Numerical Scrutinization of Three Dimensional Casson-Carreau Nano Fluid Flow

Document Type: Research Paper


1 Research Scholar in Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, A.P, India

2 Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, A.P, India

3 Department of Mathematics, Govt. Degree College, Yellandu, Bhadradri Kothagudem, Telangana, India


This study presents the computational analysis of three dimensional Casson and Carreau nanofluid flow concerning the convective conditions. To do so, the flow equations are modified to nonlinear system of ODEs after using appropriate self-similarity functions. The solution for the modified system is evaluated by numerical techniques. The results show the impacts of involving variables on flow characteristics and the outcomes of the friction factors are evaluated as well. In this study, the outcomes to local Nusselt number and Sherwood numbers are evaluated. Favourable comparison is performed with previously available outcomes. The achieved results are similar to solutions obtained by other researchers. The results are presented for flow characteristics in the case of Casson and Carreau fluids. Velocities are reduced for the growing values of permeability and velocity slip parameters in case of Casson and Carreau nanofluids. Temperature field enhances with the hike in the estimations of thermophoresis parameter and the thermal Biot number in case of Casson and Carreau nanofluids. Enhancing values of velocity slip parameter results in decrease in the skin friction coefficients and the rate of heat transfer, and rise in the rate of mass transfer in case of Casson and Carreau nanofluids.


Main Subjects

[1] Sakiadis, B.C., Boundary layer behaviour on continuous solid surfaces, AICHE Journal, 7(1), 1961, 26–28.

[2] Chamka, A.J., Aly, A.M., MHD free convection flow of a nanofluid past a vertical plate in the presence of heat generation or absorption effects, Chemical Engineering Communications, 198(3), 2010, 425–441.

[3] Hayat, T., Khan, M., Khan, M.I., Alsaedi, A., Ayub, M., Electromagnetic squeezing rotational flow of Carbon (C)- Water (H2O) Kerosene oil nanofluid past a Riga plate: A numerical study, PLOS ONE, 12(8), 2017, 180976.

[4] Hsiao, K.L., To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-Nanofluid with parameters control method, Energy, 130, 2017, 486-499.

[5] Nadeem, S., Haq, R.U.I., Akbar, N.S., Khan, Z.H., MHD three dimensional Casson fluid flow past a porous linearly stretching sheet, Alexandria Engineering Journal, 52, 2013, 577–582.

[6] Shehzad, S.A. , Hayat, T., Alsaedi, A., Three-dimensional MHD flow of Casson fluid in porous medium with heat generation, Journal of Applied Fluid Mechanics, 9, 2016, 215–223.

[7] Raju, C.S.K., Sandeep, N., Jayachandrababu, M., Sugunamma, V., Dual solutions for three-dimensional MHD flow of a nanofluid over a nonlinearly permeable stretching sheet, Alexandria Engineering Journal, 55(1), 2016, 151–162.

[8] Akbar, N.S., Nadeem, S., Khan, Z.H., Numerical simulation of peristaltic flow of a Carreau nanofluid in an asymmetric channel, Alexandria Engineering Journal, 53, 2014, 191–197.

[9] Akbar, N.S., Nadeem, S., Haq, R.U.I., Ye, S., MHD stagnation point flow of Carreau fluid toward a permeable shrinking sheet: dual solutions, Ain Shams Engineering Journal, 5, 2014, 1233–1239.

[10] Hayat, T., Bilal Ashraf, M., Shehzad, S.A., Alsaedi, A., 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, 2015, 803–813.

[11] Nagasantoshi, P., Ramana Reddy, G.V., Gnaneswara Reddy, M., Padma, P., Influence of Non-Uniform heat source on Casson and Carreau fluid flows over a stretching sheet with slip and convective conditions, International Journal of Pure and Applied Mathematics, 117(13), 2017, 363-371.

[12] Hsiao, K.L., Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet, Applied Thermal Engineering, 98, 2016, 850-861.

[13] Olanrewaju, P.O., Olanrewaju, M.A., Adesanya, A.O., Boundary layer flow of nanofluids over a moving surface in a flowing fluid in the presence of radiation, International Journal of Applied Science and Technology, 2(1), 2012, 274-285.

[14] Hsiao, K.L., Combined Electrical MHD Heat Transfer Thermal Extrusion System Using Maxwell Fluid with Radiative and Viscous Dissipation Effects, Applied Thermal Engineering, 112, 2016, 1281-1288.

[15] Hsiao, K.L., Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature, International Journal of Heat and Mass Transfer, 112, 2017, 983-990.

[16] Sandeep, N., Sugunamma, V., Mohan Krishna, P., Effects of radiation on an unsteady natural convection flow of an E G Nimonic 80a nanofluid past an infinite vertical plate, Journal of Theoretical and Applied Physics, 23, 2013, 36–43.

[17] Raju, C.S.K., Jayachandrababu, M., Sandeep, N., Chemically reacting radiative MHD Jefferey nanofluid flow over a cone in porous medium, International Journal of Engineering Research in Africa, 19, 2016, 75–90.

[18] Saleem, N., Hayat, T., Alsaedi, A., Effectsof induced magnetic field and slip condition on peristaltic transport with heat and mass transfer in a non-uniform channel, International Journal of Physical Sciences, 7(2), 2012, 191-204.

[19] Sandeep, N., Sulochana, C., 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, 738–745.

[20] Raju, C.S.K., Sandeep, N., Sulochana, C., Sugunamma, V., Effects of aligned magnetic field and radiation on the flow of ferro fluids over a flat plate with non-uniform heat source/sink, International Journal of Science and Engineering, 8(2), 2015, 151–158.

[21] As, A., Zhou, Z., Hassan, M., Bhatti, M.M., Computational study of magnetized blood flow in the presence of Gyrotactic microorganisms propelled through a permeable capillary in a stretching motion, International Journal for Multiscale Computational Engineering, 16, 2018, 303-320.

[22] Bhatti, M.M., Lu, D.Q., Head-on collision between two hydro elastic solitary waves in shallow water, Qualitative Theory of Dynamical Systems, 17, 2018, 103-122

[23] Bhatti, M.M., Lu, D.Q., Analytical Study of the Head-On Collision Process between Hydroelastic Solitary Waves in the Presence of a Uniform Current, Symmetry, 11, 2019, 333.

[24] Bhatti, M.M., Rashidi, M.M., Effects of thermo-diffusion and thermal radiation on Williamson nanofluid over a porous shrinking/stretching sheet, Journal of Molecular Liquids, 221, 2016, 567-573

[25] Nagasantoshi, P., Ramana Reddy, G.V., Gnaneswara Reddy, M., Padma, P., Heat and mass transfer of Non-Newtonian Nanofluid flow over a stretching sheet with non-uniform heat source and Variable viscosity, Journal of Nanofluids, 7, 2018, 821-832.

[26] Hayat, T., Khan, M.I., Farooq, M., Alsaedi, A., Waqas, M., Yasmeen, T., Impact of Cattaneo–Christov heat flux model in flow of variable thermal conductivity fluid over a variable thicked surface, International Journal of Heat and Mass Transfer, 99, 2016, 702–710.

[27] Hayat, T., Khan, M.I., Farooq, M., Yasmeen, T., Alsaedi, A., Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions, Journal of Molecular Liquids, 220, 2016, 49-55.

[28] Khan, M.I., Waqas, M., Hayat, T., Alsaedi, A., A comparative study of casson fluid with homogeneous-heterogeneous reactions, Journal of Colloid and Interface Science, 298(15), 2017, 85.

[29] Khan, M.I., Waqas, M., Hayat, T., Imran Khan, M., Alsaedi, A., Numerical simulation of nonlinear thermal radiation and homogeneous-heterogeneous reactions in convective flow by a variable thicked surface, Journal of Molecular Liquids, 246, 2017, 259-267.

[30] Annimasun, I.L., Raju, C.S.K., Sandeep, N., Unequal diffusivities case of homogeneous–heterogeneous reactions within viscoelastic fluid flow in the presence of induced magnetic-field and nonlinear thermal radiation, Alexgrandia Engineering Journal, 55(2), 2016, 1595–1606.

[31] Khan, M.I., Hayat, T., Imran Khan, M., Alsaedi, A., Activation energy impact in nonlinear radiative stagnation point flow of Cross nanofluid, International Communications in Heat and Mass Transfer, 91, 2018, 216-224.

[32] Bhatti, M.M., Abbas, T., Rashidi, M.M., Sayed Ali, M.E.I., Yang, Z., Entropy generation on MHD Eyring–Powell nanofluid through a permeable stretching surface, Entropy, 18, 2016, 224.

[33] Hayat, T., Khan, M.I., Quayyam, S., Alsaedi, A., Entropy generation in flow with silver and copper nanoparticles, Colloids and surfaces A, Physicochemecal and Engineering Aspects, 539, 2018, 335-346.

[34] Hayat, T., Quayyam, S., Khan, M.I., Alsaedi, A.,Entropy generation in magnetohydrodynamic radiative flow due to rotating disk in presence of viscous dissipation and Joule heating, Physics of Fluids, 30, 2018, 017101.

[35] Waleed, M., Khan, A., Khan, M.I., Hayat, T., Entropy generation minimization (EGM) of nanofluid flow by a thin moving needle with nonlinear thermal radiation, Physica B: Condensed Matters, 534, 2018, 113-119.

[36] Hayat, T., Khan, M.I., Quayyam, S., Alsaedi, A., Imran Khan, M., New thermodynamics of entropy generate on minimization with nonlinear thermal radiation and nano materials, Physics Letters A, 532(11), 2018, 749-760.

[37] Khan, M.I., Ullah, S., Hayat, T., Imran Khan, M., Alsaedi, A., Entropy generation minimization (EGM) for convection nanomaterial flow with nonlinear radiative heat flux, Journal of Molecular Liquids, 260, 2018, 279-291.

[38] Khan, M.I., Qayyum, S., Hayat, T., Imran Khan, M., Alsaedi, A., Ahmad Khan, T., Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection, Physics Letters A, 382(31), 2018, 2017-2026.

[39] Khan, N.B., Ibrahim, Z., Khan, M.I., Hayat, T., Javeed, M.F., VIV study of an elastically mounted cylinder having low mass-damping ratio using RANS model, International Journal of Heat and Mass Transfer, 121, 2018, 309-314.

[40] Hayat, T., Khan, M.I., Quayyam, S., Alsaedi, A., Modern developments about statistical declaration and probable error for skin friction and Nusselt number with copper and silver nanoparticles, Chinese Journal of Physics, 55(6), 2017, 2501-2513.

[41] Raju, C.S.K., Sandeep, N., Sugunamma, V., Jayachandrababu, M., Ramanareddy, J.V., Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface, Engineering Science and Technology, an International Journal, 19, 2016, 45-52.

[42] Hayat, T., Shezad, S. A., Alsaedi, A., Soret and Dufour effects in magnetohydrodynamic (MHD) flow of Casson fluid, Applied Mathematics and Mechanics, 33, 2012, 1301-1312.

[43] Ali, M.E., Sandeep, N., Cattaneo-Christov model for radiative heat transfer of magnetohydrodynamic Casson-ferrofluid: a numerical study, Results in Physics, 7, 2017, 21–30.

[44] Hayat, T., Asad, S., Mustafa, M., Alsaedi, A., Boundary layer flow of Carreau fluid over a convectively heated stretching sheet, Applied Mathematics and Computation, 246, 2014, 12–22.

[45] Raju, C.S.K., Sandeep, N., Unsteady three-dimensional flow of Casson–Carreau fluids past a stretching surface, Alexandria Engineering Journal, 55, 2016, 1115–1126.