17] H. Sithole, H. Mondal, P. Sibanda, Entropy generation in a second grade magnetohydrodynamic nanofluid flow over a convectively heated stretching sheet with nonlinear thermal radiation and viscous dissipation, Results in Physics, 9, 2018, 1077-1085.
[18] N. Hidouri, M. Magherbi, H. Abbassi, A. Ben Brahim, Entropy generation in double diffusive in presence of Soret effect, Progress in Computational Fluid Dynamics, 5, 2007, 237-46.
[19] L. Aracely, I. Guillermo, P. Joel, M. Joel, L. Orlando, Entropy generation analysis of MHD nanofluid flow in a porous vertical microchannel with nonlinear thermal radiation, slip flow and convective-radiative boundary conditions, International Journal of Heat and Mass Transfer, 107, 2017, 982-94.
[20] Kh.A. Maleque, Effects of binary chemical reaction and activation energy on mhd boundary layer heat and mass transfer flow with viscous dissipation and heat generation/ absorption, ISRN Thermodynamics, 2013, Article ID 284637.
[21] D. Pal, H. Mondal, Influence of chemical reaction and thermal radiation on mixed convection heat and mass transfer over a stretching sheet in Darcian porous medium with Soret and Dufour effects, Energy Conversion and Management, 62, 2012, 102-108
[22] M. Dhlamini, K. Peri, K. Kameswaran, P. Sibanda, S. Motsa, H. Mondal, Activation energy and binary chemical reaction effects in mixed convective nanofluid flow with convective boundary conditions, Journal of Computational Design and Engineering, 6(2), 2019, 149-158.
[23] F.G. Awad, S. Motsa, M. Khumalo, Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy, PloS One, 9(9), 2014, 107622.
[24] H. Sithole, H. Mondal, S. Goqo, P. Sibanda, S. Motsa, Numerical simulation of couple stress nanofluid flow in magneto-porous medium with thermal radiation and a chemical reaction, Applied Mathematics and Computation, 339, 2018, 820-836.