Approximate analytical solutions of effectiveness factors for parallel catalytic reactions

1995 ◽  
Vol 59 (2) ◽  
pp. 161-167
Author(s):  
Qiuxiang Yin ◽  
Shaofen Li
Keyword(s):  
Analytical Solutions ◽  
Catalytic Reactions ◽  
Effectiveness Factors ◽  
Approximate Analytical Solutions

Approximate analytical solutions of stability problems for skew plates under combined loading

2011 ◽  
Vol 54 (2) ◽  
pp. 115-124 ◽  
Author(s):  
N. I. Akishev ◽  
I. I. Zakirov ◽  
V. A. Ivanov ◽  
V. N. Paimushin ◽  
M. A. Shishov
Keyword(s):  
Analytical Solutions ◽  
Combined Loading ◽  
Stability Problems ◽  
Approximate Analytical Solutions

scholarly journals Approximate analytical solutions of the nonlinear reaction–diffusion–convection problems

2011 ◽  
Vol 53 (1-2) ◽  
pp. 261-268 ◽  
Author(s):  
A. Shidfar ◽  
A. Babaei ◽  
A. Molabahrami ◽  
M. Alinejadmofrad
Keyword(s):  
Analytical Solutions ◽  
Reaction Diffusion ◽  
Nonlinear Reaction ◽  
Approximate Analytical Solutions ◽  
Diffusion Convection

Approximate analytical solution for the propagation of shock wave in a mixture of small solid particles and non-ideal gas: isothermal flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Gorakh Nath
Keyword(s):  
Shock Wave ◽  
Analytical Solutions ◽  
Order Approximation ◽  
Fluid Pressure ◽  
Strong Shock ◽  
Cylindrical Symmetry ◽  
Solid Particles ◽  
Approximate Analytical Solutions ◽  
Axis Of Symmetry ◽  
Physical Variables

Abstract This paper presents the development of mathematical model to obtain the approximate analytical solutions for isothermal flows behind the strong shock (blast) wave in a van der Waals gas and small solid particles mixture. The small solid particles are continuously distributed in the mixture and the equilibrium conditions for flow are maintained. To derive the analytical solutions, the physical variables such as density, pressure, and velocity are expanded using perturbation method in power series. The solutions are derived in analytical form for first approximation, and for second order approximation the set of differential equations are also obtained. The effects of an increase in the problem parameters value on the physical variables are investigated for first order approximation. A comparison is also, made between the solution of cylindrical shock and spherical shock. It is found that the fluid density and fluid pressure become zero near the point or axis of symmetry in spherical or cylindrical symmetry, respectively, and therefore a vacuum is created near the point or axis of symmetry which is in tremendous conformity with the physical condition in laboratory to generate the shock wave.

Dynamics research of Fangzhu’s nanoscale surface

2021 ◽  
pp. 146134842110527
Author(s):  
Pinxia Wu ◽  
Weiwei Ling ◽  
Xiumei Li ◽  
Xichun He ◽  
Liangjin Xie
Keyword(s):  
Energy Balance ◽  
Analytical Solutions ◽  
Numerical Experiments ◽  
Fractal Model ◽  
Balance Method ◽  
Transform Method ◽  
Energy Balance Method ◽  
Collection Rate ◽  
Fractal Derivative ◽  
Approximate Analytical Solutions

In this paper, we mainly focus on a fractal model of Fangzhu’s nanoscale surface for water collection which is established through He’s fractal derivative. Based on the fractal two-scale transform method, the approximate analytical solutions are obtained by the energy balance method and He’s frequency–amplitude formulation method with average residuals. Some specific numerical experiments of the model show that these two methods are simple and effective and can be adopted to other nonlinear fractal oscillators. In addition, these properties of the obtained solution reveal how to enhance the collection rate of Fangzhu by adjusting the smoothness of its surfaces.

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