A New Benchmark Quality Solution for the Buoyancy-Driven Cavity by Discrete Singular Convolution

Wan, Bo

doi:10.1080/104077901752379620

Cited by 291 publications

(26 citation statements)

References 28 publications

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“…This authentication enhances self-assurance in numerical result of the present study. The current code is further confirmed by matching the result in the time-independent study of "Ghasemi et al [51], Davis [52] as well as Wan et al [53]". Ghasemi et al [51] have investigated water-alumina nanofluid within a square vessel.…”

Section: Grid Independence Test and Code Validationsupporting

confidence: 85%

“…Grid analysis for the geometrical domain for = 10 6 , = 0.05, = 10 , = 20, = 90 ∘ at = 0.1 Assessment of the current result with Holtzman et al[50] in terms of for Comparison of the present data ( ) with the study of Ghasemi et al[51], Davis[52] and Wan et al[53] for diverse Ghasemi et al[51] Davis[52] Wan et al[53] Present study Ghasemi et al[51] Current study…”

mentioning

confidence: 61%

“…An excellent agreement has been accomplished between the two studies. The results of the present study are further compared with the results of a specific situation of Davis [52] and Wan et al [53]. In this case our present study has been transferred for an air-filled square cavity with Pr 0.70 = and the mean Nusselt number is calculated for = 0 and = 10 3 − 10 6 as shown in Table 4.…”

Section: Grid Independence Test and Code Validationmentioning

confidence: 80%

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Heat Transportation in Copper Oxide-Water Nanofluid Filled Triangular Cavities

Uddin

Rahman²

2020

IJHT

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This paper performs a comparative analysis of two-dimensional transient water-copper oxide nanofluid flow and heat transportation inside a right-, acute-and obtuse-angled triangular cavity in the presence of a magnetic field. The vertical and inclined walls of the enclosure are maintained at a constant low temperature whereas the base wall is heated by a uniform thermal condition. The finite element method is used to solve the principal equations of nanofluid within the cavities along with the wall conditions. The outcomes of the present problem for a specific case are verified by the standard published numerical results. For comparative analysis, the isotherms, streamlines, the heat transfer distribution, the average heat transfer rate on the heated wall and within the cavities for the several pertinent parameters of the problem are demonstrated. The result shows that the nanofluid filled obtuse-angled triangular cavity exhibits a higher heat transfer rate for the lower and moderate values of the thermal Rayleigh number whereas for the higher thermal Rayleigh number acute-angled triangular cavity shows better heat transfer performance than that of the other two cases analyzed in the present study. The presence of a magnetic field lessens the heat transfer rate in nanofluid applications. The magnetic field inclination angle controls the flow and heat transfer of nanofluid. Nanofluid flow shows insignificant effects of the friction in cavities compared to that of the base fluid.

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Section: Grid Independence Test and Code Validationsupporting

confidence: 85%

mentioning

confidence: 61%

Section: Grid Independence Test and Code Validationmentioning

confidence: 80%

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Heat Transportation in Copper Oxide-Water Nanofluid Filled Triangular Cavities

Uddin

Rahman²

2020

IJHT

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“…Simulations were performed using a three-dimensional cubic cavity with unit dimension and the flow was subjected to gravity effects. A cubic cavity was used as the physical model due to its simple geometry [7] and its presence in several industrial applications [8]. Natural convection investigations using OB and NOB were performed to verify the potential of NOB to model flows with variable specific mass in the momentum and energy equations.…”

Section: The Physical Modelmentioning

confidence: 99%

An extension of Oberbeck–Boussinesq approximation for thermal convection problems

Duarte

Melo

Villar

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

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An extension of the Oberbeck-Boussinesq approximation (OB) with expressive thermal effects is investigated to model specific mass with a temperature-dependent approach. An expansion of OB is proposed using a mathematical formulation with null velocity divergence in the continuity equation and variable specific mass in the momentum and energy equations (NOB). The NOB method has been previously tested in the literature, and the present paper aims to carry out a quantitative analysis between NOB and OB. The specific mass is calculated based on the temperature field and a divergence-free velocity is imposed on the NOB due to the small effects of variations of the specific mass in the continuity equation, as previously demonstrated by the OB. The purpose of the NOB is to overcome the OB's restriction to single-phase flows, as well as to model the effects of specific mass variations more accurately, especially in problems with prominent thermal transfer effects, as that occur in the turbulent regime. Since the effects of a variable specific mass in the momentum and energy equations were taken into account by the NOB, it was expected that the thermal transfer results of the NOB would be improved compared with those of the OB. Then, three-dimensional natural convection simulations for a large range of Rayleigh numbers were performed using OB and NOB in a cubic cavity. Turbulence modeling was performed using Large Eddy Simulation (LES). Numerical results from both approaches were validated and all the results presented good quality. Thermal transfer was evaluated by the calculation of the Nusselt number at the heated wall and compared to experimental data from the literature. The OB and NOB provided adequate thermal transfer rate results; however, the differences between the literature and OB were higher than for NOB. Therefore, NOB is presented as a useful mathematical formulation for modeling incompressible flows with a temperature-dependent specific mass approach in single-phase or multiphase problems instead of solving the full compressible mathematical formulation. In addition, the differences between the literature and OB results increased as the Rayleigh number was raised, especially in the turbulent regime. The results of the NOB were closer to the literature than were those of the OB for the entire range of Rayleigh numbers tested. Therefore, the numerical results confirmed the higher accuracy of NOB compared to OB despite the NOB's still being an approximate model. Lastly, flow visualization allowed the identification of coherent turbulent structures near the cavity walls in the simulation with Rayleigh number 10 10. The presence of hairpin and Tollmien-Schlichting instabilities revealed the importance of modeling the three-dimensional effects of natural convection in the turbulent regime.

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“…Moreover, the works in Refs. [1][2][3][4][5] reflect the mathematician's interest in such engineering problem to test the validation of new analytical and numerical methods. Another pertinent field with applications above is the nanofluids technology.…”

Section: Introductionmentioning

confidence: 99%

Magnetic Field Effect on Mixed Convection in Lid-Driven Trapezoidal Cavities Filled With a Cu–Water Nanofluid With an Aiding or Opposing Side Wall

Chamkha

Ismael

2016

Journal of Thermal Science and Engineering Applications

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The present study investigates mixed convection inside a Cu–water nanofluid filled trapezoidal cavity under the effect of a constant magnetic field. The mixed convection is achieved by the action of lid-driving of the right hot inclined side wall in the aiding or the opposing direction. The left inclined side wall is fixed and kept isothermal at a cold temperature. The horizontal top and bottom walls are fixed and thermally insulated. The magnetic field is imposed horizontally. The problem is formulated using the stream function-vorticity procedure and solved numerically using an efficient upwind finite-difference method. The studied parameters are: the Richardson number Ri = (0.01–10), the Hartman number Ha = (0–100), the volume fraction of Cu nanoparticles φ = (0–0.05), and the inclination angle of side walls Φ = (66 deg, 70 deg, 80 deg). The results have shown that the suppression effect of the magnetic field for the aiding case is greater than that for the opposing case. Meanwhile, the enhancement of the Nusselt number due to the presence of the Cu nanoparticles is greater for opposing lid-driven case.

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A New Benchmark Quality Solution for the Buoyancy-Driven Cavity by Discrete Singular Convolution

Cited by 291 publications

References 28 publications

Heat Transportation in Copper Oxide-Water Nanofluid Filled Triangular Cavities

Heat Transportation in Copper Oxide-Water Nanofluid Filled Triangular Cavities

An extension of Oberbeck–Boussinesq approximation for thermal convection problems

Magnetic Field Effect on Mixed Convection in Lid-Driven Trapezoidal Cavities Filled With a Cu–Water Nanofluid With an Aiding or Opposing Side Wall

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