Abstract
In the present study we aim to model and examine the impact of melting and double stratification on MHD flow of Carreau liquid over a stretching sheet. Incompressible non-Newtonian liquid is electrically conducting and exposed to a constant magnetic field. The exponential space dependent internal heat source effect is incorporated in the energy expression. Mass transfer is characterized in terms of activation energy and a binary chemical reaction. In addition, Soret and Dufour phenomena are included. The boundary layer concept is utilized to simplify the governing equations. A system of ordinary differential equations is obtained through proper transformations. The coupled non-linear system is then computed by the NDSolve technique. Plots and tabulated values are arranged for interpretation of different variables. The obtained results show that the flow field is influenced appreciably by melting, the heat source, the reaction rate and the activation energy. Moreover, Nusselt and Sherwood numbers are increased by the activation energy.
References
[1] C. S. Zhou and H. Ma, Ultrasonic degradation of polysaccharide from a red algae (Porphyra yezoensis), J. Agric. Food Chem. 54 (2006), 2223–2228.10.1021/jf052763hSearch in Google Scholar PubMed
[2] A. R. Bestman, Natural convection boundary layer with suction and mass transfer in a porous medium, Int. J. Energy Res. 14 (1990), 389–396.10.1002/er.4440140403Search in Google Scholar
[3] O. D. Makinde, P. O. Olanrewaju and W. M. Charles, Unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture, Afr. Math. 22 (2011), 65–78.10.1007/s13370-011-0008-zSearch in Google Scholar
[4] K. A. Maleque, Effects of exothermic/endothermic chemical reactions with Arrhenius activation energy on MHD free convection and mass transfer flow in presence of thermal radiation, J. Thermodyn. 2013 (2013) 692516.10.1155/2013/692516Search in Google Scholar
[5] Z. Abbas, M. Sheikh and S. S. Motsa, Numerical solution of binary chemical reaction on stagnation point flow of Casson fluid over a stretching/shrinking sheet with thermal radiation, Energy 95 (2016), 12–20.10.1016/j.energy.2015.11.039Search in Google Scholar
[6] Z. Shafique, M. Mustafa and A. Mushtaq, Boundary layer flow of Maxwell fluid in rotating frame with binary chemical reaction and activation energy, Results Phys. 6 (2016), 627–633.10.1016/j.rinp.2016.09.006Search in Google Scholar
[7] M. Mustafa, J. A. Khan, T. Hayat and A. Alsaedi, Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy, Int. J. Heat Mass Transf. 108 (2017), 1340–1346.10.1016/j.ijheatmasstransfer.2017.01.029Search in Google Scholar
[8] A. Zeeshan, N. Shehzad and R. Ellahi, Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions, Results Phys. 8 (2018), 502–512.10.1016/j.rinp.2017.12.024Search in Google Scholar
[9] M. G. Reddy and N. B. Reddy, Soret and Dufour effects on steady MHD free convection flow past a semi-infinite moving vertical plate in a porous medium with viscous dissipation, Int. J. Appl. Math. Mech. 6 (2010), 1–12.10.3329/jname.v8i1.3507Search in Google Scholar
[10] T. Hayat, S. A. Shehzad and A. Alsaedi, Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid, Appl. Math. Mech. 33 (2012), 1301–1312.10.1007/s10483-012-1623-6Search in Google Scholar
[11] D. Pal and 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 Convers. Manag. 62 (2012), 102–108.10.1016/j.enconman.2012.03.017Search in Google Scholar
[12] J. V. R. Reddy, V. Sugunamma and N. Sandeep, Cross diffusion effects on MHD flow over three different geometries with Cattaneo-Christov heat flux, J. Mol. Liq. 223 (2016), 1234–1241.10.1016/j.molliq.2016.09.047Search in Google Scholar
[13] K. L. K. Lakshmi, B. J. Gireesha, R. S. R. Gorla and B. Mahanthesh, Effects of diffusion-thermo and thermo-diffusion on two-phase boundary layer flow past a stretching sheet with fluid-particle suspension and chemical reaction: A numerical study, J. Niger. Math. Soc. 35 (2016), 66–81.10.1016/j.jnnms.2015.10.003Search in Google Scholar
[14] T. Hayat, I. Ullah, T. Muhammad and A. Alsaedi, Radiative three-dimensional flow with Soret and Dufour effects, Int. J. Mech. Sci. 133 (2017), 829–837.10.1016/j.ijmecsci.2017.09.015Search in Google Scholar
[15] Q. M. Z. Zia, I. Ullah, M. Waqas, A. Alsaedi and T. Hayat, Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface, Results Phys. (2018), DOI: 10.1016/j.rinp.2018.01.001.Search in Google Scholar
[16] T. Hayat, I. Ullah, T. Muhammad and A. Alsaedi, Magnetohydrodynamic (MHD) three-dimensional flow of second grade nanofluid by a convectively heated exponentially stretching surface, J. Mol. Liq. 220 (2016), 1004–1012.10.1016/j.molliq.2016.05.024Search in Google Scholar
[17] B. Mahanthesh and B. J. Gireesha, Scrutinization of thermal radiation, viscous dissipation and Joule heating effects on Marangoni convective two-phase flow of Casson fluid with fluid-particle suspension, Results Phys. 8 (2018), 869–878.10.1016/j.rinp.2018.01.023Search in Google Scholar
[18] T. Hayat, I. Ullah, T. Muhammad, A. Alsaedi and S. A. Shehzad, Three-dimensional flow of Powell-Eyring nanofluid with heat and mass flux boundary conditions, Chin. Phys. B 25 (2016), 074701.10.1088/1674-1056/25/7/074701Search in Google Scholar
[19] B. Mahanthesh and B. J. Gireesha, Thermal Marangoni convection in two-phase flow of dusty Casson fluid, Results Phys. 8 (2018), 537–544.10.1016/j.rinp.2017.12.066Search in Google Scholar
[20] T. Hayat, I. Ullah, M. Waqas and A. Alsaedi, Flow of chemically reactive magneto Cross nanoliquid with temperature-dependent conductivity, Appl. Nanosciences 8 (2018), 1453–1460.10.1007/s13204-018-0813-xSearch in Google Scholar
[21] B. Mahanthesh, P. B. Sampath Kumar, B. J. Gireesha, S. Manjunatha and R. S. R. Gorla, Nonlinear convective and radiated flow of tangent hyperbolic liquid due to stretched surface with convective condition, Results Phys. 7 (2017), 2404–2410.10.1016/j.rinp.2017.07.012Search in Google Scholar
[22] B. Mahanthesh, B. J. Gireesha, M. Sheikholeslami, S. A. Shehzad and P. B. S. Kumar, Nonlinear Radiative Flow of Casson Nanoliquid Past a Cone and Wedge with Magnetic Dipole: Mathematical Model of Renewable Energy, J. Nanofluids 7 (2018), 1089–1100.10.1166/jon.2018.1546Search in Google Scholar
[23] P. J. Carreau, Rheological equations from molecular network theories, Trans. Soc. Rheol. 16 (1972), 99–127.10.1122/1.549276Search in Google Scholar
[24] P. J. Carreau, An analysis of the viscous behaviour of polymer solutions, Can. J. Chem. Eng. 57 (1979), 135–140.10.1002/cjce.5450570202Search in Google Scholar
[25] M. Khan, Hashim, Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet, AIP Adv. 5 (2015), 107203.10.1063/1.4932627Search in Google Scholar
[26] T. Hayat, M. Waqas, S. A Shehzad and A. Alsaedi, Stretched flow of Carreau nanofluid with convective boundary condition, Pramana J. Phys. 86 (2016), 3–17.10.1007/s12043-015-1137-ySearch in Google Scholar
[27] M. Khan, M. Y. Malik, T. Salahuddin and I. Khan, Numerical modeling of Carreau fluid due to variable thicked surface, Results Phys. 7 (2017), 2384–2390.10.1016/j.rinp.2017.07.008Search in Google Scholar
[28] T. Hayat, I. Ullah, B. Ahmad and A. Alsaedi, Radiative flow of Carreau liquid in presence of Newtonian heating and chemical reaction, Results Phys. 7 (2017), 715–722.10.1016/j.rinp.2017.01.019Search in Google Scholar
[29] M. Khan, H. Sardar and M. M. Gulzar, On radiative heat transfer in stagnation point flow of MHD Carreau fluid over a stretched surface, Results Phys. 8 (2018), 524–531.10.1016/j.rinp.2017.12.046Search in Google Scholar
[30] B. Mahanthesh, B. J. Gireesha, R. S. Reddy Gorla, F. M. Abbasi and S. A. Shehzad, Numerical solutions for magnetohydrodynamic flow of nanofluid over a bidirectional non-linear stretching surface with prescribed surface heat flux boundary, J. Magn. Magn. Mater. 417 (2016), 189–196.10.1016/j.jmmm.2016.05.051Search in Google Scholar
[31] T. Hayat, I. Ullah, A. Alsaedi, M. Waqas and B. Ahmad, Three-dimensional mixed convection flow of Sisko nanoliquid, Int. J. Mech. Sci. 133 (2017), 273–282.10.1016/j.ijmecsci.2017.07.037Search in Google Scholar
[32] B. J. Gireesha, B. Mahanthesh, R. S. R. Gorla and P. T. Manjunatha, Thermal radiation and Hall effects on boundary layer flow past a non-isothermal stretching surface embedded in porous medium with non-uniform heat source/sink and fluid-particle suspension, Heat Mass Transf. 52 (2016), 897–911.10.1007/s00231-015-1606-3Search in Google Scholar
[33] T. Hayat, I. Ullah, A. Alsaedi and S. Asghar, Flow of magneto Williamson nanoliquid towards stretching sheet with variable thickness and double stratification, Radiat. Phys. Chem. 152 (2018), 151–157.10.1016/j.radphyschem.2018.07.006Search in Google Scholar
[34] M. Sheikholeslami and H. B. Rokni, Numerical modeling of nanofluid natural convection in a semi annulus in existence of Lorentz force, Comput. Methods Appl. Mech. Eng. 317 (2017), 419–430.10.1016/j.cma.2016.12.028Search in Google Scholar
[35] T. Hayat, Z. Hussain, A. Alsaedi and B. Ahmad, Numerical study for slip flow of carbon-water nanofluids, Comput. Methods Appl. Mech. Eng. 319 (2017), 366–378.10.1016/j.cma.2017.02.021Search in Google Scholar
[36] Z. Hussain, T. Hayat, A. Alsaedi and B. Ahmad, Three-dimensional convective flow of CNTs nanofluids with heat generation/absorption effect: A numerical study, Comput. Methods Appl. Mech. Eng. 329 (2018), 40–54.10.1016/j.cma.2017.09.026Search in Google Scholar
[37] C. S. K. Rajua, N. Sandeep and A. Malvandi, Free convective heat transfer of MHD Cu-kerosene nanofluid over a cone with temperature dependent viscosity, Acta Astronaut. 129 (2016), 419–428.10.1016/j.actaastro.2016.10.011Search in Google Scholar
[38] C. S. K. Raju and N. Sandeep, MHD slip flow of a dissipative Casson fluid over a moving geometry with heat source/sink: A numerical study, Acta Astronaut. 133 (2017), 436–443.10.1016/j.actaastro.2016.11.004Search in Google Scholar
[39] A. M. Salem and M. A. El-Aziz, MHD-mixed convection and mass transfer from a vertical stretching sheet with diffusion of chemically reactive species and space- or temperature-dependent heat source, Can. J. Phys. 85 (2007), 359–373.10.1139/p07-048Search in Google Scholar
[40] T. Hayat, I. Ullah, A. Alsaedi and B. Ahmad, Numerical simulation for homogeneous–heterogeneous reactions in flow of Sisko fluid, J. Braz. Soc. Mech. Sci. Eng. 40 (2018), 73.10.1007/s40430-018-0999-6Search in Google Scholar
[41] Z. Iqbal, Z. Mehmood and B. Ahmad, Numerical study of entropy generation and melting heat transfer on MHD generalised non-Newtonian fluid (GNF): Application to optimal energy, Pramana J. Phys. 90 (2018), 64.10.1007/s12043-018-1557-6Search in Google Scholar
[42] T. Hayat, I. Ullah, A. Alsaedi and B. Ahmad, Simultaneous effects of non-linear mixed convection and radiative flow due to Riga-plate with double stratification, J. Heat Transf. 140 (2018), 102008.10.1115/1.4039994Search in Google Scholar
[43] B. J. Gireesha, P. B. S. Kumar, B. Mahanthesh, S. A. Shehzad and M. Abbasi, Nonlinear gravitational and radiation aspects in nanoliquid with exponential space dependent heat source and variable viscosity, Microgravity Sci. Technol. 30 (2018), 257–264.10.1007/s12217-018-9594-9Search in Google Scholar
[44] T. Hayat, I. Ullah, M. Farooq and A. Alsaedi, Analysis of non-linear radiative stagnation point flow of Carreau fluid with homogeneous-heterogeneous reactions, Microsyst. Technol. (2018). DOI: 10.1007/s00542-018-4157-y.Search in Google Scholar
[45] B. Mahanthesh, B. J. Gireesha, B. C. P. Kumara and N. S. Shashikumar, Marangoni convection radiative flow of dusty nanoliquid with exponential space dependent heat source, Nucl. Eng. Technol. 49 (2017), 1660–1668.10.1016/j.net.2017.08.015Search in Google Scholar
[46] B. Mahanthesh, B. J. Gireesha, N. S. Shashikumar and S. A. Shehzad, Marangoni convective MHD flow of SWCNT and MWCNT nanoliquids due to a disk with solar radiation and irregular heat source, Physica E 94 (2017), 25–30.10.1016/j.physe.2017.07.011Search in Google Scholar
[47] B. Mahanthesh, B. J. Gireesha, B. C. Prasannakumara and P. B. S. Kumar, Magneto-Thermo-Marangoni convective flow of Cu-H2O nanoliquid past an infinite disk with particle shape and exponential space based heat source effects, Results Phys. 7 (2017), 2990–2996.10.1016/j.rinp.2017.08.016Search in Google Scholar
[48] T. Hayat, I. Ullah, A. Alsaedi and S. Asghar, MHD stagnation-point flow of Sisko liquid with melting heat transfer and heat generation/absorption, J. Therm. Sci. Eng. Appl. 10 (2018) 051015.10.1115/1.4040032Search in Google Scholar
[49] M. Khan, L. Ahmad and M. Ayaz, Numerical simulation of unsteady 3D magneto-Sisko fluid flow with nonlinear thermal radiation and homogeneous-heterogeneous chemical reactions, Pramana J. Phys. 91 (2018), 13.10.1007/s12043-018-1585-2Search in Google Scholar
[50] I. L. Animasaun, Effects of thermophoresis, variable viscosity and thermal conductivity on free convective heat and mass transfer of Non-Darcian MHD dissipative casson fluid flow with suction and nth order of chemical reaction, J. Niger. Math. Soc. 34 (2015), 11–31.10.1016/j.jnnms.2014.10.008Search in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Research Articles
- Numerical Exploration of MHD Radiative Micropolar Liquid Flow Driven by Stretching Sheet with Primary Slip: A Comparative Study
- Microscale Thermal Energy Transfer Between Thin Films with Vacuum Gap at Interface
- Attainability of Maximum Work and the Reversible Efficiency of Minimally Nonlinear Irreversible Heat Engines
- Modeling Phase Behavior of Semi-Clathrate Hydrates of CO2, CH4, and N2 in Aqueous Solution of Tetra-n-butyl Ammonium Fluoride
- The Energy-Momentum Tensor in Relativistic Kinetic Theory: The Role of the Center of Mass Velocity in the Transport Equations for Multicomponent Mixtures
- Finite Time Thermodynamics: Realizability Domain of Heat to Work Converters
- Cellulose Acetate Mixed Matrix Membranes Coated with PEG/TiO2 for Removal of Pb(II) Ions from Aqueous Solutions: Combined Experimental and Quantum Chemical Modeling Investigation
- Attributes of Activation Energy and Exponential Based Heat Source in Flow of Carreau Fluid with Cross-Diffusion Effects
Articles in the same Issue
- Frontmatter
- Research Articles
- Numerical Exploration of MHD Radiative Micropolar Liquid Flow Driven by Stretching Sheet with Primary Slip: A Comparative Study
- Microscale Thermal Energy Transfer Between Thin Films with Vacuum Gap at Interface
- Attainability of Maximum Work and the Reversible Efficiency of Minimally Nonlinear Irreversible Heat Engines
- Modeling Phase Behavior of Semi-Clathrate Hydrates of CO2, CH4, and N2 in Aqueous Solution of Tetra-n-butyl Ammonium Fluoride
- The Energy-Momentum Tensor in Relativistic Kinetic Theory: The Role of the Center of Mass Velocity in the Transport Equations for Multicomponent Mixtures
- Finite Time Thermodynamics: Realizability Domain of Heat to Work Converters
- Cellulose Acetate Mixed Matrix Membranes Coated with PEG/TiO2 for Removal of Pb(II) Ions from Aqueous Solutions: Combined Experimental and Quantum Chemical Modeling Investigation
- Attributes of Activation Energy and Exponential Based Heat Source in Flow of Carreau Fluid with Cross-Diffusion Effects