Confinement-Induced Thermal Response of Bingham Plastic Fluids: Squeezing Characteristics - Gandikota, Dhana Lakshmi; Sekhar, P. Sudam; Khatua, Debnarayan (Journal of Applied Nonlinear Dynamics, 2026)
The thermal-hydrodynamic behavior of Bingham plastic fluids in confined systems has continued to remain a critical challenge for a wide variety of industrial applications-from polymer processing to oil drilling. Past studies have concentrated on isothermal squeeze flows and did not, however, comprehensively quantify the coupled effects associated with temperature-dependent viscosity, pressure gradients, and plate motion. The complete formulation of semi-analytical unification is presented here, in which the governing equations of nonlinear momentum and energy have been solved for the two important cases: (1) stationary parallel plates under squeezing flow and (2) moving plates with opposing velocities. Dimensionless velocity ($\overline{V}$), pressure ($\overline{P}$) and temperature ($\overline{T}$) profiles have been derived using the R.K. Fehlberg method validated through parametric analysis. The key results reveal that pressure gradients ($P$) dominate flow symmetry, with $\overline{U}$ peaking at 3.0 for $P=3$, while negative gradients induce flow reversal ($U=-2.08$ for $P=-2$), critical to avoiding particle settle in drilling muds. This is important to avoid particle settling in drilling muds. The temperature distributions lead to an average temperature drop achieved of 25% ($\overline{T}_m$) for the peclet numbers of $Pe > 10$, thus enabling better control of temperature during extrusion. Industrially, our model predicts a reduction 30% in extrusion defects under pressure differentials below 0.5 MPa. Bridging rheology theory with practical design, this work provides dimensionless scaling laws for optimization under confined non-Newtonian flow in energy-efficient systems.