Closed Form Solution for Parabolic Flow of a Inclined Isothermal Plate With Uniform Mass Diffusion

TL;DR

This paper derives an analytical solution for the parabolic flow of an inclined isothermal plate with uniform mass diffusion, considering chemical reactions and parabolic motion, using Laplace transforms and MATLAB visualization.

Contribution

It presents a new closed-form analytical solution for heat, velocity, and concentration profiles in a complex flow scenario involving chemical reactions and parabolic motion.

Findings

Analytical expressions for temperature, velocity, and concentration profiles.

Graphical analysis of flow characteristics for various parameters.

Insights into the effects of chemical reactions and motion on flow behavior.

Abstract

The fluid flow across an unbounded horizontal plate embedded with uniform mass diffusion is studied in this article together with the impacts of the chemical reaction and parabolic motion, while the temperature and concentration of the plate remain constant. Using initial and boundary conditions, partial differential equations were used to describe this phenomenon. Introduce some appropriate non-dimensional variables and utilize the Laplace transform method to solve the corresponding dimensionless equations. The following analytical remedies for heat, velocity and concentration profiles were produced in terms of exponential and (erfc) complementary error functions. A MATLAB programme is used to exhibit the results as graphs for various parameters. By creating graphs, we may assess the characteristics of the velocity, Heat and concentration while also studying the physical aspects for various factors.