Investigation of Power-Law Fluid on a Decelerated Rotating Disk

This study explores the behaviour of power-law fluids over decelerating rotating disks. The disk's angular velocity decreases inversely with time, and the unsteady governing equations modeling this flow yield similarity transformations that depend on the nondimensional parameter $\hat{\alpha}=\frac{\alpha}{\Omega_0}$. These transformations, introduced here for the first time in the literature, allow for a comprehensive analysis of the fluid dynamics for shear-thinning fluids within the range $0.5 < n \leq 1$. We examine the no-slip boundary condition alongside the dimensionless unsteadiness parameter, which quantifies the initial deceleration or acceleration of the disk. We present velocity profiles and the viscosity function for various values of $\hat{\alpha}$. The boundary layer problem, formulated through dimensionless momentum and continuity equations derived via similarity transformations, is solved using the \texttt{bvp4c} function in MATLAB. This numerical method, employing the 4th-order Runge-Kutta algorithm, provides approximate solutions for the $U$, $V$, and $W$ velocity profiles and the $\mu$ viscosity function, considering different deceleration parameters and the power-law index $n$. Our findings contribute novel insights into the fluid dynamics of power-law fluids in decelerating rotational systems, offering potential applications in industrial and engineering processes where such conditions are prevalent.