The double packer permeameter with long packers. An approximate analytical solution

1996 ◽  
Vol 56 (4) ◽  
pp. 281-297 ◽  
Author(s):  
G. Rehbinder
Keyword(s):  
Analytical Solution ◽  
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.

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