Accelerating and decelerating flow of radiative Sutterby fluid between permeable disks under convective constraints

The flow between two flat, radially aligned disks is of significant relevance in a wide range of industrial and technological applications. Motivated by this importance, the present study focuses on the magnetized motion of an incompressible Sutterby fluid confined between two penetrable, parallel disks subject to convective boundary conditions. The governing model is further refined by incorporating the roles of thermal radiation and internal heat generation or absorption within the energy framework. To address the resulting nonlinear system, the equations are transformed into an elliptic integral form and simplified through a suitable change of variables, which facilitates the application of the Jacobi elliptic sine-squared function for deriving exact analytical solutions corresponding to both accelerating and decelerating flow regimes. Alongside, an analytical solution for the thermal field is obtained under the prescribed boundary constraints. The findings are illustrated graphically to highlight the influence of controlling parameters on velocity and temperature distributions, revealing a parabolic velocity structure with maximum intensity at the center and minimum values near the disk boundaries. It is also revealed that both accelerating and decelerating velocities upsurge for the power law index, while declining for all the remaining factors. Moreover, temperature grows with the source parameter, whereas it decreases for thermal radiation and the Biot number.