## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Hydromagnetic flow of a Carreau fluid in a curved channel with non-linear thermal radiation

**ABSTRACT**

The study depicts the variations in the hydromagnetics flow of a Careau fluid in a semi permeable curved channel with convective boundary condition. Furthermore, Rosseland approximation is also considered to analyze the nonlinear thermal radiation effects. Curvilinear coordinates system has been adopted for the mathematical modeling of the flow equations. The attained set of governing equation are then converted into nonlinear dimensionless differential equations, by making use of similarity variables which are later treated by shooting method. In addition, the Newtonâ€˜s Raphson method is also incepted to improve the accuracy of the obtained numerical result. The velocity field and temperature distributions are affected by various involved parameter which are presented in graphs and in table form. It is noticed that the velocity profiles are influenced by the change in the Weissenberg number

**KEYWORDS**

PAPER SUBMITTED: 2017-10-11

PAPER REVISED: 2018-01-21

PAPER ACCEPTED: 2018-02-03

PUBLISHED ONLINE: 2018-03-04

- Berman, A. S., Laminar Flow in Channel With Porous Walls, J. Appl. Phys., 24 (1953) pp. 1232-1235
- Hayat, T., Abbas, Z., Heat Transfer Analysis on the MHD Flow of a Second Grade Fluid in a Channel with Porous Medium, Chaos, Solut. Frac., 38 (2008) pp. 556-567
- Kumar. J. P., et al., Fully Developed Force Convective Flow of a Micropolar and Viscous Fluids in a Vertical Channel, Appl. Maths. Modell. 34 (2010) pp. 1175-1186
- Sajid. M., et al., Homotopy Analysis for Boundary Layer Flow of a Micropolar Fluid Through a Porous Channel, Appl. Maths. Modell. 33 (2009) pp. 4120-4125
- Rassoulinejad-Mousavi, S. M., et al., Heat Transfer Through a Porous Saturated Channel With Permeable Walls Using Two Equations Energy Model. J. Porous Med., 16 (2013) pp. 241-254
- Sheikholeslami, M., et al., Analytical Investigation of MHD Nano Fluid Flow in a Semi Porous Channel, Powd. Tech., 246 (2013) pp. 327-336
- Hatami, M., et al., Nano Fluid Flow and Heat Transfer in an Asymmetric Porous Channel with Expanding or Contracting Wall, J. Molec. Liqu., 195 (2014) pp. 230-239
- Pantokratoras, A., Fang, T., Sakiadis Flow With Nonlinear Rosseland Thermal Radiation, Phys. Scrip., 87:015703
- Pantokratoras, A., Fang, T., Blasius Flow With Nonlinear Rosseland Thermal Radiation, Meccanica 49 (2014) 6 pp. 1539-1545
- Cortell, R., Fluid Flow and Radiative Nonlinear Heat Transfer Over a Stretching Sheet, J. King Saud Uni. Sci., 26 (2013).
- Kumar, K. G., et al., Nonlinear Thermal Radiation Effect on Williamson Fluid with Particle Liquid Suspension Past a Stretching Surface, Result in Physics, 7 (2017) pp. 3196-3202
- Mustafa, M., et al., Nonlinear Radiation Heat Transfer Effects in the Natural Convective Boundary Layer Flow of Nano Fluid Past a Vertical Plate: A Numerical Study, Plos One, 9 (2014) 9 pp. 1-10
- Kumar, K. G., et al., Effect of Nonlinear Thermal Radiation on Double Diffusive Mixed Convection Boundary Layer Flow of Viscoelastic NanoFluid Over a Stretching Sheet, Int. J. Mech. Eng., 12 (2017) 1.
- Naveed, M., et al., Thermophoresis and Brownian Effects on the Blasius Flow of a Nano Fluid Due to a Curved Surface With Thermal Radiation, Eur. Phys. J. Plus, (2016) 131:214.
- Hsiao, K. L., To Promote radiation Electrical MHD Activation Energy Thermal Extrusion Manufacturing System Efficiency by Using Carreau Nano Fluid With Parameters Control Method, Energy, 130 (2017) pp. 486-499
- Hsiao, K. L., Combined Electrical MHD Heat Transfer Thermal Extrusion System Using Maxwell Fluid with radiative and Viscous Dissipation Effects, Appl. Therm. Eng. 208 (2016) 8.
- Rudraswamy, N. G., et al., Combined Effect of Joule Heating and Viscous Dissipation on MHD Three Dimensonal Flow of a Jeffrey Nano Fluid, J. NanoFluid, 6 (2017) pp. 311-317
- Kumar, K. G., et al. Influence of Nonlinear thermal Radiation and Viscous Dissipation on Three Dimensional Flow of Jeffrey Nanofluid Over a Stretching Sheet in the Presence of Joule Heating, Nonlinear Eng., 6 (2016) 3 pp. 207-219
- Abbas, Z., et al., Hydromagnetic Slip Flow of Naofluid Over a Curved Stretching Surface With Heat Generation and Thermal Radiation, J. Molec. Liq. 215 (2016) pp. 756-762
- Hsiao, K. L., Stagnation Electrical MHD Nanofluid Mixed Convection With Slip Boundary on a Stretching Sheet, Appl. Therm. Eng., 98 (2016) pp. 850-861
- Hsiao, K. L., Corrigendum to "Stagnation Electrical MHD Nanofluid Mixed Convection With Slip Boundary on a Stretching Sheet"
- Kumar, K. G., et al., Radiative Heat Transfer of Carreau Fluid Over a Stretching Sheet With Fluid Particle Suspension and Temperature Jump, Results in Physics, 7 (2017) pp. 3976-3983
- Makinde, O. D., Effect of Nonlinear Thermal Radiation on MHD Boundary Layer Flow and Melting Heat Transfer of Micropolar Fluid Over a Stretching Surface With Fluid Particle Suspension, Defect Diffusion Forum, 378 (2017) pp. 125-136
- Capobianchi, M., Aziz. A., Laminar Natural Convection From an Isothermal Vertical Surface to Pseudoplastic and Dilatant fluid, ASME J. Heat Transf., (2012) 134:122502.
- Carreau, P. J., Rheological Equations From Molecular Network Theories, Trans. Soc. Rheol., 16 (1972) pp. 99-127
- Misra, J., et al., Flow and Heat Transfer of a MHD Viscoelastic Fluid in a Channel With Stretching Wall: Some Applications to Haemodynamics, Comp. Fluid, 37 (2008) 1 pp. 1-11
- Hsiao, K. L., Micropolar Nanofluid Flow With MHD and Viscous Dissipation Effects Towards a Stretching Sheet With Multimedia Feature, Int. J. Heat Mass Trasnf., 112 (2017) pp. 983-990
- Hayat, T., et al., Radiation Effects on MHD Flow of Maxwell Fluid in a Channel With Porous Mesium, Int. J. Heat Transf., 54 (2011) 4 pp. 854-862
- Raftrari, B., Vajravelu, K., Homotopy Analysis Method for MHD Viscoeleastic Fluid Flow and Heat Transfer in a Channel With a Stretching Wall, Commun. Nonlinr. Sci. Simul., 17 (2012) 11 pp. 4149-4162
- Abbas, Z., et al., Chemically Reactive Hydromagnetic Flow of a Second Grade Fluid in a Semi Porous Channel, J. Appl. Tech. Phys., 56 (2015) pp. 878-888
- Khan, M., Magnetohydrodynamic Flow of Carreau Fluid Over a Convectively Heated Surface in the Presence of Non Linear radiation, J. Magnetism Magnetic Material, 412 (2016) pp. 63-68
- Khuri, A., Stokes Flow in Curved Channel, J. Comput. Appl. Maths., 187 (2006) 2 pp. 171-191
- Wu- Shung, Fu., et al., Effects of a Porous Medium on Forced Convectyion of a Reciprocating Curved Channel, Int. Commun. Heat Mass Transf., 58 (2014) pp. 63-67
- Naveed, M., Flow and Heat Transfer in a Semi Porous Curved Channel With Radiation and Porosity Effects, J. Porous Media, 19 (2016) 5 pp. 1-11
- Abbas, Z., et al., Nonlinear Radiative Heat Transfer and Hall Effects on a Viscous Fluid in a Semi Porous Curved Channel, AIP Advanes, 5 (2015) 107124
- Sajid, M., et al., Joule Heating and Magnetohydrodynamics effects on Ferrofluid Flow in a Semi Porous Curved Channel, J. Molec. Liquid, 222 (2016) pp. 1115-1120
- Rosseland, S., Astrophysik und Atom Theoretische Grundlagen, Springer Verlag, Berlin (1931) pp. 41-44