## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Hall current and joule heating effects on free convection flow of a nanofluid over a vertical cone in presence of thermal radiation

**ABSTRACT**

The effects of Hall current and Joule heating on flow and heat transfer of a nanofluid along a vertical cone in the presence of thermal radiation is considered. The flow is subjected to a uniform strong transverse magnetic field normal to the cone surface. Similarity transformations are used to convert the nonlinear boundary layer equations for momentum and energy equations to a system of nonlinear ordinary differential equations which are then solved numerically with appropriate boundary conditions. The solutions are presented in terms of local skin-friction, local Nusselt number, velocity and temperature profiles for values of magnetic parameter, Hall parameter, Eckert number, radiation parameter, and nanoparticle volume fraction. Comparison of the numerical results made with previously published results under the special cases, the results are found to be in an excellent agreement. It is also found that, nanoparticle volume fraction parameter and types of nanofluid play an important role to significantly determine the flow behavior.

**KEYWORDS**

PAPER SUBMITTED: 2016-04-13

PAPER REVISED: 2017-03-21

PAPER ACCEPTED: 2017-03-27

PUBLISHED ONLINE: 2017-04-08

- Merk, E. J.,Prinss, J. A., Thermal convection in laminar boundary II. App. Sci. Res., 4A(1954), pp. 195-206.
- Chamkha, A. J., Non-Darcy hydromagnetic free convection from a cone and a wedge in porous media. Int. Commun. Heat Mass Transf., 23(1996), pp. 875-887.
- Hering, R. G., Grosh, R. J., Laminar free convection from a non-isothermal cone. Z. Heat and Mass Transfer, 5(1962), pp. 1059-1068.
- Alam, M. M., et al., Free convection from a vertical permeable circular cone with pressure work and non-uniform surface temperature. Nonlinear Analysis Modeling and Control, 261(2007), pp. 21-32.
- Paolucci, S.,Zikoski, Z. J., Free convective flow from a heated vertical wall immersed in a thermally stratified environment. Int. J. Heat Mass Transf., 76(2013), pp. 1062-1071.
- Gupta, A. K., et al., Laminar and steady free convection in power-law fluids from a heated spheroidal particle: A numerical study. Int. J. Heat Mass Transf., 75(2014), pp. 592-609.
- Choi, S. U. S., Enhancing thermal conductivity of fluids with nanoparticles in developments and applications of non- Newtonian flows. NSiginer HP Wang Eds ASME, 66(1995), pp. 99-105.
- Choi, S., et al., Anomalously Thermal Conductivity Enhancement in Nanotube Suspensions. Applied Physics Letter, 79(2001), pp. 2252-2254.
- Xuan, Y. Li, O., Heat Transfer Enhancement of Nanofluids. International Journal of Heat and Fluid Flow, 21(2000), pp. 58-64.
- Sheikholeslami, M., et al., Numerical investigation of MHD effects on Al2O 3water nanofluid flow and heat transfer in a semi-annulus enclosure using LBM. Energy, 60(2013), pp. 501-510.
- Wen, D., Ding, Y., Experimental Investigation into Convective Heat Transfer of Nanofluids at the Entrance Region under Laminar Flow Conditions. International Journal Heat and Mass Transfer, 47(2004), pp. 5181-5188.
- Bhattacharya, P., et al., Brownian Dynamics Simulation to Determine the Effect Thermal Conductivity of Nanofluids. Journal of Applied Physics, 95(2004), pp. 6492-6494.
- Mokmeli, A.,Saffar-Avval, M., Prediction of Nanofluid Convective Heat Transfer Using the Dispersion Model. Nonlinear Analysis Modeling and Control, 49(2010), pp. 471-478.
- Mansour, M., et al., Numerical Simulation of Mixed Convection Flows in a Square Lid-Driven Cavity Partially Heated from Below Using Nanofluid. International Communications in Heat and Mass Transfer, 37(2010), pp. 1504-1512.
- Mahdy, A., Ahmed, S. E, Laminar Free Convection over a VerticalWavy Surface Embedded in a Porous Medium Saturated with a Nanofluid. Transport in Porous Media, 91(2012), pp. 423-435.
- Khan,W., Pop, I., Boundary-Layer Flow of a Nanofluid Past a Stretching Sheet. International Journal of Heat and Mass Transfer, 53(2010), pp. 2477-2483.
- Attia, H. A., et al., Effect of porosity on the flow and heat transfer between two parallel porous plates with the Hall effect and variable properties under constant pressure gradient. Blug. Chem. Commun., 46(2014), pp. 535-544.
- Attia, H. A., et al., Effect of porosity on the flow of a dusty fluid between parallel plates with heat transfer and uniform suction and injection. European Journal of Environmental and Civil Engineering, 18(2014), pp. 241-251.
- Hassan, H. S., Symmetry Analysis for MHD Viscous Flow and Heat Transfer over a Stretching Sheet. Appl. Math., 6(2015), pp. 78-94.
- Hayat, T., et al., The Modified Decomposition Method and Pad Approximants for theMHDFlow over a Non-Linear Stretching Sheet. Nonlinear Analysis: Real World Applications, 10(2009), pp. 966-973.
- Attia, H. A. , et al., Ion slip effect on unsteady Couette flow of a dusty fluid in the presence of uniform suction and injection with heat transfer. Journal of the Brazilian Society of Mechanical Sciences and Engineering, article in press, Available online 11, (2015) February.
- Zaman, H., et al., Effects of Hall Current on MHD Boundary Layer Second-Order Viscoelastic Fluid Flow Induced by a Continuous Surface with Heat Transfer. Am. J. Comput. Math., 4(2014), pp. 143-152.
- Abo-Eldahab, E. M., El Aziz, M. A., Hall current and ohmic heating effects on mixed convection boundary layer flow of a micropolar fluid from a rotating cone with power-law variation in surface temperature. Int. Commun. Heat Mass Transf., 31(2004), pp. 751-762.
- Abdeen, M. A. M, et al., Effectiveness of porosity on transient generalized Couette flow with Hall effect and variable properties under exponential decaying pressure gradient. Int. Commun. Heat Mass Transf., 87(2013), pp. 767-775.
- Attia, H. A., et al., Heat transfer between two parallel porous plates for Couette ow under pressure gradient and Hall current. Sadhana, 40(2015), pp. 183-197.
- Reddy, M. G., et al., Effects of viscous dissipation and heat source on unsteady MHD flow over a stretching sheet. Ain Shams Eng. J., 6(2015), pp. 1195-1201.
- Shakhaoath, Kh. Md., et al., Non-Newtonian MHD Mixed Convective Power-Law Fluid Flow over a Vertical Stretching Sheet with Thermal Radiation, Heat Generation and Chemical Reaction Effects. Academic Research International, 3(2012), pp. 80-92.
- Gerdroodbary, M. B., et al., Investigation of thermal radiation on traditional Jeffery-Hamel flow to stretchable convergent/ divergent channels. Case Stud. Therm. Eng., 6(2015), pp. 28-39.
- Hayat, T., et al., Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation. J. Magn. Magn. Mater., 385(2015), pp. 222-229.
- Roy, S., Free convection over a slender vertical cone at high Prandtl numbers. ASME J. Heat Mass Transfer, 101(1974), pp. 174-176.
- Alloui, Z., et al., Natural Convection of Nanofluids in a Shallow Cavity Heated from Below. International Journal of Thermal Sciences, 50(2011), pp. 385-393.
- Kakac, S., Pramuanjaroenkij, A., Review of convective heat transfer enhancement with nanofluids, International Journal of Heat and Mass Transfer, 52(2009), pp. 3187-3196.