This manuscript focuses on the leading-edge accretion and heat absorption performance of Casson fluids in rolling mills. Casson fluid flow associated with leading-edge accretion is used to understand and improve the performance of coolant for heat exchangers. We investigate the unsteady Casson fluid flow over a flat surface with a moving slot. Using the Blasius-Rayleigh-Stokes variable, the governing equations are converted to ODE system and solved by the bvp4c procedure in MATLAB. The results examine the effects of accretion rate on Casson fluid flow and compare both non-Newtonian and Newtonian fluids. This analysis demonstrates that non-Newtonian fluid flow has better heat transfer efficiency with increasing leading-edge accretion. Increasing the Prandtl number and Casson fluid parameter reduces the heat transfer efficiency near the surface. By accounting for nonlinear velocity, momentum, thermal interactions, Blasius-Rayleigh-Stokes conditions, and conduction, this research delves into under explored aspects of fluid dynamics, highlighting its originality and contribution to the field.