MHD Casson Nanofluid Past a Stretching Sheet with the Effects of Viscous Dissipation, Chemical Reaction and Heat Source/Sink

Document Type : Research Paper


1 Department of Humanities and Sciences (Mathematics), CVR College of Engineering, Hyderabad-501510, Telangana State, India

2 Department of Mathematics, GITAM University, Hyderabad-502329, Telangana State, India


The effects of viscous dissipation, chemical reaction and activation energy on the two-dimensional hydromagnetic convective heat and mass transfer flow of a Casson nanofluid fluid over a stretching sheet with thermal radiation, have been discussed in detail. The formulated highly nonlinear equations for the above-mentioned flow are converted into first-order ordinary differential equations (ODEs). The shooting method along with Adams-Bash forth Moulton method is used to solve the BVP by using the Fortran language program. The numerical results are computed by choosing different values of the involved physical parameters and compared with earlier published results and excellent validation of the present numerical results has been achieved for local Nusselt number and local Sherwood number. The graphical numerical results of different physical quantities of interest are presented to analyze their dynamics under the varying physical quantities. From the results, it has been remarked that the heat transfer rate escalates for the large values of radiation parameter, viscous dissipation for the Casson nanofluid.


[1] L. J. Crane, Flow past a stretching plate, Zeitschrift fur angewandte Mathematik und Physik, 21(4), 1970, 645-647.
[2] K. B. Pavlov, Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface, Magnitnaya Gidrodinamika, 4(1), 1974, 146-147.
[3] T. Fang and J. Zhang, Closed-form exact solutions of MHD viscous flow over a shrinking sheet, Communications in Nonlinear Science and Numerical Simulation, 14(7), 2009, 2853-2857.
[4] H. I. Andersson, K. H. Bech, and B. S. Dandapat, Magnetohydrodynamic flow of a power-law fluid over a stretching sheet, International Journal of Non-Linear Mechanics, 27(6), 1992, 929-936.
[5] K. Bhattacharyya and G. C. Layek, chemically reactive solute distribution in MHD boundary layer flow over a permeable stretching sheet with suction or blowing, Chemical Engineering Communications, 197(12), 2010, 1527-1540.
[6] K. Bhattacharyya, Effects of radiation and heat source/sink on unsteady MHD boundary layer ow and heat transfer over a shrinking sheet with suction/injection, Frontiers of Chemical Science and Engineering, 5(3), 2011, 376-384.
[7] H. Tabaei, M. A. Moghimi, A. Kimiaeifar, and M. A. Moghimi, Homotopy analysis and differential quadrature solution of the problem of free-convective magnetohydrodynamic flow over a stretching sheet with the hall effect and mass transfer taken into account, Journal of Applied Mechanics and Technical Physics, 52(4), 2011, 624.
[8] S. P. Anjali Devi, B. Ganga, Effects of viscous and Joules dissipation on MHD flow, heat and mass transfer past a stretching porous surface embedded in a porous medium, Nonlinear Analysis: Modelling and Control, 14, 2009, 303-314.
[9] O. D. Makinde, W. N. Mutuku, Hydromagnetic thermal boundary layer of nanofluids over a convectively heated at plate with viscous dissipation and Ohmic heating, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 76, 2014, 181-192.
[10] S. E. Ahmed, A. K. Hussein, H. A. Mohammed, S. Sivasankaran, Boundary layer flow and heat transfer due to permeable stretching tube in the presence of heat source/sink utilizing nanofluids, Applied Mathematics and Computation, 238, 2014, 149-162.
[11] S. Akilu, M. Narahari, Effects of heat generation or absorption on free convection flow of a nanofluid past an isothermal inclined plate, Advanced Materials Research, 970, 2014, 267-271.
[12] T. R. Mahapatra and A. S. Gupta, Heat transfer in stagnation-point flow towards a stretching sheet, Heat and Mass Transfer, 38(6), 2002, 517-521.
[13] R. Nazar, N. Amin, D. Filip, and L. Pop, Stagnation point ow of a micropolar fluid towards a stretching sheet, International Journal of Non-Linear Mechanics, 39(7), 2004, 1227-1235.
[14] A. Raptis, C. Perdikis, and H. S. Takhar, Effect of thermal radiation on MHD flow, Applied Mathematics and Computation, 153(3), 2004, 645-649.
[15] A. Ishak, Jafar, R. A. Nazar, and L. Pop, MHD stagnation point flow towards a stretching sheet, Physica A: Statistical Mechanics and its Applications, 388(17), 2009, 3377-3383.
[16] N. S. Akbar, S. Nadeem, R. U. Haq, and Z. H. Khan, Radiation effects on MHD stagnation point ow of nanofluid towards a stretching surface with convective boundary condition, Chinese Journal of Aeronautics, 26(6), 2013, 1389-1397.
[17] R. U. Haq, S. Nadeem, Z. H. Khan, and N. S. Akbar, Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet, Physica E: Low-dimensional Systems and Nanostructures, 65, 2015, 17-23.
[18] M. Farooq, M. I. Khan, M. Waqas, T. Hayat, A. Alsaedi, and M. I. Khan, MHD stagnation point ow of viscoelastic nanofluid with non-linear radiation effects, Journal of Molecular Liquids, 221, 2016, 1097-1103.
[19] R. K. Dash, K. N. Mehta, and G. Jayaraman, Casson fluid flow in a pipe filled with a homogeneous porous medium, International Journal of Engineering Science, 34(10), 1996, 1145-1156.
[20] J. Venkatesan, D. S. Sankar, K. Hemalatha, and Y. Yatim, Mathematical analysis of Casson fluid model for blood rheology in stenosed narrow arteries, Journal of Applied Mathematics, 13, 2013, 1-11.
[21] T. Hayat, S. A. Shehzad, S. A. Alsaedi, and M. S. Alhothuali, Mixed convection stagnation point flow of Casson fluid with convective boundary conditions, Chinese Physics Letters, 29(11), 2012, 114704.
[22] S. Mukhopadhyay, P. R. De, K. Bhattacharyya, and G. Layek, Casson fluid flow over an unsteady stretching surface, Ain Shams Engineering Journal, 4(4), 2013, 933-938.
[23] S. Mukhopadhyay, Casson fluid flow and heat transfer over a nonlinearly stretching surface, Chinese Physics B, 22(7), 2013, 074701.
[24] S. Nadeem, R. U. Haq, N. S. Akbar, and Z. Khan, MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet, Alexandria Engineering Journal, 52(4), 2013, 577-582.
[25] A. Khalid, I. Khan, A. Khan, and S. Shafie, Unsteady MHD free convection flow of Casson fluid past over an oscillating vertical plate embedded in a porous medium, Engineering Science and Technology, an International Journal, 18(3), 2015, 309-317.
[26] M. I. Khan, M. Waqas, T. Hayat, and A. Alsaedi, A comparative study of Casson fluid with homogeneous-heterogeneous reactions, Journal of Colloid and Interface Science, 498, 2017, 85-90.
[27] Z. Shah, S. Islam, H. Ayaz, and S. Khan, Radiative heat and mass transfer analysis of micropolar nanofluid flow of Casson fluid between two rotating parallel plates with effects of hall current, Journal of Heat Transfer, 141(2), 2019, 022401.
[28] S. Mei, C. Qi, M. Liu, F. Fan, L. Liang, Effects of paralleled magnetic field on thermo-hydraulic performances of Fe3O4-water nanofluids in a circular tube, International Journal of Heat and Mass Transfer, 134, 2019, 704-721.
[29] C. Qi, T. Luo, M. Liu, F. Fan, Y. Yan, Experimental study on the flow and heat transfer characteristics of nanofluids in double-tube heat exchangers based on thermal efficiency assessment, Energy Conservation and Management, 197, 2019, 111870
[30] C. Qi, M. Liu, T. Luo, Y. Pan, Z. Rao, Effects of twisted tape structures on thermo-hydraulic performances of nanofluids in a triangular tube, International Journal of Heat and Mass Transfer, 127(Part C), 2018, 146-159.
[31] T. Hayat, M. Bilal Ashraf, S.A. Shehzad, A. Alsaedi, Mixed Convection Flow of Casson Nanofluid over a Stretching Sheet with Convectively Heated Chemical Reaction and Heat Source/Sink, Journal of Applied Fluid Mechanics, 8(4), 2015, 803-813.