Mathematical Solutions of Free Convection Flow of Casson Fluid in Channel with Accelerated Plate

This research develops mathematical solutions for Casson fluid flow with free convective phenomena within channels with an accelerated plate. The study transforms the governing energy and momentum equations into the dimensionless form using appropriate variables. The Laplace transformation is used to acquire analytical solutions. Dimensionless parameters, such as the Prandtl number, Grashof number, accelerated parameter, and Casson fluid parameter, are determined, which are further investigated for their impacts on the flow and thermal behaviour. Visual representations of the mathematical results for velocity and temperature are presented using MATHCAD software through graphical plots. The study observes that fluid velocity increases with higher values of Gr but decreases with increased Pr. Additionally, temperature profiles exhibit a decrease with higher Prandtl numbers and an increase with time. The obtained results are validated by comparing them with published results in limiting cases, showing good agreement, and confirming the accuracy and reliability of the research outcomes.