Analytical Solution of Non-Isothermal Diffusion-Reaction Processes and Effectiveness Factors

Abstract

The mathematical modeling of nonlinear boundary value problems in catalytically chemical reactor is discussed. In this paper, we obtain the approximate analytical solution and the effectiveness factors for the evolution of single-step transformations under non-isothermal conditions using homotopy perturbation method. We have applied it to many reaction models and obtained very simple analytical expressions for the shape of the corresponding transformation rate peaks. These analytical solutions represent a significant simplification of the system’s description allowing easy curve fitting to experiment. The accuracy achieved with our method is checked against several reaction models and numerical results. A satisfactory agreement is noted.

Semi-analytical Expressions of a Non-linear Reaction-Diffusion (R-D) Equations in a Mixed Quadratic-Cubic Autocatalytic Reactions

“…The Homotopy analysis technique use homotopy concepts from the topology to generate the convergence series solution for non-linear systems. HAM was proposed by Shi-Jun Liao in 1992 and has been strongly utilized to solve many problems in Physical and Chemical Science [23][24][25][26][27][28]. HAM does not need a small parameter to develop a perturbation solution and hence is applicable for both weakly and strongly non-linear problems.…”

Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method

“…The HPM uses the imbedding parameter p as a small parameter, and only a few iterations are needed to search for an asymptotic solution. Using this method [17][18][19], we can obtain solution to the eqns. (1) -(3) as follows: 12 = a , the steepness of 2 N increases with 2 a however falling of 2 N is faster along with increasing 22 a than 1 N .…”

Analysis of non-linear reaction-diffusion processes with Michaelis-Menten kinetics by a new Homotopy perturbation method

“…Most models of real life problems are still very difficult to solve. Therefore, approximate analytical solutions such as Homotopy perturbation method (HPM) [10][11][12][13][14][15][16][17][18][19][20][21][22][23] were introduced. This method is the most effective and convenient ones for both linear and non-linear equations.…”

“…The HPM is unique in its applicability, accuracy and efficiency. The HPM [18][19][20][21][22][23] uses the imbedding parameter p as a small parameter, and only a few iterations are needed to search for an asymptotic solution. The law of mass action of oxygen uptake leads to the following non-linear equations…”