Thermodynamic analysis of natural convection supercritical water flow past a stretching sheet using an equation of state approach

2020 ◽  
Author(s):  
Hussain Basha ◽  
G. Janardhana Reddy ◽  
N.S. Venkata Narayanan
Keyword(s):  
Thermal Expansion ◽  
Equation Of State ◽  
Thermal Expansion Coefficient ◽  
Supercritical Fluid ◽  
Expansion Coefficient ◽  
Supercritical Water ◽  
Stretching Sheet ◽  
Reduced Pressure ◽  
Flow Past ◽  
Reduced Temperature

Present numerical study examines the free convection heat transfer characteristics of supercritical water flow past a stretching sheet. A suitable equation for thermal expansion coefficient in supercritical fluid region is derived based on the equation of state approach (EOS) in terms of compressibility factor, pressure and temperature. In the present study Redlich-Kwong equation of state (RK-EOS) is used to calculate the thermal expansion coefficient in supercritical region. The values of thermal expansion coefficient calculated through RK-EOS lies close to the NIST data values when compared to the other equations of state like VW-EOS (Van der Waals equation of state) and Ideal gas-EOS. Also, the behaviour of Nusselt number is studied to characterize the heat transfer characteristics of supercritical water. However, the equations governing the supercritical fluid flow past a stretching sheet are coupled and nonlinear in nature. Hence, Runge-Kutta fourth-order integration scheme with shooting technique (RK-SM) is used to solve these equations. Numerical computations are performed for supercritical water (SCW) under the influence of various control parameters. Similarity solutions are obtained in terms of flow profiles in supercritical fluid region. Present study reports that, the normal velocity profile decreases and temperature field increases for the increasing values of reduced pressure and reduced temperature. Also, axial velocity profile shows the dual behaviour for the increasing values of unsteady parameter, reduced temperature and reduced pressure in the supercritical boundary layer region. Further, the component of normal velocity profile decays for the increasing values of unsteady parameter in supercritical fluid region. The calculated values of thermal expansion coefficient using Redlich-Kwong equation of state lies in the proximity of NIST data values when compared to Van der Waals and Ideal gas equations of state. Also, the local skin-friction coefficient decreases for the increasing values of reduced pressure and reduced temperature.

Heat Transfer Characteristics of Nitrogen in Supercritical Region Using Redlich-Kwong Equation of State

2019 ◽  
Vol 17 (10) ◽  
Author(s):  
Hussain Basha ◽  
G. Janardhana Reddy ◽  
N. S. Venkata Narayanan
Keyword(s):  
Heat Transfer ◽  
Thermal Expansion ◽  
Equation Of State ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Physical Parameters ◽  
Heat Transfer Characteristics ◽  
Reduced Pressure ◽  
Supercritical Region ◽  
Transfer Characteristics

Abstract The present paper studies through numerical methods, the thermodynamic heat transfer characteristics of free convection flow of supercritical nitrogen over a vertical cylinder. In the present analysis, the values of volumetric thermal expansion coefficient ($\beta$) are evaluated based on Redlich-Kwong equation of state (RK-EOS) and Van der Waals equation of state (VW-EOS). The calculated analytical thermal expansion coefficient values using RK-EOS are very close to NIST data values in comparison with VW-EOS. A set of coupled nonlinear partial differential equations (PDEs) governing the supercritical fluid (SCF) flow are derived, converted into non-dimensional form with the help of suitable dimensionless quantities and solved using Crank-Nicolson implicit finite difference method. The simulations are carried out for nitrogen in the supercritical region. The obtained numerical data is expressed in terms of graphs and tables for various values of physical parameters. The increasing value of reduced temperature decreases the average Nusselt number and skin-friction coefficient, whereas amplifying value of reduced pressure enhance the heat transfer rate and wall shear stress in the SCF region. Present results are compared with the previous results and the two are found to be in good agreement, i. e. the numerically generated results found to be in agreement with existing results.

Transient Natural Convection Heat Transfer to CO2 in the Supercritical Region

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
G. Janardhana Reddy ◽  
Hussain Basha ◽  
N. S. Venkata Narayanan
Keyword(s):  
Carbon Dioxide ◽  
Thermal Expansion ◽  
Equation Of State ◽  
Supercritical Carbon Dioxide ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Physical Parameters ◽  
Reduced Pressure ◽  
Supercritical Region ◽  
Supercritical Carbon

Present research paper investigates the transient laminar free convective supercritical carbon dioxide flow past a semi-infinite vertical cylinder using numerical methods. Two new thermodynamic models for the supercritical fluid (SCF) flow are considered. Based on these models, for supercritical carbon dioxide, two new equations for thermal expansion coefficient are obtained on the basis of Redlich–Kwong equation of state (RK-EOS) and Van der Waals equation of state (VW-EOS). Based on the calculated values of thermal expansion coefficient, it is shown that not only RK-EOS is closer to experimental values but also gives greater accuracy when compared to VW-EOS validating RK-EOS as suitable model for predicting natural convective properties of carbon dioxide under supercritical condition. The governing equations of SCF flow are solved numerically using Crank–Nicolson implicit finite difference scheme. Numerical simulations are performed for carbon dioxide in the region of its critical point. Results in subcritical, supercritical, and near-critical regions are shown graphically and discussed for different physical parameters. From the obtained numerical results, it is clear that the steady-state time increases for the increasing values of reduced temperature and reduced pressure for carbon dioxide in supercritical region.

Determination of the Equation of State of Polyisobutylene

1969 ◽  
Vol 42 (5) ◽  
pp. 1409-1411
Author(s):  
B. E. Eichinger ◽  
P. J. Flory
Keyword(s):  
Thermal Expansion ◽  
Equation Of State ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Pressure Coefficient ◽  
Experimental Results ◽  
Characteristic Parameters ◽  
Thermal Pressure

Abstract The density, thermal expansion coefficient, and thermal pressure coefficient for polyisobutylene of mol wt 40,000 have been accurately determined from 0 to 150°. Results are compared with the reduced equation of state employed in the theory of solutions. The characteristic parameters v*, T*, and p* required for the treatment of polyisobutylene solutions are obtained from the experimental results.

Equation of state and thermal expansion of metals with FCC structure: Application to Cu, Al and Ni

2014 ◽  
Vol 28 (26) ◽  
pp. 1450209
Author(s):  
Pham Dinh Tam ◽  
Nguyen Quang Hoc ◽  
Bui Duc Tinh ◽  
Nguyen Duc Hien
Keyword(s):  
Thermal Expansion ◽  
Equation Of State ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Analytic Form ◽  
Lattice Parameter ◽  
Different Temperatures ◽  
Simple Analytic Form ◽  
Fcc Structure ◽  
Good Agreement

The equation of state, the expressions of lattice parameter and thermal expansion coefficient in general form are obtained by the statistical moment method. Applying to Cu , Al and Ni metals, we determine these properties in simple analytic form for each metal. Numerical results for the thermal expansion coefficient of these metals in different temperatures and pressures are in good agreement with experiments.

Transient Flow and Heat Transfer Characteristics of non-Newtonian Supercritical Third-Grade Fluid (CO2) past a Vertical Cylinder

2018 ◽  
Vol 16 (8) ◽  
Author(s):  
G. Janardhana Reddy ◽  
Ashwini Hiremath ◽  
Hussain Basha ◽  
N.S. Venkata Narayanan
Keyword(s):  
Heat Transfer ◽  
Thermal Expansion ◽  
Thermal Expansion Coefficient ◽  
Vertical Cylinder ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Reduced Pressure ◽  
Fluid Parameter ◽  
Grade Fluid ◽  
Reduced Temperature

Abstract The present study deals with the time-dependent natural convective supercritical third-grade fluid flow past a vertical cylinder. A new thermodynamic model for the supercritical carbon di-oxide (CO2) has been derived. In this model the thermal expansion coefficient is characterized as a function of pressure, temperature and compressibility factor. This model uses the Redlich-Kwong equation of state (RK-EOS). The numerically calculated thermal expansion coefficient values of CO2 are validated with available experimental results. The governing non-linear coupled partial differential equations are solved by using Crank-Nicolson method. The obtained numerical data is described in terms of velocity, temperature, skin-friction and Nusselt number through the graphs and tables for the different set of physical parameters. It is observed that the unsteady velocity is an increasing function of reduced pressure and reduced temperature; whereas it is a decreasing function with respect to third-grade fluid parameter. The temperature field is enhanced near the critical point for the increasing values of third-grade fluid parameter. In supercritical fluid region for the increasing values of reduced pressure and reduced temperature, the skin-friction values are magnified against time. Also, the average heat transfer rate decreases for increasing values of third-grade fluid parameter.

The effect of thermal expansion coefficient on unsteady non-Newtonian supercritical Casson fluid flow past a vertical cylinder

Pramana ◽  
2019 ◽  
Vol 93 (2) ◽  
Author(s):  
Ashwini Hiremath ◽  
Hussain Basha ◽  
Bhaskerreddy Kethireddy ◽  
G Janardhana Reddy ◽  
N S Venkata Narayanan
Keyword(s):  
Thermal Expansion ◽  
Fluid Flow ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Vertical Cylinder ◽  
Casson Fluid ◽  
Flow Past

scholarly journals INFLUENCE OF SIZE AND PRESSURE ON THE TEMPERATURE DEPENDENCIES OF THERMODYNAMIC PROPERTIES OF PLATINUM

2021 ◽  
pp. 465-474
Author(s):  
Сергей Петрович Крамынин
Keyword(s):  
Heat Capacity ◽  
Thermal Expansion ◽  
Elastic Modulus ◽  
Equation Of State ◽  
Surface Energy ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Interatomic Interaction ◽  
Isobaric Heat Capacity ◽  
Temperature Dependences

Основываясь на параметрах парного потенциала межатомного взаимодействия Ми-Леннард-Джонса для Pt, и используя RP-модель нанокристалла, изучены температурные, барические и размерные зависимости следующих свойств: модуля упругости, коэффициента теплового расширения, изобарной теплоемкости и поверхностной энергии. Расчет уравнения состояния Pt показал хорошее согласие с экспериментом. Уравнение состояния было рассчитано вдоль пяти изотерм: T = 300, 1300, 1500, 1700, 1900 К. Впервые с единых позиций выполнены расчеты температурных зависимостей указанных свойств Pt в диапазоне от 0 K до 1500 K вдоль изобар 0 и 50 ГПа. Расчеты указанных зависимостей проведены как для макро-, так и для нанокристалла кубической формы из 306 атомов. Показано, что при изобарно-изотермическом уменьшении размера нанокристалла Pt происходит уменьшение значений модуля упругости и поверхностной энергии, а значения коэффициента теплового расширения и изобарной теплоемкости увеличиваются на исследуемом интервале температур. Based on the parameters of the pair interatomic interaction potential of the Mie-Lennard-Jones for Pt, and using the RP-model of the nanocrystal, the temperature, pressure and size dependencies of the following properties are studied: elastic modulus, thermal expansion coefficient, isobaric heat capacity, and surface energy. The calculation of the equation of state showed good agreement with experiment. The equation of state was calculated along five isotherms: T = 300, 1300,1500, 1700, 1900 K. For the first time, calculations of the temperature dependences of the above properties of Pt in the range from 0 to 1500 K along 0 and 50 GPa isobars were performed from a unified standpoint. Calculations of these dependencies were carried out for both macro- and cubic nanocrystals of 306 atoms. It is shown that with an isobaric-isothermal decrease in the nanocrystal size, the values of the elastic modulus and surface energy decrease, while the values of the thermal expansion coefficient and isobaric heat capacity increase over the investigated temperature range.

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