Flow features of natural convection in a parallelogrammic enclosure

Aldridge, K. D.; Yao, H.

doi:10.1016/s0735-1933(01)00296-2

Cited by 22 publications

(12 citation statements)

References 7 publications

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“…The average Nusselt number values along the hot left sidewall increase as the external Rayleigh number increases. 10. The average Nusselt number along the hot left sidewall does not explain any significant change for different values of inclination angles and external Rayleigh numbers when the internal Rayleigh numbers are in the range from 10 5 to 10 6 .…”

mentioning

confidence: 80%

“…The overall Nusselt number for the parallelogram enclosure can be several times higher or lower than that for the corresponding rectangular or square enclosures [6,7]. Natural convection problems in a parallelogram enclosure have been previously studied [8][9][10][11], for various values of Rayleigh number, Prandtl number, aspect ratio, and inclination angle. It has been noticed from the literature review that there is a wide range of investigations related to the flow and convective heat transfer in rectangular or square enclosures driven by buoyancy and shear forces, but there is a limited work related to parallelogram enclosures.…”

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confidence: 99%

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Numerical Simulation of Natural Convection in a Parallelogrammic Enclosure Containing Volumetric Heat Source with Non‐uniformly Heated Left Sidewall

Hussain

Hussein

Kadim

2013

Heat Trans. Asian Res.

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The influence of the external Rayleigh number, inclination angle, and internal Rayleigh number on natural convection within an air-filled parallelogrammic enclosure containing a volumetric source has been investigated numerically. The left sidewall of the enclosure is subjected to a non-uniformly hot temperature and the right sidewall experiences a uniform cold temperature while the remaining top and bottom walls are kept adiabatic. The physical problems are represented mathematically by various sets of governing equations along with the corresponding boundary conditions. Buoyancy forces are taken into account during the analysis of the present investigation. By using the finite volume method, the dimensionless governing equations are discretized numerically based on a non-uniform collocated grid system. Results are obtained for a wide range of external Rayleigh numbers varying from 10 3 to 10 6 with internal Rayleigh numbers varying from (0) to (10 8 ) while the left sidewall from vertical is varied as 0, 30, -30, 60, and -60°, respectively. In the present study, the obtained results are presented in terms of streamlines, isotherms, and average Nusselt number along the hot and cold sidewalls. Two pairs of rotating vortices are observed due to the non-uniform heating process while the shape of this rotating vortices is sensitive to the inclination angle. Furthermore, the flow field circulation and the average Nusselt number increase remarkably with the increase in the external Rayleigh number. The results of the present work are compared with other published results and give excellent agreement.

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confidence: 80%

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confidence: 99%

Numerical Simulation of Natural Convection in a Parallelogrammic Enclosure Containing Volumetric Heat Source with Non‐uniformly Heated Left Sidewall

Hussain

Hussein

Kadim

2013

Heat Trans. Asian Res.

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“…The changing the parameters of geometric form is a suitable method to increase the thermal performance. So that many researchers have investigated to enhance the heat transfer in the parallelogramic enclosure with the various cross sectional shapes using conventional working fluids and varied methods Chung and Trefethen, (1982); Seki et al, (1983); Hyun and Choi, (1990); Aldridge and Yao, (2001) ;Baïri, (2008); Saleh et al, (2011). Systematic and comprehensive numerical results of the fluid flow and thermal patterns evolutions are presented for tilt angles 0°, ±15°, ±30°, ±45°, ±60°; and different values of Rayleigh numbers 10 5 , 10 6 , and 10 7 .…”

Section: Frontiers In Heat and Mass Transfermentioning

confidence: 99%

Characteristics of Natural Convection Flow and Heat Transfer of Parallelogramic Enclosure With an Inner Circular Cylinder Using Liquid Nanofluids

Abdulkadhim¹,

Majdi²,

Abed³

2018

Frontiers in Heat and Mass Transfer

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Fluid flow and natural convection heat transfer in a parallelogram enclosure with an inner circular cylinder using Cu-water nanofluid are studied numerically. Dimensionless Navier-Stokes and energy equations are solved numerically using finite element method based two-dimensional flow and steady-state conditions. This study evaluates the effect of different concentrations of Cu-water nanofluids (0% to 6%) with different Rayleigh numbers 10 3 ≤ Ra ≤ 10 6 under isotherm wall temperatures. The effects of geometrical parameters of the parallelogram enclosure (inclination angle in range of 0 ≤ α≤ 30 and location of inner circular cylinder-0.2 ≤ H ≤ +0.2 on the flow field and heat transfer are examined. The results are presented in terms of streamlines, isotherms, local and average Nusselt number. It is found that the inclination angle has a significant effect on flow pattern and heat transfer and the inclination angle of 30 o at a vertical location H=-0.2 gives better fluid flow strength. Moreover, the maximum heat transfer enhancement is obtained when the circular cylinder moves vertically downward up to H=-0.1 and the inclination angle is 30 o. The results also indicate that as the Rayleigh number, nanofluid concentration increase, the rate of heat transfer will increase.

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“…The problem is solved by the finite volume numerical approach and they considered various physical parameters that describe nanofluids characteristics and thus presented results in a graphical form. Various research studies 8‐11 are available in the literature considering natural convection flow in such a parallelogrammic enclosure using different boundary conditions. From these studies, it can be concluded that these types of physical models like parallelogrammic or skewed are useful in many mechanical devices to perform as a thermal inhibitor or promoter 7 .…”

Section: Introductionmentioning

confidence: 99%

Study of mixed convection flow of power‐law fluids in a skewed lid‐driven cavity

et al. 2021

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This study conducts a numerical simulation of mixed (combined) convective non‐Newtonian fluid flow inside a two‐dimensional cavity (skewed) having a moving lid. The upper and bottom extremities of the cavity with different temperatures and two insulated side walls cause natural convection. Moreover, the forced convection is maintained by the motion of the lid with constant velocity. The governing equations are nondimensionalized with appropriate transformations and then transformed into curvilinear coordinates. A finite volume numerical procedure with a collocated grid arrangement is used to solve these equations. Comparisons with previously reported results are carried out, which shows an excellent agreement. Non‐Newtonian behaviors such as pseudo‐plastic (shear‐thinning) and dilatant (shear‐thickening) are considered using the power‐law model, and thus the power‐law index is chosen accordingly. A wide range of the governing dimensionless parameters which affect the mixed convection flow inside the skewed cavity, including Grashof number ( 1 0 2 ≤ G r ≤ 5 × 1 0 4 ), Richardson number ( 0.000625 ≤ R i ≤ 5 ), Reynolds number ( R e = 100 and 400), and power‐law index ( 0.7 ≤ n ≤ 1.3 ). The Prandtl number ( P r = 10) is fixed and the skew angles ( φ = 4 5 ∘ , 9 0 ∘ , and 13 5 ∘ ) are considered for acute, right‐angle, and obtuse angles. The obtained numerical outcomes of the study are shown graphically and also in tabular form for vertical and horizontal velocities, streamlines, isotherms, temperature distributions, and the rate of heat transfer and insight physics of the flow features, are discussed thereafter. It can be concluded that the rate of heat transfer in the present case is sensitive to the skew‐angle as well as power‐law index, and the maximum heat transfer occurs in the case of dilatant (shear‐thickening) fluid.

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Flow features of natural convection in a parallelogrammic enclosure

Cited by 22 publications

References 7 publications

Numerical Simulation of Natural Convection in a Parallelogrammic Enclosure Containing Volumetric Heat Source with Non‐uniformly Heated Left Sidewall

Numerical Simulation of Natural Convection in a Parallelogrammic Enclosure Containing Volumetric Heat Source with Non‐uniformly Heated Left Sidewall

Characteristics of Natural Convection Flow and Heat Transfer of Parallelogramic Enclosure With an Inner Circular Cylinder Using Liquid Nanofluids

Study of mixed convection flow of power‐law fluids in a skewed lid‐driven cavity

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