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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Confinement-Induced Thermal Response of Bingham Plastic Fluids: Squeezing Characteristics

Journal of Applied Nonlinear Dynamics 15(3) (2026) 503--518 | DOI:10.5890/JAND.2026.09.001

Dhana Lakshmi Gandikota$^1$, P. Sudam Sekhar$^1$, Debnarayan Khatua$^2$

$^1$ Department of Mathematics and Statistics, Vignan's Foundation for Science, Technology and Research, Guntur, Vadodara, Andhra Pradesh, 522213, India

$2$ Department of Applied Science and Humanities, Parul Institute of Technology, Parul University, Waghodia, Gujarat, 391760, India

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Abstract

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.

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