Simulation of combined convective-radiative heat transfer of hybrid nanofluid flow inside an open trapezoidal enclosure considering the magnetic force impacts
Introduction
It is particularly important to assess fluid flow inside various enclosures in the design of thermal equipment and engineering systems. Heat exchangers, solar ponds, nuclear tools and electronic cooling systems are among the most important of these equipment. As a result, several researchers examined this issue from different perspectives [1], [2], [3], [4], [5]. Mahmoodabadi et al. [6] assessed the incompressible laminar convection flow in a three dimensional enclosure. They utilized the improved meshless local Petrov-Galerkin (MLPG) scheme to solve the governing equations. Atashafrooz and Shafie [7] examined the entropy generation analysis inside an enclosure with diagonal side walls via the modified blocked-off technique. Saha et al. [8] assessed the influences of baffle shape on the hydrothermal treatment of air flow in a rectangular enclosure. They described that maximum heat transfer rate is related to the plane baffles. Bhowmick et al. [9] investigated the chaotic natural convection fluid flow inside a V-shaped chamber.
A major concern of thermal science researchers is the control of heat transfer rates for the optimal design of engineering systems. So far, many studies have been done by various researchers in this field. These studies have proposed the various techniques and schemes to predict and control the thermal behaviors of fluid flow in different geometries. One of the practical and useful methods presented in this field is the technique of adding the solid nanoparticles with high thermal conductivity to the base fluids with low thermal conductivity (formation of nanofluids) [10], [11], [12]. In fact, by adding a certain concentration of solid nanoparticles to the base fluids, the heat transfer rate in engineering systems can be significantly increased [13], [14], [15]. Recently, Sheikholeslami and Jafaryar [16] ad Sheikholeslami [17], [18], [19] analyzed the thermal treatment of different solar systems in the existence of various nanoparticles. They showed that the use of solid nanoparticles along with other technologies have the significant impacts on the performance of solar systems.
Another useful method proposed in this field is to apply a magnetic field in the flow domain (MHD flow) [20], [21], [22], [23], [24], [25]. In this type of flow, the Lorentz force plays an important role in determining hydrothermal behaviors [26], [27]. Due to the importance of magnetic field and solid nanoparticles in controlling the heat transfer rate, several scholars have investigated the interaction impacts of these parameters on convection fluid flow in different enclosures [28], [29], [30], [31], [32]. Rashidi et al. [33] applied the high-order compact method to simulate the influences of Hartmann number and volume fractions of hybrid nanoparticles on mixed convection flow inside a square enclosure. Yan et al. [34] compared the magnitudes of heat transfer rates for mixed convection flow in tall and narrow enclosures filled with hybrid nanofluid by computing the average Nusselt numbers. Fu et al. [35] assessed the interacting impacts of the nanoparticles concentration and baffles characteristics on the hydrothermal trends of –ethylene glycol nanofluid flow in an enclosure by utilizing the lattice Boltzmann method. Rostami et al. [36] simulated the mixed convection flow of MHD –ethylene glycol nanofluid in an enclosure filled with porous media. Results of that paper indicate that magnitudes of streamlines and Nusselt numbers are significantly dependent on the nanoparticle concentration and Rayleigh and Hartmann numbers. Al-Farhany et al. [37] examined the natural convection of nanofluid flow inside a U-shaped porous enclosure in the existence of two baffles and an incline magnetic field. Bhatti et al. [38], [39], [40] analyzed the effects of different magnetic hybrid nanoparticles on hydrothermal behaviors of fluid flow through vertical parallel plates, flat elastic surface and tapered stenosed artery. These researches showed that the use of magnetic hybrid nanoparticles leads to an improvement in hydrothermal treatment of different systems. Acharya [41] investigated the influences of a circular cylinder on hydrothermal behaviors of magnetized hybrid nanofluid flow in a three-dimensional cavity under different thermal boundary conditions. It can be concluded that the cold and heated cylinders respectively render the highest and lowest heat transference.
Another concern of thermal science researchers is the accurate simulation of heating systems. By considering the effects of radiative heat transfer along with conductive and convective heat transfer mechanisms, more accurate results could be achieved in simulation of thermal systems [42], [43], [44]. So far, several researchers assessed the interaction effects of radiative and convective heat transfer mechanisms in heating systems [45], [46], [47], [48], [49]. A number of these studies have been related to the MHD or nanofluid flow in various geometries [50], [51], [52], [53], [54], [55], including the enclosure geometry [56], [57], [58], [59], [60]. Among these researches, Shah et al. [61] evaluated the impacts of Lorentz force, thermal radiation and nanoparticles shape on treatment of Darcy nanofluid flow inside a porous chamber. Khetib et al. [62] simulated the magnetic force and thermal radiation impacts on free convection flow of nanofluid inside an inclined enclosure. Chammam et al. [63] applied the finite element approach to assess the thermal radiation role on treatment of MHD free convection flow of nanofluid inside a complex enclosure. Khan et al. [64] utilized the lattice Boltzmann technique to investigate the radiation influences on convective heat transfer and entropy generation for MHD nanofluid flow in a closed chamber. Sreedevi and Reddy [65] assessed the role of magnetic force and thermal radiation on hydrothermal trends of the ethylene glycol- nanofluid flow inside a square cavity by employing the Tiwari-Das model. They reported that highest values of heat transfer rate between hot and cold walls occur for maximum magnitudes of radiation parameter.
Although so far, several researches have been performed to assess the combined radiative-convective heat transfer in different geometries; but according to the knowledge of authors, the effects of radiative heat transfer on the forced convection flow of a hybrid nanofluid in the existence of an axial external magnetic field inside an open trapezoidal enclosure has not been considered by other researchers. Since, this type of enclosure has many applications in the thermal equipment and engineering industries; therefore, in this study, the interaction impacts of thermal radiation, magnetic force and concentration of hybrid nanoparticles of alumina and copper oxide on the thermal behaviors of fluid flow in an open trapezoidal enclosure are examined for the first time. It should be noted that to model the diagonal walls of this enclosure, the effective embedded boundary method is applied. In fact, the accuracy of this method is much higher than other common methods used in previous studies.
Section snippets
Problem identification
The problem studied in this research is as an open trapezoidal enclosure with two independent inlet and outlet ducts. The geometry of this enclosure is shown in Fig. 1. Based on this figure, the slope of the enclosure side walls relative to the horizontal axis is considered equal to . The enclosure height and the length of its bottom wall are respectively equal to and . Also, the lengths of the inlet and outlet ducts are respectively regarded equal to and , while the height of
Governing equations
The vector forms of governing equations for forced connection flow of a hybrid nanofluid in the presence of the thermal radiation and magnetic field impacts are expressed as follows [27], [51], [66]:
In which, and .
The parameters , , and represent respectively the density, dynamic viscosity, specific heat and thermal conductivity of the hybrid
Numerical solution
To obtain the dimensionless velocity and temperature fields in the trapezoidal enclosure, the non-dimensional form of the governing equations (continuity, momentum and energy equations) are first discretized using the finite volume method (integration on the volume of each element) and SIMPLE algorithm. Then, these discrete equations are solved by applying a hybrid method and three-diagonal matrix approach. This scenario continues as long as the convergence criteria are met as follows:
Code validation
To ensure the accuracy of the numerical calculations performed in the present study, the results of the written computer program are validated with the findings presented by different scholars. In Table 2, the average Nusselt number values along the bottom wall of a square enclosure are compared with those presented by Yan et al. [34] and Chamkha and Abu Nada [70] for different magnitudes of Richardson numbers and nanoparticles concentrations . These comparisons obviously
Results and discussion
First, to evaluate the impacts of thermal radiation, magnetic force and concentration of hybrid nanoparticles on the thermal treatment of fluid flow in the open trapezoidal enclosure, distributions of dimensionless isotherms are presented in Fig. 4(a) and (b) for different values of radiative parameter , Hartmann number and volume fractions of hybrid nanoparticles . Also, to better understand and interpret the details of these treatment, the variations of dimensionless temperature along
Conclusion
In this study, the impacts of radiative parameter, volume fraction of hybrid alumina-copper oxide nanoparticles and magnetic force on the thermal treatment of forced convection fluid flow in an open trapezoidal have been assessed. Embedded boundary method has been employed to model the inclined side walls of this enclosure. The results of this research could be abridged as follows:
- •
The magnetic force has a significant influence on the trends and magnitudes of and , whilst the
CRediT authorship contribution statement
Meysam Atashafrooz: Conceptualization, Supervision, Methodology, Formal analysis, Validation, Writing – original draft, Writing – review & editing. Hasan Sajjadi: Formal analysis, Investigation, Data curation, Writing – review & editing. Amin Amiri Delouei: Formal analysis, Investigation, Data curation, Writing – review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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