Journal of Engineering

Volume 2018, Article ID 7827324, 11 pages

https://doi.org/10.1155/2018/7827324

## Effect of Microstructure and Exothermic Reaction on the Thermal Convection in an Enclosure of Nanoliquid with Continuous and Discontinuous Heating from below

Department of Mathematics, Faculty of Science, Jouf University, 24241 Sakaka Aljawf, Saudi Arabia

Correspondence should be addressed to Abeer Alhashash; moc.liamg@hsahsahlareeba.rd

Received 24 May 2018; Revised 27 July 2018; Accepted 13 August 2018; Published 3 September 2018

Academic Editor: Sergio Nardini

Copyright © 2018 Abeer Alhashash. 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

Effect of continuous and discontinuous external heating and internal exothermic reaction on thermal convection of micropolar nanoliquid is studied in the present work. The liquid in the enclosure is a water-based nanoliquid containing Cu nanoparticles. The governing equations are solved numerically using the iterative finite difference method (FDM). The studied parameters are the material viscosity (), nanoparticles volume fraction (), and the internal heating (). It is found that the convective flow acceleration by adding nanoparticles is retarded by the microrotation and the suppression has a great impact on the weak exothermic reaction for both cases. Increasing the internal reaction decreases the heat transfer rate at the hot wall but increases the heat transfer rate at the cool wall for both cases, Newtonian or micropolar nanoliquid.

#### 1. Introduction

Today electrical machines are commonly used in the industry. It is desirable to have machines which are as small, efficient, and long lasting. To be able to make the machines smaller without reducing the power, it is important to get a better cooling of the machine, preferably by using natural convection. The convection describes the exchange of thermal energy between physical systems depending on the thermal, velocity, and pressure, by dissipating heat. Heat transfer rate could be improved by modifying thermophysical properties of the liquid. Using solid nanoparticles having very high thermal conductivities dispersed in liquid would substantially modify the liquid properties. This technique is proposed by Choi [1] and the new liquid is called nanoliquid. Nanoparticles are basically metal, oxides, and some other compounds such as graphene. This engineered liquids have potential applications, for example, heat exchanger, building construction, micro electromechanical systems, nuclear reactors, geothermal power, solar cells, electronics cooling, and so forth. Khanafer et al. [2] and Jou and Tzeng [3] obtained 25% augmentation in the heat transfer rate with 20% weight fractions of the suspended Cu nanoparticles. The Ag, Cu, CuO, , or nanoparticles are utilized by Öǧüt [4]. They reported 155% augmentation in the heat transfer rate utilizing 20% weight fractions of the Ag nanoparticles. Rashmi et al. [5] filled the enclosure with nanoparticle. They reported a reduction in heat transfer rate with an increment percentage of the nanoparticle for a particular heating parameter. Sheikhzadeh et al. [6] considered the Brownian and thermophoresis diffusions and found the heat transfer reduction by increasing the bulk volume fraction of nanoparticles. Boulahia et al. [7] observed that the heat transfer rate increases with decreasing the nanoparticle diameter and the highest values of the heat transfer rate occur at 25nm diameter. Motlaghc and Soltanipour [8] reported about 26% augmentation in the heat transfer rate with 4% weight fractions of the solid nanoparticles. Liao [9] investigated systematically the influence of the Rayleigh number on the heat transfer behavior with increasing nanoparticle volume fraction to 6%. He built a correlation equation for reproducing the critical Rayleigh number with the averaged temperature.

Heat transfer performance strongly depends on the media, i.e., liquid. Aydin and Pop [10] and Saleem et al. [11] showed that micropolar liquid give lower heat transfer values than those of the Newtonian liquid. Micropolar liquid is a subset of the non-Newtonian liquid. It is composed of dumb-bell structural molecules or small and stiff cylindrical components, for example, liquid mixtures, polymer liquid, animal blood, and engine oil. The earlier study of micropolar liquid in enclosures was conducted by Jena and Bhattacharyya [12]. They compared convection stability for several values of micropolar liquid parameters. Wang and Hsu [13] studied the influence of material parameter, geometry aspect ratio, and geometry orientation for the enclosure filled with micropolar liquid at unsteady and stationary conditions. They found that angles of inclination at the maximum values of the heat transfer were coincident for various micropolar liquid in the range of aspect ratio 1.75 to 0.75. Hsu and Chen [14] concluded that thermal performance of a micropolar liquid reduces with the vortex viscosity enhancement and stability of micropolar liquid is higher than that of the stability of Newtonian liquid. A heat sources effect was later included by Hsu et al. [15]. Hsu and Hong [16] investigated the microstructure in an open cavity and found that increasing the Grashof number increases both heat transfer rate and liquid circulation. Gibanov et al. [17] found that an increase in the vortex viscosity parameter leads to attenuation of the convective flow and heat transfer inside a trapezoidal enclosure. Later, Miroshnichenko et al. [18] analyzed the effects of Rayleigh number, Prandtl number, vortex viscosity parameter, and the heater location on streamlines, isotherms, and vorticity profile. Sheremet et al. [19] studied a right-angled wavy triangular enclosure and obtained an essential heat transfer reduction and liquid flow attenuation with vortex viscosity parameter. Turk and Tezer-Sezgin [20] observed that the streamlines and microrotation contours are similar to altering magnitudes. Recently, Ali et al. [21] observed that the expansion of isotherms toward the top boundary surface for greater values of the micropolar parameter and the Nusselt numbers decrease with change in the behavior of the liquid from Newtonian to micropolar.

The vehicle of the current investigation is to study a natural convection heat transfer in a square enclosure filled with micropolar nanoliquid when the bottom boundary is continuously and discontinuously heated at temperature. The top boundary is adiabatic, while the side boundaries walls have constant temperature where . The liquid in the enclosure is a water-based nanoliquid containing Cu nanoparticles. Quadratic heat profile is assumed to be generated internally by the exothermic reaction. An exothermic reaction is a chemical reaction that releases energy by light or heat and the typical application of this process occurs in chemical industry. Similar research conducted by Bourantas and Loukopoulos [22] for continuously heating left wall showed that the microrotation of the nanoparticles decreases heat transfer and should not therefore be neglected when computing heat and liquid flow of micropolar liquid, as nanoliquid. Hashemi et al. [23] and Izadi et al. [24] investigated the copper-water micropolar nanoliquid inside a porous enclosure with continuous heating left wall. The nanoparticles are translating, rotating, and choosing a discontinuous thermal condition along the bottom wall which could have a great impact on the heat transfer rate. Systematical comparison between continuous and discontinuous heating cases is also carried out.

#### 2. Mathematical Formulation

A schematic diagram of a square enclosure with micropolar nanoliquid is shown in Figure 1. The liquid in the enclosure is a water-based nanoliquid containing Cu nanoparticles. Quadratic heat profile is generated internally by the exothermic reaction. The bottom boundary is continuously and discontinuously heated while the top boundary is adiabatic and side boundaries walls have constant low temperature. The governing equation is based on conservation laws of mass, momentum, and energy with appropriate rheological models and equations. For micropolar nanoliquid flow the continuity equation, linear momentum equation, angular momentum equation and energy equations are given as follows:where subscript is nanoliquid, and are the velocity components along and axes, is the liquid temperature, is the component of the microrotation vector normal to the plane, is the magnitude of the acceleration due to gravity, is the density, is the dynamic viscosity, is the vortex viscosity, is the spin-gradient viscosity, is the micro-inertia density, and is a constant with values , with , called strong concentration of microelements. Further, we assume that has the following form:The viscosity of the nanoliquid can be approximated as viscosity of a base liquid if it contains dilute suspension of fine spherical particles, which is given by Brinkman [25] aswhere is the solid volume fraction of nanoparticles. Thermal diffusivity of the nanoliquid iswhere the heat capacitance of the nanoliquid given isand stands for the effective thermal conductivity of nanoliquid restricted to spherical nanoparticles is approximated by the Maxwell-Garnetss (MG), Öǧüt [4] model:The thermophysical properties of liquid and the solid copper phases are given by Khanafer et al. [2]. The appropriate the boundary conditions are as follows: