Journal of Nanoscience

Volume 2016 (2016), Article ID 9708562, 11 pages

http://dx.doi.org/10.1155/2016/9708562

## Heat and Mass Transfer on Squeezing Unsteady MHD Nanofluid Flow between Parallel Plates with Slip Velocity Effect

Department of Mathematics, Statistics and Computer Science, G. B. Pant University of Agriculture and Technology, Pantnagar, Uttarakhand, India

Received 30 June 2016; Revised 17 October 2016; Accepted 24 October 2016

Academic Editor: In Cheol Bang

Copyright © 2016 Khilap Singh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Heat and mass transfer behavior of unsteady flow of squeezing nanofluids between two parallel plates in the sight of uniform magnetic field with slip velocity effect is investigated. The governing equations representing fluid flow have been transformed into nonlinear ordinary differential equations using similarity transformation. The equations thus obtained have been solved numerically using Runge-Kutta-Fehlberg method with shooting technique. Effects on the behavior of velocity, temperature, and concentration for various values of relevant parameters are illustrated graphically. The skin-friction coefficient and heat and mass transfer rate are also tabulated for various governing parameters. The results indicate that, for nanofluid flow, the rates of heat and mass transfer are inversely proportional to nanoparticle volume fraction and magnetic parameter. The rate of mass transfer increases with increasing values of Schmidt number and squeeze number.

#### 1. Introduction

The study of heat and mass transfer in unsteady squeezing viscous nanofluid flow between two parallel plates is a stimulating topic of exploration because of its industrial use and intense biological situations, some of which include processing of polymer, compression, power transmitting, lubricant system, transient loading of mechanical components and the squeezed films in power transmission, food processing, and cooling water, modeling of synthetics transportation inside living bodies, hydromechanical machinery, chemical processing equipment, and crop destruction due to freezing. The first work on the squeezing flow under lubrication approximation was studied by Stefan [1]. The flow analysis between two parallel plates of Cu-water squeezing nanofluid was investigated by Domairry and Hatami [2]. Pourmehran et al. [3] studied the unsteady flow of squeezing nanofluid between parallel plates. Gupta and Ray [4] proposed a problem of unsteady flow of a squeezing nanofluid between two parallel plates. The squeezing flow of Cu-water (or kerosene) nanofluid between two parallel plates under the effects of viscous dissipation and velocity slip was investigated by Khan et al. [5]. Dib et al. [6] obtained an approximate analytic solution of squeezing unsteady nanofluid flow.

The word nanofluid represents the fluid in which particles of size with order of nanometer (diameter < 100 nm) are mixed in the base fluid. The nanoparticles used in nanofluids are generally made of metals (Al, Cu), oxides (Al_{2}O_{3}, CuO, TiO_{2}, and SiO_{2}), carbides (SiC), nitrides (AlN, SiN), and nonmetal (graphite, carbon nanotubes) and the base fluid is usually a conductive fluid, such as water or ethylene glycol. Other base fluids are toluene, oil, other lubricants, biofluids, and polymer solution. Nanoparticles are present up to 5% volume fraction in nanofluids. The conventional heat transfer fluids are poor conductors of heat. Nanofluids make an edge over them because they have high heat transfer capability. Since these heating/cooling fluids play a vital role in the development of energy efficient heat transfer equipment for energy supply, to raise the thermal conductivity of these fluids, nanosized conducting metal particles are added to them. Therefore, their proper understanding is a must to use them efficiently in modern industry. Applications of nanofluids include microelectronics, fuel cells, and pharmaceutical processes. Choi and Eastman [7] were the first to propose the term nanofluid that represents the fluid in which nanoscale particles are suspended in the base fluid with low thermal conductivity such as water, ethylene glycol, and oil. In recent years, many researchers have studied and reported nanofluid technology experimentally or numerically in the presence of heat transfer [8–23].

Ibrahim and Shankar [24] studied MHD nanofluid flow and heat transfer over a stretching sheet in the presence of thermal radiation and slip conditions. Malvandi and Ganji [25] investigated effect of magnetic field on heat transfer of alumina/water nanofluid inside a circular microchannel. Ul Haq et al. [26] obtained the influence of thermal radiation and slip on MHD nanofluid flow passed over a stretching sheet. Govindaraju et al. [27] solved the problem of magneto-hydrodynamic nanofluid flow on entropy generation in a stretching sheet with slip velocity. The problem based on effects of Stefan blowing and the slips on bioconvection nanofluid flow over a horizontal plate in motion was numerically investigated by Uddin et al. [28]. Hsiao [29] studied the MHD mixed-convection stagnation flow of a nanofluid over stretching sheet in the presence of slip. Kameswaran et al. [30] investigated chemical reaction and viscous dissipation effects on nanofluid flow through stretching or shrinking sheet. Matin and Pop [31] studied heat and mass transfer flow of a nanofluid with chemical reaction in porous channel. Pal and Mandal [32] observed mixed-convection heat and mass transfer stagnation-point flow in nanofluids through stretching/shrinking sheet in a porous medium with thermal radiation. The nanofluid flow and heat transfer in porous medium in the presence of magnetic field and radiation were made by Zhang et al. [33]. Elshehabey and Ahmed [34] analyzed effect of mixed convection in nanofluid flow with sinusoidal distribution of temperature on the both vertical walls using Buongiorno’s nanofluid model.

The novelty of the present study is to account for the slip velocity, magnetic field, and mass transfer on squeezing unsteady nanofluid flow and heat transfer between two parallel plates. In this study, authors have applied Runge-Kutta-Fehlberg fourth-fifth-order method with shooting technique to find the solution of nonlinear differential equations. The effects of governing parameters such as slip, magnetic, and squeeze number, Schmidt number, and nanoparticle volume fraction on velocity, temperature, and concentration as well as on skin-friction coefficient, Nusselt, and Sherwood number are investigated. To the best of our best knowledge such investigation is not studied in the scientific literature. Some analytical methods for squeezing unsteady nanofluid flow can be found in [4, 6].

#### 2. Mathematical Formulation

We consider an unsteady two-dimensional flow to observe heat and mass transfer of a squeezing nanofluid in the middle of two parallel plates extended infinitely and implanted in a system occupied with nanofluid (water as a base fluid) containing different types of nanoparticles, that is, copper (Cu), silver (Ag), alumina (Al_{2}O_{3}), and titanium oxide (TiO_{2}) with slip velocity effect. The thermophysical properties of the nanofluids are given in Table 1. A transverse magnetic field of variable strength is imposed in direction perpendicular to both the plates. The distance between two plates is , where is the initial position (at time ). Flow is incompressible with no chemical reaction in system. Further, viscous dissipation effects are retained. The graphical model support to the present study has been given in Figure 1. The governing equations representing flow are as follows: The associated boundary conditions are given as where