## THERMAL SCIENCE

International Scientific Journal

### THE EFFECT OF VARIABLE MAGNETIC FIELD ON HEAT TRANSFER AND FLOW ANALYSIS OF UNSTEADY SQUEEZING NANOFLUID FLOW BETWEEN PARALLEL PLATES USING GALERKIN METHOD

**ABSTRACT**

This paper presents a thermal and flow analysis of an unsteady squeezing nanofluid flow and heat transfer using nanofluid based on Brinkman model in presence of variable magnetic field. Galerkin method is used to solve the non-linear differential equations governing the problem. Squeezing flow between parallel plates is very applicable in the many industries and it means that one or both of the parallel plates have vacillation. The effects of active parameters such as the Hartman number, squeeze number, and heat source parameter are discussed. Results for temperature distribution and velocity profile, Nusselt number, and skin friction coefficient by Galerkin method are presented. As can be seen in results, the values of Nusselt number and skin friction coefficient for CuO is better than Al2O3. Also, according to figures, as nanofluid volume fraction increases, Nusselt number increases and skin friction coefficient decreases, increase in the Hartman number results in an increase in velocity and temperature profiles and an increase in squeeze number can be associated with the decrease in the velocity.

**KEYWORDS**

PAPER SUBMITTED: 2016-05-24

PAPER REVISED: 2016-06-27

PAPER ACCEPTED: 2016-06-30

PUBLISHED ONLINE: 2016-08-07

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**5**, PAGES [2057 - 2067]

- Choi, S.U.S., Enhancing thermal conductivity of fluids with nanoparticles, ASME Fluids Eng. Div 231 (1995), 7.
- S.K. Das, S.U.S.C., W. Yu, T. Pradeep, Nanofluids: Science and Technology, Wiley, Hoboken, NJ, (2007)
- Buongiorno, J., Convective transport in nanofluids, ASME J. Heat Transf. 128 (2006), 11.
- Kakac, S., Pramuanjaroenkij, A., Review of convective heat transfer enhancement with nanofluids. International Journal of Heat and Mass Transfer, 52 (2009), 13, pp. 3187-3196.
- Fan, J., Wang, L., Review of heat conduction in nanofluids, Journal of Heat Transfer, 133 (2011), 4, 040801.
- Rahimi-Gorji, M., Pourmehran, O., Hatami, M., Ganji, D., Statistical optimization of microchannel heat sink (MCHS) geometry cooled by different nanofluids using RSM analysis, The European Physical Journal Plus, 130 (2015), 2, pp. 1-21.
- Malvandi, A., Ganji, D., Magnetic field and slip effects on free convection inside a vertical enclosure filled with alumina/water nanofluid, Chemical Engineering Research and Design, 94 (2015), pp. 355-364.
- Mosayebidorcheh, S., Ganji, D., Farzinpoor, M., Approximate solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient, Propulsion and Power Research, 3(2014), 1, pp.41-47.
- Joneidi, A., Domairry, G., Babaelahi, M., Effect of mass transfer on a flow in the magnetohydrodynamic squeeze film between two parallel disks with one porous disk, Chemical Engineering Communications, 198 (2010), 3, pp. 299-311.
- Pourmehran, O., Rahimi-Gorji, M., Ganji, D., Heat transfer and flow analysis of nanofluid flow induced by a stretching sheet in the presence of an external magnetic field, Journal of the Taiwan Institute of Chemical Engineers, (2016).
- Khanafer, K., Vafai, K., Lightstone, M., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, International Journal of Heat and Mass Transfer, 46 (2003), 19, pp. 3639-3653.
- Hatami, M., Ganji, D., Natural convection of sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates by analytical and numerical methods, Case Studies in Thermal Engineering, 2, pp. 14-22 (2014).
- Pourmehran, O., Rahimi-Gorji, M., Hatami, M., Sahebi, S., Domairry, G., Numerical optimization of microchannel heat sink (MCHS) performance cooled by KKL based nanofluids in saturated porous medium, Journal of the Taiwan Institute of Chemical Engineers, 55 (2015), pp. 49-68.
- Khan, W., Pop, I., Boundary-layer flow of a nanofluid past a stretching sheet, International Journal of Heat and Mass Transfer, 53 (2010),11, pp. 2477-2483.
- Mahmood, M., Asghar, S., Hossain, M., Squeezed flow and heat transfer over a porous surface for viscous fluid, Heat and Mass Transfer, 44 (2007), 2, pp. 165-173.
- Domairry, G., Aziz, A., Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by homotopy perturbation method, Mathematical Problems in Engineering, (2009).
- Ozisik, M.N., Heat conduction. John Wiley & Sons, (1993)
- Rahimi-Gorji, M., Pourmehran, O., Gorji-Bandpy, M., Ganji, D., An analytical investigation on unsteady motion of vertically falling spherical particles in non-Newtonian fluid by Collocation Method, Ain Shams Engineering Journal, 6 (2014), 2, pp.531-540.
- Pourmehran, O., Rahimi-Gorji, M., Gorji-Bandpy, M., Ganji, D., Analytical investigation of squeezing unsteady nanofluid flow between parallel plates by LSM and CM, Alexandria Engineering Journal, 54 (2015), 1, pp. 17-26.
- Hendi, F.A., Albugami, A.M., Numerical solution for Fredholm-Volterra integral equation of the second kind by using collocation and Galerkin methods, Journal of King Saud University-Science, 22 (2010), 1, pp. 37-40.
- Mohammadi, F., Hosseini, M., Mohyud-Din, S.T., Legendre wavelet galerkin method for solving ordinary differential equations with non-analytic solution, International Journal of Systems Science, 42 (2011), 4, pp. 579-585.
- Hatami, M., Hatami, J., Ganji, D., Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel, Computer methods and programs in biomedicine, 113 (2014), 2, pp. 632-641.
- Brinkman, H., The viscosity of concentrated suspensions and solutions, The Journal of Chemical Physics 20 (1952), 4, p. 571.
- Oztop, H.F., Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid Flow, 29 (2008), 5, pp. 1326-1336.
- Mustafa, M., Hayat, T., Obaidat, S., On heat and mass transfer in the unsteady squeezing flow between parallel plates, Meccanica, 47 (2012), 7, pp. 1581-1589.