Dynamics of submicron deposition in Reiner–Rivlin fluid confined between spinning and stretching coaxial disks: A comparative approach

This research explores particle deposition driven by thermophoresis in the flow of a Reiner–Rivlin fluid confined between coaxial disks, which undergo simultaneous stretching and rotational motion within their respective planes. The paper aims to derive accurate momentum transport equations for Reiner–Rivlin fluids specific to the current flow problem, addressing inaccuracies present in the existing literature. The study formulates coupled heat and mass transport phenomena, incorporating the thermophoretic deposition effect, which modifies the advection–diffusion equation by introducing additional terms. Two solution methodologies are employed to analyze the resulting similarity equations: (a) the homotopy analytical scheme and (b) MATLAB’s built-in numerical solver. The convergence of the series solution derived from the homotopy approach is demonstrated through the so-called [Formula: see text]-curves. To refine the convergence interval of [Formula: see text], the residuals of all equations are evaluated at the lower boundary. The results confirm that homotopy solutions maintain accuracy beyond six decimal places and exhibit strong agreement with the corresponding numerical solutions. The radial and azimuthal stresses required at the boundaries and particle deposition velocity are scrutinized for a broad range of the material fluid parameter. A notable result is that boosting thermophoretic strength results in a considerable rise in concentration distribution. The cooling rate of the lower disk rises when viscous fluid is replaced with Reiner–Rivlin fluid, and this effect becomes pronounced with a rise in the Reynolds number. As anticipated, graphical representations of particle deposition velocity and axial thermophoretic velocity reveal a direct correlation with the thermophoretic diffusion coefficient.