Semi analytical expressions of a non-linear boundary value problem for immobilized enzyme in porous planar, cylindrical and spherical

  • R.R. Subanya E.M.G Yadava Women’s College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India
  • Ananthaswamy Vembu The Madura College, Madurai, Tamil Nadu, India.
  • Seenith Sivasundaram College of Science, Engineering and Mathematics, Daytona Beach, Florida 321114, USA


This study presents comparison approximate analytical solutions of immobilized enzyme in porous planar, cylindrical, and spherical particle using two approach of Homotopy analysis method. The diffusion reaction model for immobilized enzyme systems in porous, obeying reversible Michaelis - Menten kinetics with product inhibition effects, is the mathematical model that we took into consideration in this research.  NHAM and -HAM were used to establish analytical equations for the dimensionless concentration profile and effectiveness factor for planar, cylindrical, and spherical particles in this model. At the same order of approximation, -HAM can offer greater accuracy than HAM. Additionally, -HAM has two auxiliary parameters, and this method makes it simple to control and alter the convergence region. It can be seen through a comparison of solutions obtained by -HAM, NHAM, and numerical solutions (MATLAB) that -HAM is a reliable and accurate method for resolving nonlinear differential equations. Our analytical findings, which are given graphically with tabular data and great consistency with prior work, demonstrate the realization of our investigation.