A Two-Factor Model of the Term Structure: An Approximate Analytical Solution

1984 ◽  
Vol 19 (4) ◽  
pp. 413 ◽  
Author(s):  
Stephen M. Schaefer ◽  
Eduardo S. Schwartz
Keyword(s):  
Analytical Solution ◽  
Term Structure ◽  
Factor Model ◽  
Approximate Analytical Solution

Numerical Approximations to Solution of Biochemical Reaction Model

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Transformation Method ◽  
Reaction Model ◽  
Biochemical Reaction ◽  
Graphical Form ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

New Approximate Analytical Solution of the Diode-Resistance Equation

2021 ◽  
pp. 153665
Author(s):  
José A. Gazquez ◽  
Manuel Fernandez-Ros ◽  
Blas Torrecillas ◽  
José Carmona ◽  
Nuria Novas
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Resistance Equation

A General Correlation for Pool Film Boiling Heat Transfer From a Horizontal Cylinder to Subcooled Liquid: Part 2—Experimental Data for Various Liquids and Its Correlation

1990 ◽  
Vol 112 (2) ◽  
pp. 441-450 ◽  
Author(s):  
A. Sakurai ◽  
M. Shiotsu ◽  
K. Hata
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Analytical Solution ◽  
Boiling Heat Transfer ◽  
Radiation Effects ◽  
Approximate Analytical Solution ◽  
Horizontal Cylinder ◽  
Film Boiling ◽  
System Pressure ◽  
Horizontal Cylinders

Experimental data of pool film boiling heat transfer from horizontal cylinders in various liquids such as water, ethanol, isopropanol, Freon-113, Freon-11, liquid nitrogen, and liquid argon for wide ranges of system pressure, liquid subcooling, surface superheat and cylinder diameter are reported. These experimental data are compared with a rigorous numerical solution and an approximate analytical solution derived from a theoretical model based on laminar boundary layer theory for pool film boiling heat transfer from horizontal cylinders including the effects of liquid subcooling and radiation from the cylinder. A new correlation was developed by slightly modifying the approximate analytical solution to agree better with the experimental data. The values calculated from the correlation agree with the authors’ data within ± 10 percent, and also with other researchers’ data for various liquids including those with large radiation effects, though these other data were obtained mainly under saturated conditions at atmospheric pressure.

scholarly journals Analytical solution of integro-differential equations describing the process of intense boiling of a superheated liquid

2021 ◽  
Author(s):  
Irina Alexandrova ◽  
Alexander Ivanov ◽  
Dmitri Alexandrov
Keyword(s):  
Distribution Function ◽  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Initial Distribution ◽  
Size Distribution Function ◽  
Superheated Liquid ◽  
Balance Equations ◽  
The Laplace Transform ◽  
And Shifts ◽  
Initial Distribution Function

In this article, an approximate analytical solution of an integro-differential system of equations is constructed, which describes the process of intense boiling of a superheated liquid. The kinetic and balance equations for the bubble-size distribution function and liquid temperature are solved analytically using the Laplace transform and saddle-point methods with allowance for an arbitrary dependence of the bubble growth rate on temperature. The rate of bubble appearance therewith is considered in accordance with the Dering-Volmer and Frenkel-Zeldovich-Kagan nucleation theories. It is shown that the initial distribution function decreases with increasing the dimensionless size of bubbles and shifts to their greater values with time.

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