Transport and Kinetics in Biofiltration Membranes: New Analytical Expressions for Concentration Profiles of Hydrophilic and Hydrophobic VOCs Using Taylor’s Series and Akbari- Ganji methods.

Abstract

The mathematical models of biofiltration of mixtures of hydrophilic (methanol) and hydrophobic ( pinene) volatile organic compounds (VOCs) are explored in this paper. This model is based on diffusion equations that contain a nonlinear term linked to the enzymatic reaction's Michaelis-Menten kinetics. An approximate analytical expression of methanol and pinene concentration profiles in the air and biofilm phase were derived using Taylor's series and Akbari-Ganji's methods. In addition, the numerical simulation of the problem using the Matlab programme to investigate the system's dynamics is reported in this work. Graphic results are presented to illustrate the solution, and numerical data is analyzed. The analytical and numerical data are in good agreement.

Modelling of Irreversible Homogeneous Reaction on Finite Diffusion Layers

“…One of the toughest challenges, especially across a wide range of science and engineering applications, is solving nonlinear differential equations. Recently, the construction of an analytical solution has been the focus of numerous analytical techniques, such as the homotopy perturbation method (HPM) [14][15][16][17][18][19][20][21][22][23][24][25][26], the variational iteration method [27][28][29][30][31][32], the homotopy analysis method [33][34][35][36][37], the Akbari-Ganji method [38][39][40][41][42][43], the Taylor series method [44][45][46][47], and the differential transform method. Jalili et al [48][49][50] discussed the heat exchange in nanoparticles and solved the momentum and energy equation numerically.…”