Numerical Solutions for the Free Convection flow in Chamfered enclosures

Abstract

In natural convection mechanism, the fluid’s motion is independent of the externally implanted source. During free convection, the heated fluid flows due to the difference in densities, occurring as a result of temperature gradients. Thus the density gradient is the only motivating force behind the natural convection, which causes the bulk movement of molecules within the fluid. Natural convection has gained massive attention from the researchers, because of its presence in both nature and engineering applications [1–4]. Natural convection is one of the easiest ad cheap method of cooling. That is why it has numerous applications including solar energy systems [5], cooling of electronic circuits [6], heat exchanger [7] and many more [8,9]. To be more specific natural convection plays a vital role in different fields like astrophysics, geophysics, metrology and many more. In addition to that natural convection also contributes to the different phenomena occurring in nature like bio-heat transfer, oceanic currents, heat transfer in the stellar atmosphere, and greenhouse effects. The free convection phenomenon also depends on various geometric shapes, fluid flow, and thermal distribution. Researchers presented different theoretical, experimental and numerical approaches with the sole purpose of the investigation of natural convection in cavities. To determine the influence of Rayleigh number and eccentricity on the conventional transfer of heat by natural means, a study is conducted by Kuehn and Goldstein [10]. Results recorded that local heat exchange on the cylinders significantly depend upon the eccentricity of the inner cylinder. Kim and Viskanta [11] investigated the influence of wall conductance in square enclosures that are oriented differently. Numerical solutions for the two dimensional equation of energy, motion and heat transfer of a Boussinesq fluid are evaluated. Natural convection is ascertained by Sharif and Mohammad [12] under the existence of constant heat flux. The behavior and impact of parameters like aspect ratio, longitudinal dimensions of heat source, and inclination angle, on fluid flow, are examined. The results are expressed in the context of streamlines and isothermal contours. Kuehn and Goldstein [13] presented a work for the analysis of the natural convection within the horizontal annulus via experimental and theoretical approach. The obtained DRSML QAU ii results show a good comparison with the numerical results. Simulations for the free convection flow between cold outer square cylinder and the hot inner one is carried out by Lee et al. [14]. They have used the immersed-boundary method for the observation of two dimensional free convection. Obtained outcomes were reported by virtue of streamlines and thermal contours. Xu et al. [15] numerically simulated the peculiarity of laminar free convection between the warmed chamber and its round about fenced in area. Results confirm that the inclination angle of the inner geometry shows a minor effect on the average Nusselt number. Karimi et al. [16] examined the unsteady free convective flow from the heat sources that are held inside a square enclosure. They revealed in their review that the distance between two intensity producing cylinders is liable for the variations in normal Nusselt number. Because of the implications and significance of natural convection, many researchers endorsed theoretical and observational studies on the phenomenon of natural convection in enclosures that are having different configurations, subjected to different terms and conditions [17–19]. Researchers add bodies whether it is active or not inside the cavity for the purpose to restrain the heat conductivity rate. The examination of natural convection in enclosure of square shape, which is heated and encapsulated with a cold circular cylinder, is done by Nabavizadeh et al.[20] . It is reported in the results that the heat conduction coefficient is affected by the alternations in amplitude. Under the volumetric heat source object, the phenomenon of natural convection is evaluated by Oztop et al.[21]. It is explored the heat transmission rate along the flow situation is greatly influenced by both the function of the wavy wall as well as the ratio of internal and external Rayleigh numbers. Free convection driven flow in a cold enclosure having two heat sources of equal diameter is presented by Yoon et al. [22] . For the phenomenon of laminar natural convection, under the existence and inexistence of heat-generating sources (internal bodies), Pandey et al. [23] developed an observational and mathematical study. Roy [24] has concentrated on the impact of nanoparticles on regular convection inside a square impacted by the different geometrical shapes at the center locale. His results portray that rectangle- ellipse- circle is the order according to shapes, in which the fluid intensity enhances, while for the mean Nusselt number the order is circle- ellipse- rectangle. Cho et al. [25] mathematically and experimentally deliberated the mechanism of natural convection generated by two heat sources kept inside a square cavity DRSML QAU iii with vertical barriers. Results depict that the flow regime’s transition depends on the variation in the aspect ratio. Selimefendigil and Öztop [26] numerically examined the heat transfer for free convection nanofluid within the cavity containing obstacles (with varying shapes). Results report that by considering obstacles, the thermal and flow profile have maximum behavior against Rayleigh number, while the heat exchange rate gets slow if the obstacles are not considered. The variation in flow dynamics in natural convection flow originated by heat generating source rooted inside an enclosure is studied by Oh et al. [27]. The impact of Rayleigh number ranging from 103 to 104 upon isotherms, average Nusselt number and the streamlines are noted. Wang et al.[28] proposed a mathematical investigation on heat exchange, as a source of natural convection in circular cylinder and presented the influence of flow controlling parameters on flow and thermal distribution. Sahi et al. [29] interpreted the magnetic field’s impact on the natural convection in a grooved rectangular enclosure subjected to isothermal boundary conditions. Yasin et al. [30] elucidated the consequences of both the uniform and nonuniform warmed bars on free convection stream within the porous enclosure. The study of the behavior and interactions of conducting liquid with the electromagnetic forces is termed as magnetohydrodynamics (MHD). Magnetic field involved Lorentz force whereas buoyancy force generates the fluid’s movement in free convection. These two forces oppose each other, thus the impact of magnetic field on free convection affect the flow dynamics. Study of the free convective flow under the action of external magnetic effects, is used by many researchers as a subject of interest. This is due to its wide range of applications in different fields of science and technology. Wang and Zhou [31] numerically simulated the phenomenon of external natural convection upon the liquid metal under various magnetic effect intensities. It is noted that the heat exchange and the liquid metal flow rate is enhanced under the application of magnetic field. Rebhi et al. [32] presented a numerical study of free convection in a porous enclosure holding an electrically conductive liquid. The results of the investigation show how that the magnetic field and inertial effects both have an impact on natural convection. Yu et al. [33] numerically examined the effect of a magnetic field with different horizontal inclinations on free convection in an electrically conducting fluid. They found that the inclination angle enhances the heat exchange rate whenever the aspect ratio is less or more than 1. DRSML QAU iv Nanofluids are viewed as another class of fluids, comprising of suspended nano-sized particles (1 − 100𝑛𝑚) inside a base fluid. . Nanofluids hold many important properties like higher heat conduction, stability, decreased possibilities of disintegration, decrease in siphoning power, and many more. These properties are utilizing nanofluid in numerous applications like intensity move [34], cooling of electronics such as microelectronics, energy components, drug processes, hybrid-powered engines [35], household refrigerating appliances, chiller heat exchangers, boiler fuel gas reduction, and biomedical field [36–38]. Because of efficient heat transfer characteristics and the wide range of its applications, nanofluids grab the attention of the modern-day research and scientists are exploring its importance and modification in various aspects. For the analysis of the improvement of thermal conduction of nanofluids, a hypothetical investigation is presented by Xaun and Li [39]. Das and Choi [40] presented a detailed review that spotlights on the intensity move system inside the nanofluid The review examines all the issues regarding convection, boiling and convective heat flux of nanofluid. For heat move upgrade of nanofluid within the sight of applied magnetic field, a review study is presented by Wang et al. [41]. Sabour et al. [42] presented a hypothetical report for the examination of free convection of nanofluids inside an enclosure. Basak and Chamkha [43] carried out a mathematical study for the nanofluid heatline analysis on free convection. Analysis is made for the square cavity with various boundary conditions. Tzou [44] discussed the instability of nanofluid in natural convection. Study for the heat transfer enhancement under thermophoresis and the Brownian motion effect is carried out by Haddad et al. [45]. The study of nanofluid natural convection within the enclosures having different geometric configuration is presented by Sadeghi et al. [46].For different geometric enclosures they have investigated both the relationship between the thermophysical properties and the manner in which they influence each other. Bourantas et al. [47] analyzed free convection of nanofluids in porous media. The impact of porous medium upon the cooling of nanofluids is presented by them. For the analysis of three dimensional natural convection of nanofluids a numerical work is presented by Ravink et al. [48]. Results are obtained via three-dimensional element based solver. Sheikholeslami et al. [49] have explored the effect of magnetic field upon the free convection of nanofluids within the enclosures. DRSML QAU v Entropy generation implies the measure of irreversibility in a system. Entropy varies directly with the temperature. Augmentation in the Rayleigh number lifts the peculiarity of free convection, as an outcome the typical entropy generation increases. Entropy generation in nanofluids is considered as a subject of discussion by various researchers. For instance, Mehrez et al. [50] mathematically examined the variations in thermal transmission rate and the irreversibilities for Copper-water nanofluid under the external magnetic effects. The results portray that the strength of magnetic effects has a significant impact on entropy generation, heat exchange, temperature profile, and the local Nusselt number. For the determination of regular convection and irreversibilities in a trapezoidal-shaped container having Cu-water nanofluid, Mahmoudi et al. [51] conducted a study. Results not only illustrate that the magnetic effect enhances the behavior of irreversibilities within the system but also indicate that the addition of nanoparticles causes a reduction in the irreversibilities. Mahian et al. [52] carried out an analytical study of the law of increased entropy in a vertically held annulus containing a nanofluid having 𝑇𝑖𝑂2 as nanoparticles in water based fluid. For the analysis of entropy generation within nanofluids a comprehensive review work is presented by Mahian et al. [53]. Results highlight the behavior of entropy generation in accordance with the heat exchange in nanofluids. Animasaun et al. [54] presented a theoretical review regarding the influence of Brownian motion upon the motion adopted by different kinds of nanofluids. Results explain that, due to the Brownian motion the Nusselt number increases significantly. Parvin et al. [55] presented the deportment of entropy formation and heat exchange due to forced convection via direct absorption solar collector. The effect of the volume proportion of nanoparticles, Reynolds number, average entropy production, Bejan number, and collector efficiency on heat transmission is investigated. Al-Rashed et al. [56] noted the variations in entropy generation and natural convection under different considered Rayleigh number and the volumetric proportion of solid nanoparticles. A cubical cavity having water − 𝐴𝑙2𝑂3 nanofluid is considered. Ellahi et al. [57] developed a mathematical model for the natural convection boundary layer in an inverted cone. 𝐶𝑢−𝐻2𝑂 is taken as the nanofluid and the influence of the nanoparticles shape upon the irreversibilities is investigated. Rahimi et al. [58] provided a numerical investigation that focuses on the phenomenon of natural convection and entropy generation. Results depict that entropy generation varies directly with the Rayleigh number and inversely for DRSML QAU vi the nanoparticles volume fraction. Sheikholeslami et al. [59] provided analytical solutions for the study of the effect of magnetic field on heat transfer in 𝐶𝑢𝑂 − 𝑤𝑎𝑡𝑒𝑟 nanofluid inside an enclosure having a heated base. The obtained results reveal that by increasing the length of the heat source and Hartmann number, the heat transfer enhances and it decreases with the increase in Rayleigh number. A numerical interpretation of natural convection along with entropy generation in a partially heated triangular cavity having 𝐶𝑢 −water nanofluid is conducted by Bondareva et al. [60]. It is noticed that large Rayleigh numbers leads to the augmentation in heat transmission while the flow rate diminishes because of addition of solid nanoparticles. Sheikholeslami and Ganji [61] investigated the phenomenon of free convection under an applied magnetic field in a cavity containing 𝐶𝑢𝑂 − 𝑤𝑎𝑡𝑒𝑟 as a nanofluid. Results are obtained against different parameters, and evaluation depict the intensifying entropy generation against larger Rayleigh parameter and decline with respect to the Hartmann number. Patel et al. [62] proposed a micro-convective model to analyze the thermal conduction of nanofluids. Results portray that the Brownian motion causes enhancement in thermal conductivity of nanofluids. Mliki et al. [63] numerically interpreted the phenomenon of natural convection for 𝐶𝑢 − 𝑤𝑎𝑡𝑒𝑟 nanofluid in a cavity and different heating modes on vertical walls. Outcomes reveal that heat transfer is influenced by nanoparticles volume fraction. The main purpose of this dissertation is to obtain the numerical solutions for the free convection flow in enclosures with the heat generating sources. It contains three chapters. Chapter one is all about the fundamental laws and definitions regarding fluid dynamics. Second chapter presents Finite Element Analysis of free convective flow in chamfered enclosure. Chapter three elaborates the Entropy analysis for nanoliquid free convection flow in a partially adiabatic enclosure.