Abstract
A mathematical model to describe the enzyme reaction, mass transfer and heat effects in the calorimetric system is discussed. The model is based on non-stationary diffusion Equation containing a nonlinear term related to immobilize liver esterase by flow calorimetry. This paper presents the complex numerical methods (Adomian decomposition method, Homotopy analysis and perturbation method) to solve the non-linear differential Equations that depict the diffusion coupled with a non-linear reaction terms. Approximate analytical expressions for substrate concentration have been derived for all values of parameters α, β and γE. These analytical results are compared with the available numerical results and are found to be in good agreement.
Highlights
Flow reaction calorimetry has several advantages over a batch calorimetry method
Immobilized biocatalysts (IMB)enzymes or whole cells are used in various areas of analytical, medical, and industrial applications
The analytical solution represented by Eq.11 contains the auxiliary parameter h, which gives the convergence region and rate of approximation for the homotopy analysis method
Summary
Flow reaction calorimetry has several advantages over a batch calorimetry method. The operation at a calorimetric experiment can be made exceedingly simple and equilibration time prior to the experiment can be omitted. Enzyme kinetic parameters cannot be determined experimental data. For this purpose many experimental techniques can be used, that are more or less laborious and time consuming. Fedor Malik [7] has developed the mathematical model describing the enzyme reaction, mass transfer and heat effects in the calorimetric system. To my knowledge no rigorous analytical solutions of the substrate of phenyl acetate hydrolysis with steadystate conditions for all values of parameters , and E have been reported. The purpose of this communication is to derive approximate analytical expressions for the steady-state concentration of substrate using Adomian decomposition method, Homotopy analysis and perturbation method
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