scholarly journals An Analytical Investigation of Natural Convection of a Van Der Waals Gas over a Vertical Plate

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 121
Author(s):  
Andriy A. Avramenko ◽  
Igor V. Shevchuk ◽  
Margarita M. Kovetskaya
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Vertical Plate ◽  
Van Der Waals ◽  
Nonlinear Effects ◽  
Analytical Investigation ◽  
Ideal Gas ◽  
Van Der Waals Gas ◽  
Van Der Waals Equation ◽  
Nusselt Numbers

The study focused on a theoretical study of natural convection in a van der Waals gas near a vertical plate. A novel simplified form of the van der Waals equation derived in the study enabled analytical modeling of fluid flow and heat transfer. Analytical solutions were obtained for the velocity and temperature profiles, as well as the Nusselt numbers. It was revealed that nonlinear effects considered by the van der Waals equation of state contribute to acceleration or deceleration of the flow. This caused respective enhancement or deterioration of heat transfer. Results for a van der Waals gas were compared with respective computations using an ideal gas model. Limits of the applicability of the simplified van der Waals equations were pinpointed.

scholarly journals An Integral Method for Natural Convection of Van Der Waals Gases over a Vertical Plate

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4537
Author(s):  
A. A. Avramenko ◽  
I. V. Shevchuk ◽  
Yu. Yu. Kovetskaya ◽  
N. P. Dmitrenko
Keyword(s):  
Natural Convection ◽  
Integral Method ◽  
Van Der Waals ◽  
Analytical Form ◽  
Ideal Gas ◽  
Heated Plate ◽  
Van Der Waals Gas ◽  
Transfer Coefficients ◽  
Nusselt Numbers ◽  
Energy Equations

This paper focuses on a study of natural convection in a van der Waals gas over a vertical heated plate. In this paper, for the first time, an approximate analytical solution of the problem was obtained using an integral method for momentum and energy equations. A novel simplified form of the van der Waals equation for real gases enabled estimating the effects of the dimensionless van der Waals parameters on the normalized heat transfer coefficients and Nusselt numbers in an analytical form. Trends in the variation of the Nusselt number depending on the nature of the interaction between gas molecules and the wall were analyzed. The results of computations for a van der Waals gas were compared with the results for an ideal gas.

Heat Transfer by Natural Convection From an Array of Short, Wall-Attached Horizontal Cylinders

1982 ◽  
Vol 104 (1) ◽  
pp. 125-131 ◽  
Author(s):  
E. M. Sparrow ◽  
D. S. Cook ◽  
G. M. Chrysler
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Plate ◽  
Diameter Ratio ◽  
Nusselt Numbers ◽  
Cylinder Length ◽  
Horizontal Cylinders ◽  
Length To Diameter Ratio

Per-cylinder natural convection Nusselt numbers were measured for an in-line array of short horizontal cylinders that were affixed to a convectively participating vertical plate. The effect of cylinder length-to-diameter ratio, intercylinder spacing, position at which the cylinder is attached to the vertical plate, and Rayleigh number were investigated. The experiments were performed in air. It was found that the extent to which a given cylinder in the array was affected by cylinders situated below it depended on the Rayleigh number, with enhanced heat transfer coefficients being more likely at higher Rayleigh numbers. Greater enhancement occurred at larger intercylinder spacings. The qualitative characteristics of the Nusselt number results were insensitive to the cylinder length-to-diameter ratio, but the longer cylinders exhibited higher values of the Nusselt number. For the most part, the Nusselt numbers for the wall-attached horizontal cylinders fell below those for the classical horizontal cylinder of infinite length.

Effects of Insulated and Isothermal Baffles on Pseudosteady-State Natural Convection Inside Spherical Containers

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Yuping Duan ◽  
S. F. Hosseinizadeh ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Enhancement ◽  
Numerical Procedure ◽  
Boussinesq Approximation ◽  
Transfer Enhancement ◽  
Nusselt Numbers ◽  
Extended Surface ◽  
Parametric Studies ◽  
Thermal Layer

The effects of insulated and isothermal thin baffles on pseudosteady-state natural convection within spherical containers were studied computationally. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables. Natural convection effect is modeled via the Boussinesq approximation. Parametric studies were performed for a Prandtl number of 0.7. For Rayleigh numbers of 104, 105, 106, and 107, baffles with three lengths positioned at five different locations were investigated (120 cases). The fluid that is heated adjacent to the sphere rises replacing the colder fluid, which sinks downward through the stratified stable thermal layer. For high Ra number cases, the hot fluid at the bottom of the sphere is also observed to rise along the symmetry axis and encounter the sinking colder fluid, thus causing oscillations in the temperature and flow fields. Due to flow obstruction (blockage or confinement) effect of baffles and also because of the extra heating afforded by the isothermal baffle, multi-cell recirculating vortices are observed. This additional heat is directly linked to creation of another recirculating vortex next to the baffle. In effect, hot fluid is directed into the center of the sphere disrupting thermal stratified layers. For the majority of the baffles investigated, the Nusselt numbers were generally lower than the reference cases with no baffle. The extent of heat transfer modification depends on Ra, length, and location of the extended surface. With an insulated baffle, the lowest amount of absorbed heat corresponds to a baffle positioned horizontally. Placing a baffle near the top of the sphere for high Ra number cases can lead to heat transfer enhancement that is linked to disturbance of the thermal boundary layer. With isothermal baffles, heat transfer enhancement is achieved for a baffle placed near the bottom of the sphere due to interaction of the counterclockwise rotating vortex and the stratified layer. For some high Ra cases, strong fluctuations of the flow and thermal fields indicating departure from the pseudosteady-state were observed.

Laminar Natural Convection in a Discretely Heated Cavity: II—Comparisons of Experimental and Theoretical Results

1995 ◽  
Vol 117 (4) ◽  
pp. 910-917 ◽  
Author(s):  
T. J. Heindel ◽  
F. P. Incropera ◽  
S. Ramadhyani
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Nusselt Numbers ◽  
Numerical Predictions ◽  
Number Flow ◽  
Experimental Geometry

Three-dimensional numerical predictions and experimental data have been obtained for natural convection from a 3 × 3 array of discrete heat sources flush-mounted on one vertical wall of a rectangular cavity and cooled by the opposing wall. Predictions performed in a companion paper (Heindel et al., 1995a) revealed that three-dimensional edge effects are significant and that, with increasing Rayleigh number, flow and heat transfer become more uniform across each heater face. The three-dimensional predictions are in excellent agreement with the data of this study, whereas a two-dimensional model of the experimental geometry underpredicts average heat transfer by as much as 20 percent. Experimental row-averaged Nusselt numbers are well correlated with a Rayleigh number exponent of 0.25 for RaLz ≲ 1.2 × 108.

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