scholarly journals Thermodynamic Properties of Vapors from Speed of Sound

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Muhamed Bijedić ◽  
Sabina Begić
Keyword(s):  
Thermodynamic Properties ◽  
Differential Equations ◽  
Speed Of Sound ◽  
Numerical Procedure ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Ideal Gas ◽  
Temperature Range ◽  
Initial Values ◽  
Initial Boundary Value

A numerical procedure for deriving the thermodynamic properties (Z, cv, and cp) of the vapor phase in the subcritical temperature range from the speed of sound is presented. The set of differential equations connecting these properties with the speed of sound is solved as the initial-value problem in T-ϕ domain (ϕ=ρ/ρsat). The initial values of Z and ∂Z/∂Tρ are specified along the isotherm T0 with the highest temperature, at a several values of ϕ [0.1, 1.0]. The values of Z are generated by the reference equation of state, while the values of ∂Z/∂Tρ are derived from the speed of sound, by solving another set of differential equations in T-ρ domain in the transcritical temperature range. This set of equations is solved as the initial-boundary-value problem. The initial values of Z and cv are specified along the isochore in the limit of the ideal gas, at several isotherms distributed according to the Chebyshev points of the second kind. The boundary values of Z are specified along the same isotherm T0 and along another isotherm with a higher temperature, at several values of ρ. The procedure is tested on Ar, N2, CH4, and CO2, with the mean AADs for Z, cv, and cp at 0.0003%, 0.0046%, and 0.0061%, respectively (0.0007%, 0.0130%, and 0.0189% along the saturation line).

DYNAMICS OF MULTISECTION SEMICONDUCTOR LASERS

2005 ◽  
Vol 9 (1) ◽  
pp. 51-66 ◽  
Author(s):  
J. Sieber ◽  
M. Radžiūnas ◽  
K. R. Schneider
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Semiconductor Lasers ◽  
Invariant Manifolds ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Low Dimension ◽  
Global Existence And Uniqueness ◽  
Numerical Bifurcation ◽  
Initial Boundary Value

We investigate the longitudinal dynamics of multisection semiconductor lasers based on a model, where a hyperbolic system of partial differential equations is nonlinearly coupled with a system of ordinary differential equations. We present analytic results for that system: global existence and uniqueness of the initial‐boundary value problem, and existence of attracting invariant manifolds of low dimension. The flow on these manifolds is approximately described by the so‐called mode approximations which are systems of ordinary differential equations. Finally, we present a detailed numerical bifurcation analysis of the two-mode approximation system and compare it with the simulated dynamics of the full PDE model.

scholarly journals SPECIAL SPLINES OF HYPERBOLIC TYPE FOR THE SOLUTIONS OF HEAT AND MASS TRANSFER 3-D PROBLEMS IN POROUS MULTI-LAYERED AXIAL SYMMETRY DOMAIN

2017 ◽  
Vol 22 (4) ◽  
pp. 425-440
Author(s):  
Harijs Kalis ◽  
Andris Buikis ◽  
Aivars Aboltins ◽  
Ilmars Kangro
Keyword(s):  
Differential Equations ◽  
Transfer Problem ◽  
Circular Cross Section ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Rate Of Change ◽  
Wood Block ◽  
Initial Value ◽  
Special Integral ◽  
Initial Boundary Value

In this paper we study the problem of the diffusion of one substance through the pores of a porous multi layered material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. As an example we consider circular cross section wood-block with two layers in the radial direction. We consider the transfer of heat process. We derive the system of two partial differential equations (PDEs) - one expressing the rate of change of concentration of water vapour in the air spaces and the other - the rate of change of temperature in every layer. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM) with special integral splines. This procedure allows reduce the 3-D axis-symmetrical transfer problem in multi-layered domain described by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order.

scholarly journals The analytical solution of the 3D model with Robin's boundary conditions for 2 peat layers

2015 ◽  
Vol 3 ◽  
pp. 186
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stationary Problem ◽  
Elliptic Type ◽  
Exponential Spline ◽  
Initial Boundary Value

<p>In this paper we consider averaging methods for solving the 3-D boundary value problem in domain containing 2 layers of the peat block. We consider the metal concentration in the peat blocks. Using experimental data the mathematical model for calculation of concentration of metal in different points in every peat layer is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations of second order with piece-wise diffusion coefficients in every direction and peat layers.</p><p>The special parabolic and exponential spline, which interpolation middle integral values of piece-wise smooth function, are considered. With the help of this splines is reduce the problems of mathematical physics in 3-D with piece-wise coefficients to respect one coordinate to problems for system of equations in 2-D. This procedure allows reduce the 3-D problem to a problem of 2-D and 1-D problems and the solution of the approximated problem is obtained analytically.</p><p>The solution of corresponding averaged 2-D initial-boundary value problem is obtained also numerically, using for approach differential equations the discretization in space applying the central differences. The approximation of the 2-D non-stationary problem is based on the implicit finite-difference and alternating direction (ADI) methods. The numerical solution is compared with the analytical solution.</p>

scholarly journals ON MATHEMATICAL MODELLING OF THE 2-D FILTRATION PROBLEM IN POROUS AXIAL SYMMETRICAL CYLINDER

2017 ◽  
Vol 3 ◽  
pp. 129
Author(s):  
Ilmārs Kangro ◽  
Harijs Kalis ◽  
Ērika Teirumnieka ◽  
Edmunds Teirumnieks
Keyword(s):  
Differential Equations ◽  
Transfer Problem ◽  
Initial Boundary ◽  
Axial Direction ◽  
Initial Boundary Value Problem ◽  
Rate Of Change ◽  
Filtration Problem ◽  
Dirty Water ◽  
Round Cylinder ◽  
Initial Boundary Value

In this paper we study diffusion and convection filtration problem of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances. As an example we consider round cylinder with filtration process in the axial direction. The cylinder is filled with sorbent i.e. absorbent material that passed through dirty water or liquid solutions. We can derive the system of two partial differential equations (PDEs). One equation is expressing the rate of change of concentration of water in the pores of the sorbent and the other - the rate of change of concentration in the sorbent or kinetically equation for absorption. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM). This procedure allows reducing the 2-D axis-symmetrical mass transfer problem described by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order.

scholarly journals Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations

2020 ◽  
Vol 100 (4) ◽  
pp. 5-16
Author(s):  
A.T. Assanova ◽  
◽  
Zh.S. Tokmurzin ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Periodic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Hyperbolic Type ◽  
Order System ◽  
Partial Differential ◽  
Initial Boundary Value

A semi-periodic initial boundary-value problem for a fourth-order system of partial differential equations is considered. Using the method of functional parametrization, an additional parameter is carried out and the studied problem is reduced to the equivalent semi-periodic problem for a system of integro-differential equations of hyperbolic type second order with functional parameters and integral relations. An interrelation between the semi-periodic problem for the system of integro-differential equations of hyperbolic type and a family of Cauchy problems for a system of ordinary differential equations is established. Algorithms for finding of solutions to an equivalent problem are constructed and their convergence is proved. Sufficient conditions of a unique solvability to the semi-periodic initial boundary value problem for the fourth-order system of partial differential equations are obtained.

Deviation of the Calculated of Density of Refrigerant Fluids in Both Super and Sub Critical Regions

2011 ◽  
Author(s):  
Neda Mobinipouya
Keyword(s):  
Thermodynamic Properties ◽  
Speed Of Sound ◽  
Equations Of State ◽  
Numerical Procedure ◽  
Corresponding States ◽  
Temperature Range ◽  
Critical Regions ◽  
Two Parameter ◽  
Good Agreement

A numerical procedure has successfully predicted accurate values of thermodynamic properties in seven cubic equations of state (EOS) in predicting thermodynamic properties of nine ozone-safe refrigerants both in super and sub-critical regions. Refrigerants include R22, R32, R123, R124, R125, R134a, R141b, R143, and R152a and equations of state, considered here, are Ihm-Song-Mason (ISM), Peng-Robinson (PR) [2], Redlich-Kwong (RK), Soave-Redlikh-Kwong (SRK), Modified Redlickh-Kwong (MRK), Nasrifar-Moshfeghian (NM), and TCC were shown in this paper. In general, the results are in favor of the preference of TCC and PR EOS over other remaining EOS’s in predicting gas densities of all aforementioned refrigerants in both super and sub critical regions. Typically, PR and SRK are in good agreement with those obtained from recent correlations and speed of sound measurements. Therefore, these two EOS stand over other EOS both in sub and super critical regions. All EOS follow two-parameter principle of corresponding states at T/Tc higher than 8 and lower than 1 except NM EOS. In the temperature range 1<T/Tc<8, PR and SRK still follow above mentioned principle. The same trend has been observed for other refrigerants.

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