Convection of Cu-water nanofluid in a vented T-shaped cavity in the presence of magnetic field

doi:10.1016/j.ijthermalsci.2015.02.014

International Journal of Thermal Sciences

Volume 94, August 2015, Pages 50-60

https://doi.org/10.1016/j.ijthermalsci.2015.02.014 Get rights and content

Highlights

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Magnetohydrodynamic mixed convection of a nanofluid in a vented T-shaped cavity is studied.
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Effects of Re, Ri, Ha, solid volume fraction and cavity aspect ratio on heat transfer are examined.
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The presence of nanoparticles enhances the heat transfer except at Re = 400.
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At higher Reynolds numbers, the effect of Hartmann number on the average Nusselt number is more significant.
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By increasing the cavity aspect ratio, the effect of nanofluid on heat transfer increases.

Abstract

This paper presents the results of a numerical study on the mixed convection of Cu-water nanofluid in a T-shaped cavity in the presence of a uniform magnetic field. Some sections of the bottom walls of the cavity are heated at a constant temperature and the other walls are thermally insulated. The nanofluid at a relatively low temperature enters from the bottom and exits from the top of the cavity. The governing equations are solved numerically with a finite volume approach using the SIMPLE algorithm. The effects of parameters such as Reynolds number (10 ≤ Re ≤ 400), Richardson number (0.01 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 80), solid volume fraction (0 ≤ φ ≤ 0.06), and cavity aspect ratio (0.1 ≤ AR ≤ 0.4) on the fluid flow and the thermal performance of the cavity are studied. The results indicate that the presence of nanoparticles enhances the heat transfer except at Re = 100 and Ha < 10 as well as Re = 400 and Ha < 60, where pure water has a slightly higher heat transfer rate compared to the nanofluid. The influence of nanofluid on the heat transfer enhancement increases as AR increases. For Ri = 0.01 and 1, the maximum heat transfer rate is obtained at AR = 0.4; however, for Ri = 10, the maximum heat transfer rate occurs at AR = 0.1.

Introduction

Mixed convection heat transfer has always been of great interest because of its wide applications in different areas such as cooling of electronic devices cooling, chemical processing equipment and solar energy collectors [1], [2], [3], [4], [5]. Sidik et al. [6] developed a point-force scheme to simulate a particle laden flow under the effects of mixed convection and studied the hydrodynamic removal of contaminants contained in a cavity. Their results showed that the variation of Grashof number had a noticeable impact on the observed flow pattern and particle removal efficiency. Najam et al. [7] numerically studied the laminar unsteady mixed convection in a two-dimensional horizontal channel. The channel contained heating blocks which were periodically mounted on its lower wall while its upper wall was maintained at a relatively lower constant temperature. The fully-developed forced flow was found to considerably reduce the heat transfer through the cold surface of the channel at relatively large Reynolds numbers. Aminossadati and Ghasemi [8] numerically investigated the mixed convection heat transfer in a two-dimensional horizontal channel with an open cavity. They found that at a fixed Richardson number, all three different heating modes corresponded to noticeable improvements in the heat transfer mechanism as the cavity aspect ratio increased.

In integrated electronic circuit boards with increasing package density, an effective heat removal process is required to ensure satisfactory operation of high heat generating components. Numerous innovative heat transfer strategies have been proposed and the fluid flow and heat transfer characteristics of such strategies have been experimentally and numerically investigated as detailed by Incropera [9] and Peterson and Ortega [10]. In the past few decades, mixed convection heat transfer has been a great interest for many engineering and science researchers in the electronic industry. The main objective of their studies has been to understand the fundamentals of various cooling strategies and to achieve a high performance cooling method which meets the heat removal needs of electronic devices with certain geometries [11], [12], [13], [14]. Alami et al. [15] presented a numerical study of natural convection from a two dimensional ‘‘T’’ form cavity with rectangular heated blocks. Their results showed that the heat transfer variation with the Rayleigh number was similar to that for the case of the vertical smooth or ribbed channels. Mezrhab et al. [16] carried out a numerical study of heat transfer and fluid flow in a T-shaped cavity and showed that the average Nusselt number increased with increasing the height of the cavity, especially in the presence of surface radiation. Bakkas et al. [17] conducted a numerical investigation of laminar steady natural convection flow in a two-dimensional horizontal channel containing heating rectangular blocks that were periodically mounted on its lower wall. Their results showed that there were situations where the difference between the Nusselt numbers corresponding to the two different solutions reached 34% for the same set of governing parameters.

In recent years, studies on nanofluid flow and heat transfer in cavities and enclosures have attracted considerable attention. Nanofluids are fluids containing nanometer-sized particles; these fluids are engineered colloidal suspensions of nanoparticles in a base fluid, which have a better suspension stability compared to millimeter or micrometer sized ones. Nanofluids have novel properties that make them potentially useful in many applications. They exhibit enhanced thermal conductivity and the convective heat transfer coefficient compared to the base fluid [18], [19], [20], [21]. Therefore, the nanofluids are expected to transfer heat at a higher rate than ordinary fluids (for example, water). This allows for more efficient heating or cooling while reducing energy consumption [22], [23], [24], [25]. Pishkar and Ghasemi [26] numerically studied the thermal performance of two fins mounted on the bottom wall of a horizontal channel and cooled with either pure water or a Cu-water nanofluid. Their results showed that the influence of the solid volume fraction on the increase of heat transfer was more noticeable at higher values of the Reynolds number. Mahmoudi et al. [27] numerically studied the mixed convection flow and temperature fields in a vented square cavity subjected to an external Cu–water nanofluid. Their results showed that for the higher values of Reynolds and Richardson numbers, the presence of nanoparticles had greater influence on the improvement of the heat transfer performance. Shahi et al. [28] conducted a numerical investigation on mixed convection flow of a Cu–water nanofluid in a square cavity with inlet and outlet ports. Their results showed that the increase of solid concentration led to the increase of the average Nusselt number at the heat source surface and the decrease in the average bulk temperature. Sourtiji et al. [29] performed a numerical study on the mixed convection flow and the heat transfer inside a square cavity with inlet and outlet ports. Their results showed that the average Nusselt number was an increasing function of the Reynolds number, the Richardson number and the volume fraction of nanofluid.

The study of magnetic field has important applications in physics and engineering. Heat and mass transfer problems in the presence of magnetic field effects have attracted great interest of engineers and scientists for decades [30], [31], [32], [33], [34]. In this context, amongst previous studies, some have tried to obtain a basic understanding of heat transfer characteristics in an enclosure in the presence of magnetic field [35], [36], [37], [38]. Mixed convection in a magnetic field has been studied in recent years by several researchers. Rahman et al. [39] numerically studied the development of magnetic field effect on mixed convective flow in a horizontal channel with a bottom-heated open enclosure. Their results indicated that the mixed convective parameters strongly affect the flow phenomenon and temperature field inside the cavity; whereas in the channel, these effects are less significant. Rahman et al. [40] numerically carried out a study on mixed convection in an open channel with a square cavity which was partially or fully heated on the left side. It was observed that the length of heater was insignificant on the flow field at higher values of Hartmann number.

A review of earlier studies indicates that the mixed convection of Nanofluids in a T-shaped cavity placed in a magnetic field has not been investigated. The results of this study can be useful in the thermal design of electronic equipment, which can be inadvertently under the influence of magnetic field. In this article, a numerical study of the mixed convection heat transfer of Cu-water Nanofluid in a T-shaped cavity under the influence of magnetic field has been considered. The effects of parameters such as the Reynolds number, the Richardson number, the Hartmann number, the solid volume fraction of nanofluids and the cavity aspect ratio on the heat transfer rate of the cavity have been investigated.

Section snippets

Problem description

Fig. 1 shows a schematic diagram of the two-dimensional T-shaped cavity considered in this study. The cavity has equal length and height of L. The walls of the cavity AB, BC, DE and EF with the length of H are maintained at a relatively high temperature; and the other walls are thermally insulated. The nanofluid enters the cavity from below at a relatively low temperature. The ratio of entrance length (for nanofluid) to the cavity length is l₀/L = 0.2. The direction of gravity force is downward

Mathematical formulation

The equations that govern the conservation of mass, momentum and energy can be written as follows [20], [40]: $\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0 u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = \frac{1}{ρ_{n f}} [- \frac{\partial p}{\partial x} + μ_{n f} (\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}})] u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} = \frac{1}{ρ_{n f}} [- \frac{\partial p}{\partial y} + μ_{n f} (\frac{\partial^{2} v}{\partial x^{2}} + \frac{\partial^{2} v}{\partial y^{2}})] + {(ρ β)}_{n f} g (T - T_{c}) - σ_{n f} B_{0}^{2} v u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = α_{n f} [\frac{\partial^{2} T}{\partial x} + \frac{\partial^{2} T}{\partial y^{2}}]$

Variables u, v and T are the velocity components in the x, y direction and temperature, respectively. The dimensionless form of the governing equations can be obtained by introducing the dimensionless variables. These are defined as follows: $X = \frac{x}{L}$

Numerical technique

A FORTRAN computer code is developed to model the considered geometry. The governing equation (3) with the stated boundary conditions are solved numerically by the control volume method. The computational domain has been set into grids using displaced network method. To solve the algebraic equations simultaneity, SIMPLE algorithms, the details of which are presented in Ref. [46], have been used. Given that the basis of the solving algorithm lays on an iterative technique, the following

Grid independency and code validation

In order to validate the developed computer code, a comparison has been made between the results of the present study and those from other references. Firstly, a square cavity with a nanofluid entering and exiting through vertical walls of the cavity has been considered and the results of the average Nusselt number are compared with the results of Shahi et al. [28] (Fig. 2). A comparison has also been conducted for the air flow in a diagonal square-shaped cavity under the influence of a

Results and discussion

This section presents the effects of parameters such as Reynolds number (10 ≤ Re ≤ 400), Richardson number (0.01 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 80), solid volume fraction (0 ≤ φ ≤ 0.06), and cavity aspect ratio (0.1 ≤ AR ≤ 0.4) on streamlines, isotherms, vertical velocity and Nusselt number.

Conclusions

This paper presents the results of a numerical study on the mixed convection heat transfer inside a T-shaped cavity that allows entering and exiting a nanofluid (pure water also considered). The cavity is under the influence of a magnetic field. The governing equations are solved using the SIMPE algorithm and the results of flow and temperature fields as well as the heat transfer rate are presented for different values of Re, Ha, Ri, AR and φ. It is found that at low values of Re, Nu_m increases