Semi-analytical modeling of compact flow with mass and heat exchange: a python-based approach

Abstract

In this paper, the compact flow with mass and heat exchange for a two-dimensional incompressible viscous fluid between two parallel plates is investigated using semi-analytical methods. The study of compact flow with mass and heat exchange has numerous applications in medicine, including modeling blood flow in vessels, designing controlled drug delivery systems, simulating heat transfer in the body, and designing bioreactors for cell culture. The governing partial differential equations (PDE) are transformed into dimensionless nonlinear ordinary differential equations (ODE) using an appropriate transformation. Then, the equations are solved using the Akbari–Ganji method (AGM) and differential transform method (DTM). Python has been used as a powerful tool for solving engineering problems in this research. The innovation of this research is the use of semi-analytical methods to derive explicit solutions for flow, temperature, and concentration profiles in a complex squeezing flow system, implemented entirely in Python for enhanced accuracy and efficiency. Also, the Nusselt number, skin friction coefficient and Sherwood number have been investigated using ANOVA analysis. The results show that increasing Ec from 1 to 3 at η = 0.4 increases the temperature profile by 45.28 %. Also, increasing S from -1.5 to 1.5 increases the temperature profile by 8.2 % at η = 0.2. The results show that increasing S increases the temperature and concentration profile due to stronger pressure effects. Also, increasing γ significantly reduces the concentration profile and Sherwood number. ANOVA was also used to examine the simultaneous effect of different parameters on the skin friction coefficient, Nusselt number, and Sherwood number.