## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Boundary layer flow of a copper-water nanofluid over a permeable shrinking cylinder with homogenous-hetrogenous reactions: Dual solutions

**ABSTRACT**

This research addresses the axi-symmetric flow of a copper (Cu)-water nanofluid past a porous shrinking cylinder in the presence of homogeneous-heterogeneous reactions. Using a similarity transformation, the basic partial differential equations are converted into ordinary differential equations. The transformed equations are solved using bvp4c numerically from Matlab for several values of the physical parameters. The physical impact of governing parameters on the velocity profile, temperature profile, concentration profile as well as the skin friction coefficient and the heat transfer rate are discussed carefully. The results indicate that the multiple solutions only exist when a certain value of suction is implemented through the permeable cylinder. Further, the curvature parameter accelerates the boundary layer separation. ''(0) f '(0) q -g

**KEYWORDS**

PAPER SUBMITTED: 2016-06-13

PAPER REVISED: 2017-04-04

PAPER ACCEPTED: 2017-04-28

PUBLISHED ONLINE: 2017-05-06

- Choi, S.U.S., Enhancing thermal conductivity of fluids with nanoparticles, Develop Appl. Non- New. Flows, 231 (1995), pp. 99-105.
- Makinde, O. D., Aziz, A., Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, Int. J. Thermal Sci., 50 (2011), pp. 1326-1332.
- Mustafa, M., et al., Stagnation point flow of nanofluid over a stretching sheet, Int. J. Thermal Sci., 50 (2011), pp. 5588-5594.
- Hady, F. M., et al., Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet, Nanoscale Res. Lett., 7 (2012), pp. 229-242.
- Hamad, M. A. A., Ferdows, M., Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet, Math. Mech. Eng. Ed., 33 (2012), pp. 923-930.
- Das, K., Mixed convection stagnation point flow and heat transfer of Cu-water nanofluids towards a shrinking sheet, Heat Tran. Asian Res., 42 (2013), pp. 230-242.
- Ibrahim, W., et al., MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet, Int. J. Heat Mass Transfer, 56 (2013), pp. 1-9.
- Mansur, S., et al., The magnetohydrodynamic stagnation point flow of a nanofluid over a stretching/shrinking sheet with suction, PloS ONE, 10 (2015), pp. 1-14.
- Hayat, T., et al., Stagnation point flow of carbon nanotubes over stretching cylinder with slip conditions, Open Phys., 13 (2015), pp. 188-197.
- Dhanai, R., et al., Multiple solutions of MHD boundary layer flow and heat transfer behavior of nanofluids induced by a power-law stretching/shrinking permeable sheet with viscous dissipation, Powder Tech., 273 (2015), pp. 62-70.
- Faiza, A. S., Effects of radiation on convection heat transfer of cu-water nanofluid past a moving wedge, Thermal Science, 20 (2016), 2, pp. 437-447.
- Wang, C.Y., Fluid flow due to a stretching cylinder, Phys. Fluids, 31 (1988), pp. 446-468.
- Ishak, A., et al., Uniform suction/blowing on flow and heat transfer due to a stretching cylinder, Math. Model., 32 (2008), pp. 2059-2066.
- Mukhopadhyay, S., Chemically reactive solute transfer in boundary layer slip flow along a stretching cylinder, Front. Chem. Sci. Eng., 5 (2011), pp. 385-391.
- Mukhopadhyay, S., MHD boundary layer slip flow along a stretching cylinder, Ain Shams Eng. J., 4, (2013), pp. 317-324.
- Bhattacharyya, K., Boundary layer flow and heat transfer over a permeable shrinking cylinder with mass suction, Acta Tech., 58 (2013), pp. 253-262.
- N. Najib, N. Bachok, N.Md. Arifin, and A. Ishak, "Stagnation point flow and mass transfer with chemical reaction past a stretching/shrinking cylinder," Sci. Rep. 4, 1-7 (2014).
- Hayat, T., et al., Flow of variable thermal conductivity fluid due to inclined stretching cylinder with viscous dissipation and thermal radiation, Appl. Math. Mech. Eng. Ed., 35 (2014), pp. 717-728.
- Omar, N.S. et al., Stagnation point flow over a stretching or shrinking cylinder in a copper-water nanofluid, Indian J. Sci. Tech., 8 (2015), pp. 1-7.
- Hayat, T., et al., Impact of magnetohydrodynamics in bidirectional flow of nanofluid subject to second order slip velocity and homogeneous-heterogeneous reactions, J. Mag. Magnet. Mater., 395 (2015), pp. 294-302.
- Merkin, J. H., A model for isothermal homogeneous-heterogeneous reactions in boundary layer flow, Math. Comput. Model., 24 (1996), pp. 125-136.
- Kameswaran, P. K., et al., Homogeneous-heterogeneous reactions in a nanofluid flow due to a porous stretching sheet, Int. J. Heat Mass Transfer, 57 (2013), pp. 465-472.
- Nandkeolyar, R., et al., Heat transfer on nanofluid flow with homogeneous-heterogeneous reactions and internal heat generation, J. Heat Transfer, 136 (2014), 122001.
- Das, M., et al., Mixed convection and nonlinear radiation in the stagnation point nanofluid flow towards a stretching sheet with homogenous-heterogeneous reactions effects, Procedia Eng., 127 (2015), pp. 1018-1025.
- Hayat, T., et al., Homogeneous-heterogeneous reactions in the stagnation point flow of carbon nanotubes with Newtonian heating, AIP Advances, 5 (2015), 027130.
- Chaudhary, M. A., Merkin, J. H., A Simple isothermal model for homogeneous-heterogeneous reactions in boundary layer flow: I. Equal diffusivities, Fluid Dyn. Res., 16 (1995), pp. 311-333.
- Merkin, J. H., On dual solution occurring in mixed convection in a porous medium, J. Eng. Math., 20 (1985). pp. 171-179.
- Weidman, P. D., et al., The effect of transpiration on self similar boundary layer flow over moving surfaces, Int. J. Eng. Sci., 44 (2006), pp. 730-737.
- Khan, M., et al., On unsteady heat and mass transfer in Carreau nanofluid flow over expanding or contracting cylinder with convective surface conditions, J. Mol. Liq., 231 (2017), pp. 474-484.
- Harris, S. D., et al., Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip, Transp. Porous Media, 77 (2009), pp. 267-285.
- Oztop, H. F., Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow, 29 (2008), pp. 243-255.