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.

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.

Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas

2019 ◽  
Vol 20 (3-4) ◽  
pp. 461-473 ◽  
Author(s):  
Jinhuan Wang ◽  
Yicheng Pang ◽  
Yu Zhang
Keyword(s):  
Euler Equations ◽  
Van Der Waals ◽  
Vacuum State ◽  
Ideal Gas ◽  
Transport Equations ◽  
Rarefaction Waves ◽  
Van Der Waals Gas ◽  
Riemann Solutions ◽  
Riemann Solution ◽  
Isentropic Euler Equations

AbstractIn this paper, we consider limit behaviors of Riemann solutions to the isentropic Euler equations for a non-ideal gas (i.e. van der Waals gas) as the pressure vanishes. Firstly, the Riemann problem of the isentropic Euler equations for van der Waals gas is solved. Then it is proved that, as the pressure vanishes, any Riemann solution containing two shock waves to the isentropic Euler equation for van der Waals gas converges to the delta shock solution to the transport equations and any Riemann solution containing two rarefaction waves tends to the vacuum state solution to the transport equations. Finally, some numerical simulations completely coinciding with the theoretical analysis are demonstrated.

Natural Convection Heat Transfer From Horizontal Rectangular Ducts

2006 ◽  
Vol 129 (9) ◽  
pp. 1195-1202 ◽  
Author(s):  
Mohamed E. Ali
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Nusselt Numbers ◽  
Aspect Ratios ◽  
Rayleigh Numbers

Experimental investigations have been reported on steady state natural convection from the outer surface of horizontal ducts in air. Five ducts have been used with aspect ratios (Γ=duct height/duct width) of 2, 1, and 0.5. The ducts are heated using internal constant heat flux heating elements. The temperatures along the surface and peripheral directions of the duct wall are measured. Longitudinal (circumference averaged) heat transfer coefficients along the side of each duct are obtained for laminar and transition regimes of natural convection heat transfer. Total overall averaged heat transfer coefficients are also obtained. Longitudinal (circumference averaged) Nusselt numbers are evaluated and correlated using the modified Rayleigh numbers for transition regime using the axial distance as a characteristic length. Furthermore, total overall averaged Nusselt numbers are correlated with the modified Rayleigh numbers, the aspect ratio, and area ratio for the laminar and transition regimes. The longitudinal or total averaged heat transfer coefficients are observed to decrease in the laminar region and to increase in the transition region. Laminar regimes are obtained only at very small heat fluxes, otherwise, transitions are observed.

Experimental and Computational Analysis of Natural Convection Over Flat Plate

2008 ◽  
Author(s):  
Farhana Afroz ◽  
Chowdhury Md. Feroz
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Flat Plate ◽  
Convection Heat Transfer ◽  
Boussinesq Approximation ◽  
Heat Fluxes ◽  
Navier Stokes ◽  
Heated Plate ◽  
Wide Range ◽  
Energy Equations

Natural convection heat transfer over a flat plate with a heat source at bottom side of plate is studied experimentally and numerically. We consider the two-dimensional problem of both steady and unsteady natural convection over the flat plate at vertical, horizontal and inclined position. Experimental analysis is done for three different constant heat fluxes for each angle position. The Navier-Stokes and Energy equations with the Boussinesq approximation are written in Cartesian coordinate system. The problem is solved in the physical variables on the basis of a completely implicit Finite element Method order to examine the heat transfer characteristics. To see the effects of different angle position phenomena of natural convection over flat plate, the computational results presented in the form of streamlines for a wide range of Grashof number at different heat fluxes. The average Nusselt number of heated plate for different angle position has been observed.

scholarly journals On the van der Waals Gas, Contact Geometry and the Toda Chain

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 554
Author(s):  
Diego Alarcón ◽  
P. Fernández de Córdoba ◽  
J. Isidro ◽  
Carlos Orea
Keyword(s):  
Van Der Waals ◽  
Toda Chain ◽  
Contact Geometry ◽  
Ideal Gas ◽  
Van Der Waals Gas ◽  
The Ideal

A Toda–chain symmetry is shown to underlie the van der Waals gas and its close cousin, the ideal gas. Links to contact geometry are explored.

Effect on Natural Convection of the Distance Between an Inclined Discretely Heated Plate and a Parallel Shroud Below

2002 ◽  
Vol 124 (3) ◽  
pp. 441-451 ◽  
Author(s):  
Oronzio Manca ◽  
Sergio Nardini ◽  
Vincenzo Naso
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Heated Plate ◽  
Heat Sources ◽  
Channel Spacing ◽  
Nusselt Numbers ◽  
Test Conditions ◽  
Inclination Angles ◽  
Rayleigh Numbers ◽  
Opposite Tendency

An experimental study on air natural convection on an inclined discretely heated plate with a parallel shroud below was carried out. Three heated strips were located in different positions on the upper wall. The distance between the walls, b, was changed in the range 7.0–40.0 mm and two values of the heat flux dissipated by the heaters were taken into account. Several inclination angles between the vertical and the horizontal were tested. The wall temperature distribution as a function of the channel spacing and the inclination angle, the source heat flux, the number and the arrangement of the heat sources are presented. The analysis shows that, for angles not greater than 85 deg, increasing the distance between walls does not reduce the wall temperatures, whereas at greater tilting angles (>85 deg) there is an opposite tendency. This is confirmed by flow visualization at angles equal to 85 deg and 90 deg and b=20.0 and 32.3 mm. Dimensionless maximum wall temperatures are correlated to the process parameters in the ranges 1.2s˙104⩽Ral cos θ⩽8.6s˙105; 0 deg⩽θ⩽88 deg; 0.48⩽l/b⩽1.6 and 10⩽L/b⩽32.6 with 1.0⩽d/l⩽3.0; the agreement with experimental data is good. The spacing which yields the best thermal performance of the channel is given. Local Nusselt numbers are evaluated and correlated to the local Rayleigh numbers and the tilting angles in the ranges 20⩽Rax′⩽8.0s˙105 and 0 deg⩽θ⩽88 deg. The exponent of monomial correlations between local Nusselt and Rayleigh numbers are in the 0.23–0.26 range. Comparisons with data from the literature, in terms of Nusselt number, exhibited minor discrepancies, mainly because of some difference in test conditions and of heat conduction in the channel walls.

scholarly journals Increase in Axial Compressibility in a Spinning Van der Waals Gas

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 137
Author(s):  
Yun Liu ◽  
Hao Liu ◽  
Zhen-Guo Fu ◽  
Weimin Zhou
Keyword(s):  
Van Der Waals ◽  
Axial Direction ◽  
Md Simulations ◽  
High Energy ◽  
Ideal Gas ◽  
High Energy Density ◽  
Van Der Waals Gas ◽  
Equation Of States ◽  
Dense State ◽  
The Ideal

We investigated the adiabatic compression along the axial direction of a spinning Van der Waals gas by applying theoretical analysis and molecular dynamics (MD) simulations. Based on the analytical results, the rotation-induced compressibility increase effect is significant in a Van der Waals gas, while the attraction term in the Van der Waals equation of states (EOS) contributes significantly to the compressibility increase in a spinning system. We conducted MD simulations to the axial compression of a spinning gas, whose state is far from the ideal gas state, and further demonstrated that the rotation-induced compressibility increase effect in a dense state is robust, implying that such a phenomenon can be detected in experiments under high-energy-density conditions.

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