Effect of heat generation and heat absorption on natural convection of Cu-water nanofluid in a wavy enclosure under magnetic field

Highlights

• MHD natural convection of nanofluid is studied in a wavy enclosure with a cylinder.

• Heat generation and absorption are more significant at low Ra.

• Ra and q are the most effective parameters for Nu.

• Ha and q considerably loses its significance at high Ra.

• High Hartmann numbers may restrict convection by up to 33%.

Abstract

Taking a more complex engineering geometry into account, magnetohydrodynamic natural convection of nanofluid (Cu-water) in a wavy walled enclosure having a circular hot cylinder inside is investigated by employing Galerkin-weighted residual formulation. In order to investigate the flow and heat transfer characteristics from several perspectives and increase the ability of adaptation to various engineering applications, the influences of the Hartmann number, Ha, Rayleigh number, Ra, and nanoparticle concentration are examined in detail. In addition to that, heat generation and heat absorption situations are also considered within the present work, which are simulated by a heat coefficient in a range of −10 ≤ q ≤ +10. The results revealed that increasing Ha has an insignificant effect on Nusselt number, Nu, at low Ra, however, it significantly pulls Nu down up to 33% for higher Ra, because of restricting convection. It is found that the heat coefficient, q, has a remarkable impact on Nu at low Ra, while its significance is diminished when Ra is increased. For q < 0, the heat absorption creates a heat sink, which increases Nu up to 34%, while the heat generation (q > 0) conversely reduces Nu up to 48%. Besides, variation in heat coefficient does not considerably affect the improvement impact of nanoparticles.

Introduction

The natural convective heat transfer in enclosures are an important field of thermal engineering due to the usage in a wide-range engineering applications such as glazing insulation techniques, cooling operations of electronics, solar systems and electrical machinery [1]. In order to perform the heat transfer inside the enclosures, various fluids are utilized such as air [[2], [3], [4]], water, oil or ethylene glycol [5]. However, these conventional fluids are usually claimed to have poor thermal conductivity, which leads to insufficient heat transfer [6]. Therefore, researchers put a significant effort on the enhancement of heat transfer capability of such fluids by theoretical and experimental studies [7]. As first introduced by Choi [8], dispersion of nanoparticles having a diameter of 1 to 100 nm into the thermal working fluid in order to promote its thermal conductivity is called nanofluids, and they have been adopted by many researchers having studies in the literature, [[9], [10], [11], [12]] to cite a few, as a promising solution to this challenging field. For the aforementioned heat transfer purposes, nanofluids are utilized in enclosures with various shapes such as square [[13], [14], [15]], L-shaped [16,17], C-shaped [18] and U-shaped [19,20] depending on the application area or heat transfer improvements. Furthermore, presence of magnetic field is considered in some studies in order to reveal the influences of magnetic field on nanofluids, due to the fact that these type of fluids may contain metallic nanoparticles. Sheikholeslami et al. [21] investigated the influence of magnetic field on free convection of Cu-water nanofluid that is filled in a half annulus, and they reported that presence of magnetic field significantly influences the flow field and decreases mean Nusselt number, Nu. Qi et al. [22] carried out an experimental study on the free convection of nanofluid that is subjected to magnetic effects in a tilted rectangular cavity. It was shown that the heat transfer performance is increased up to a certain point by the addition of nanoparticles and then it is decreased. Furthermore, they concluded that the horizontally applied magnetic field is insignificant on the heat transfer enhancement, while the vertical one improves the heat transfer. Hussam et al. [23] examined the natural convection behaviour of Cu-water nanofluid in a square enclosure under magnetic effects where the left wall is subjected to an oscillating temperature. They stated that the amplitude and frequency of the oscillation has a remarkable impact on heat transfer. Besides, it is noted that the Hartmann number plays a major role in the variation of Nu with respect to nanoparticle volume concentration. As a different enclosure geometry, Ma et al. [24] numerically explored natural convective heat transfer in a baffled U-shaped cavity considering the effects of magnetic field. They showed that the impact of magnetic field on Nu is more remarkable for higher Rayleigh numbers, Ra, and the change of Nusselt number with respect to Ra is more significant when the Hartmann number is smaller. A similar numerical work is carried out by Mliki et al. [25] focusing on the magneto-hydrodynamic (MHD) natural convection of nanofluid having CuO particles in an enclosure with C-shape regarding various inclination angles. They reported that the mean Nusselt number is augmented as the aspect ratio, inclination angle and nanoparticle volume fraction is increased, while the convection currents are retarded by magnetic effects. Considering the magnetohydrodynamic natural convection of Cu-water nanofluid in a rhombic enclosure, Dutta et al. [26] performed a numerical study where various parameters such as Rayleigh and Hartmann numbers together with nanoparticle concentrations are taken into account. Similar to the interpretations of above mentioned works, their results indicated that the influence of Hartmann number is not noticeable at low Ra, while it is significant at higher ones. Farooq [27] previously investigated the heat transfer performance of Ag-water nanofluid in a similar oblique cavity and concluded that the particle concentration and skew angle are the most prominent parameters.

Although there are significant number of studies that considers the natural convection in various cavities, the geometries are a bit more complicated in engineering applications [28], which includes the embedded bodies inside the enclosures [29]. Regarding these cavities having an embedded body inside, free convection in a square cavity having a cylinder with constant temperature inside was studied by Kimet al. [30], reporting that the location of the cylinder has a considerable impact on heat transfer performance. Sheikholeslami et al. [31] conducted a numerical study that investigates the natural convection in a circular cavity having a sinusoidal cylinder inside, considering the parameters of Rayleigh number, amplitude values andnumber of undulations, and their results show that the mean Nu is strongly dependent on these three parameters. Similarly, Jabbar et al. [32] explored the natural convection in a sinusoidal enclosurecontaning a circular cylinder, and concluded that the heat transfer is pronounced by increasing Rayleigh number and that the non-dimensional amplitudes damps the flow. Considering the natural convective heat transfer of various nanofluids in such cavities, Mliki et al. [33] conducted a numerical study that considers the magnetic field and heat generating/absorbing element inside the cavity. Their results revealed the heat transfer improvement caused by nanoparticles for all examined Hartmann and Rayleigh numbers, additionally, a more noticeable influence of heat generation or absorption at the lowest investigated Rayleigh number compared to higher ones. Abbasi et al. [34] performed a numerical study and examined the free convection of nanofluids in an incinerator model under magnetic effect, and having a heating block inside. In this comprehensive study where the parameters such as Ra and Ha, tilt angle and particle concentration are examined, their results showed that the generated entropy increases with increasing Rayleigh number, enclosure dimensions and nanoparticle volume fraction,and reduces by strengthening of magnetic field. Besides, they indicated that the heat transfer is not noticeably affected with the increment of Hartmann number. Selimefendigil and Oztop [35] explored the MHD natural convection in a square cavity with square, diamond or circular shaped obstacles, and concluded that the heat transfer is remarkably reduced by these obstacles compared to no-obstacle case, however, this reduction rate is decreased by increasing Hartmann number. In a recent study, Tayebi and Chamkha [36] numerically examined the MHD free convective heat transfer of nanofluid inside a cavity that has a conductive hollow cylinder in the centre, and they concluded that the hollow cylinder has a remarkable role in flow control and heat transfer characteristics as well as in irreversibility.

In addition to the complex geometries simulating the engineering applications, the general shape of the enclosures are also improved in order to contribute the enhancement of heat transfer inside the cavity, together with nanoparticle utilization. For this further improvement, increasing the heat transfer area by using wavy walls comes up as an effective option that is considered by numerous researchers [[37], [38], [39], [40]]. As a promoted researcher in the subject of natural convection in complex engineering geometries, Mahmud et al. [41] stated that the heat transfer is fallen up to a certain waviness point and it is again increased in their study about wavy walled enclosure. Another study considering a similar geometry, however, having a cylindrical block inside the enclosure, is conducted by Hatami [42] and the outcomes pointed out that optimum geometrical parameters for the inner cylinder and wavy walls should be obtained for maximizing the heat transfer. Cho et al. [43] concluded in their work focusing on the convection of nanofluids in wavy enclosures that the utilization of water based nanofluids in complex geometries such as wavy enclosure may be beneficial in engineering applications due to their desirable heat transfer characteristics together with low irreversibility and energy losses. Hashim et al. [44] focused on the alumina-water nanofluid in wavy-wall enclosure and their results showed that increment in undulation number improves heat transfer at low Ra, while it exhibits a non-linear behaviour in high Rayleigh numbers. Sheremet et al. [45] explored MHD free convection in a tilted cavity that has a wavy wall and is heated from corner, considering various parameters including the inclination of magnetic field. They concluded that an increase in magnetic field results in a decrement in heat transfer rate, and inclination of the magnetic field has a considerable impact on buoyancy forces.

Regarding the literature review presented above in the present paper, there is a significant effort put by researchers on heat transfer enhancement in enclosures not only by nanofluids but also by various modifications on the geometry. All in all, it is obvious that these techniques can improve the heat transfer performance in enclosures, however, there are limited studies in the literature that consider magnetic field, wavy structure and also heat generation and absorption together, according to the widest knowledge of authors, although there are numerous works considering these parameters separately or in simpler geometries. Therefore, in the present study, the natural convection of Cu-water nanofluid in a wavy enclosure that contains a heat generating/absorbing circular element and that is subjected to a magnetic field is investigated numerically by employing a finite element method based on Galerkin weighted residual formulation. In order to deepen the understanding of the influence of various parameters on heat transfer enhancement, Hartmann number (0 ≤ Ha ≤ 60), Rayleigh number (10³ ≤ Ra ≤ 10⁷), heat coefficient (−10 ≤ q ≤ +10) representing the generation or absorption of heat, and nanoparticle volume fraction (0 ≤ ϕ ≤ 0.06) are all considered together within the present numerical work. The outcomes of the computations regarding the aforementioned parameters are presented by the contours of streamlines and isotherms as well as a mean Nusselt number, Nu, in order to attain a clear vision to the flow and heat transfer characteristics.