Analytical and numerical approach for the analysis of heat transfer of squeezing flow between two parallel plates

This research offers a thorough examination of thermal transmission within the context of the squeezing flow of a Casson fluid that is confined within two circular plates aligned in parallel. The development of a feasible mathematical framework involves combining the principles of conservation with appropriate similarity transformations. The resulting framework generates a couple of strongly non-linear ordinary differential equations. To tackle these equations, established analytical methods like the (HPM) and its variation, the Least Square Homotopy Perturbation Method (LSHPM), are employed. Additionally, for the validation of the analytical findings, a numerical approach using the BVP5C technique is utilized. A comparative evaluation reveals that the LSHPM consistently provides results of exceptional accuracy compared to the traditional HPM. The investigation delves into observing how the flow performs when experiencing diverse variations in physical attributes, elucidating the complexities through comprehensive visual representations. It is worth noting that the presented problem is subject to specific parameter limitations, which are extensively discussed and taken into account throughout the study. The investigation encompasses a thorough analysis across a range of parameters, including the squeeze number, the Casson fluid parameter, the Prandtl number, the Eckert number and. Notably, an acceleration in the rate of motion is observed concerning the squeeze number and the Casson fluid parameter. In terms of the temperature profile, it is revealed that this profile demonstrates a decreasing trend in relation to both the squeeze number and the Casson fluid parameter. Conversely, it displays an increasing trend with respect to the Prandtl number and the Eckert number.