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.

This study presents a comparative analysis of the engineering applications of single-walled and multi-walled carbon nanotubes (SWCNTs and MWCNTs). The investigation focuses on the three-dimensional rotating flow of a nanofluid with nonlinear convection over an elongated surface. The heat transfer characteristics are examined under the influence of nonlinear radiation, an irregular heat source, and convective boundary conditions. Water serves as the base fluid, embedded with both SWCNTs and MWCNTs. Solutions are derived using the shooting technique, and the results are comprehensively displayed through tables and graphical representations. Detailed discussions of various flow field characteristics are provided. The findings indicate that MWCNTs exhibit a higher heat transfer coefficient compared to SWCNTs. Additionally, the presence of irregular heat sources enhances the temperature of the nanofluid.

In this paper, we study boundedness, persistence and rate of convergence of system of difference equations of exponential form $r_{n+1}=\frac{\lambda +e^{-(\mu r_{n}+\xi s_{n})}}{\delta +\mu r_{n}+\xi s_{n}}, \ s_{n+1}=\frac{\lambda +e^{-(\mu s_{n}+\xi t_{n})}}{\delta +\mu s_{n}+\xi t_{n}}, \ t_{n+1}=\frac{\lambda +e^{-(\mu t_{n}+\xi r_{n})}}{\delta +\mu t_{n}+\xi r_{n}},$ where $n=0, 1, 2,\cdots$ and $\lambda $, $\mu $, $\xi $ and $\delta $ are non-negative constants and the initial conditions $r_{0}$, $s_{0}$, $t_{0}$ are non-negative real values.

Lymphatic filariasis is a major cause of long-term disability worldwide, caused by infected female mosquitoes. To manage and control the disease, a deterministic model of ordinary differential equations that includes protected human and treatment compartments is developed, accounting for how access to treatment and movement between affected and unaffected areas influence disease spread. The analysis of the model is carried out by examining the computation of the basic reproduction number utilizing the Next-generation approach and the equilibrium states through the fixed-point and Lyapunov methods. The analysis established the conditions for the local and global stability of the equilibrium states. The sensitivity analysis is further performed using normalized forward sensitivity indices, Latin hypercube sampling and Partial Rank Correlation Coefficient (LHS/PRCC) techniques. The findings from the sensitivity analysis suggest that the rates at which mosquitoes bite and die influence lymphatic filariasis disease dynamics. This is supported by numerical simulation outcomes showing that increasing mosquito mortality and reducing the biting rate can significantly lower infection rates in both human and mosquito populations. It is recommended that public awareness campaigns on the use of insecticide-treated nets, indoor residual spraying, and mass drug administration be implemented to reduce the burden of lymphatic filariasis in the population.

This paper presents a novel six-dimensional (6D) chaotic dynamic system with a simple structure consisting of thirteen terms, including absolute value and hyperbolic tangent functions. The new 6D system, which lacks equilibrium points, exhibits hidden attractors and displays a range of dynamic behaviors such as chaotic, chaotic 2-torus, and hyperchaotic states. A comprehensive dynamical analysis is conducted, featuring bifurcation diagrams, Lyapunov exponents, Kaplan-Yorke dimensions, multistability, and offset boosting control. The proposed system, despite its structural simplicity, exhibits intricate chaotic dynamics, making it suitable for various practical applications.

The importance of the Allee effect in studying extinction vulnerability is widely recognized by researchers, and neglecting it could adversely impact the management of threatened or exploited populations [1]. In this article, we examine a discrete predator-prey model where the prey population is associated with two component Allee effects. We derive sufficient conditions for the existence and local stability nature of the fixed points of the system. The occurrence of Neimark-Sacker bifurcation is established, and sufficient conditions are obtained along with the normal form. Numerically, we demonstrate that the system exhibits Neimark-Sacker bifurcation for various system parameters. Additionally, the numerical simulations indicate that certain system parameters have threshold values, above or below which the populations are driven to extinction due to the impact of the double Allee effect.

This article investigates the mathematical models of amperometric biosensors. The given models is constructed which depends on diffusion equations of the non-linear element pertaining with an enzyme process. The approximate analytical solutions for both time - independent and time - dependent conditions of concentrations are provided in non-dimensional and dimensional for all values of the parameters. The semi-analytical expressions for the substrate, product concentrations and current are attained by utilising the new homotopy perturbation method (NHPM). The new homotopy perturbation technique is employing to solve the biosensors models like non-linear reaction-diffusion model in amperometric biosensors, potentiometric biosensors and michaelis-menten kinetics. On comparing the numerical simulation with our findings, a good fit is reached. The impacts of several parameters, including the Thiele modulus, saturation parameter, maximal enzymatic rate, the ratio of diffusion coefficients, Michaelis constant, substrate concentration in the bulk solution and thickness of the enzyme membrane are graphically represented for concentration and current.

The present study examines the unsteady MHD flow of nanofluid consisting of silver and titanium dioxide nanoparticles dispersed in water over a rotating semi-infinite vertically moving permeable plate with magnetic field, buoyancy effect, Dufour effect, viscous dissipation and Soret effect under constant heat source. The core governing relations are made dimensionless with suitable non-dimensionless variables, and the resulting consequent equations are solved by Galerkin FEM. The graphical representations depicting concentration, temperature, and velocity profiles for various different parameters are incorporated. Nusselt number; skin friction, and Sherwood numbers are also tabulated. The velocity profile accounts for increased Dufour effect, Eckert number, and Soret effect, while the trend of decreasing is reversed for increased rotation parameter. Concentration profile enhances for intensified Soret number. The study also reveals that Nusselt number declines for the suction parameter, the Sherwood number appends for the Soret number, & also the chemical reaction parameter. The study of MHD rotating vertical moving plates has potential applications in energy systems, fusion reactors, industrial coolants, and biomedical devices.