Significance of the study Precision drug delivery in biological microvasculature remains a critical challenge in nanomedicine, where controlling heat and mass transfer through non-Newtonian nanofluid flows offers transformative potential for the development of smart, heat-activated therapeutic systems. Aim of the study: This study aims to investigate the electroosmotic peristaltic flow of a Casson-based Tetra-hybrid nanofluid through biological microchannels, examining how electroosmotic forces, magnetic fields, Joule heating, and laser irradiation collectively modulate nanoparticle transport and drug release efficiency. Research methodology: A multi-physics computational framework integrating AI-neural networks with electrokinetic analysis is employed, incorporating viscous dissipation, nonlinear mixed convection with the governing nonlinear partial differential equations solved numerically using Mathematica 13.2's NDSolve command. Conclusion: Results demonstrate that electroosmotic forces significantly enhance nanoparticle transport efficiency during peristaltic motion mapping identifies critical zones of thermal and viscous energy dissipation, and the Tetra-hybrid nanofluid configuration exhibits superior thermal management performance compared to Mono- and Tri-hybrid alternatives. Furthermore, the combined laser irradiation and Joule heating effects confirm the feasibility of controlled, heat-triggered drug release, establishing this framework as a viable computational strategy for designing intelligent, non-invasive nano-bio therapeutic systems.
The equivalence ratio (ER) plays a critical role in governing fuel combustion and combustion stability. However, its influence on the evolution of flame-flow-acoustic coupling under high-enthalpy conditions remains inadequately understood. This study investigates the combustion process in a supersonic combustor under varying equivalence ratios using experiments conducted in a ground-connected pulse-combustion wind tunnel. High-speed optical imaging and synchronized multi-point wall pressure measurements were employed to capture the spatiotemporal dynamics of flame oscillations. Modal decomposition and other analytical methods were utilized to identify the primary mechanisms driving combustion oscillations. Results revealed that, across all tested equivalence ratios, combustion oscillations were predominantly influenced by flow-induced mechanisms governing flame upstream propagation and downstream retreat. The dominant oscillation frequency decreased as the equivalence ratio increased, ranging from 228 Hz to 82 Hz. Additionally, as the equivalence ratio rose, the combustion oscillation mechanism became increasingly dominated by acoustic effects, accompanied by a notable enhancement in oscillation energy. Quantitative analysis using the Rayleigh index demonstrated a progressive strengthening of thermoacoustic feedback with increasing equivalence ratio. This study provides quantitative insights into how equivalence ratio affects combustion oscillation modes, frequency shifts, and the intensity of thermoacoustic coupling under high-enthalpy supersonic combustion conditions. These findings are crucial for designing combustion stability margins in scramjet engines, thereby contributing to the advancement of hypersonic vehicle technology.
This study used an extended modified Sardar-sub equation method (EMSSEA) to examine the optical soliton solutions of the truncated time M-fractional paraxial wave model (PWM) that was missing in the literature. To encourage the fractional order, we employed the truncated-time M-fractional derivative. The few optical wave examples of the paraxial wave condition can be crucial in illuminating the elements of optical soliton arrangements in optics and photonics for the study of different real cycles, such as the production of light through optical frameworks like focal points, mirrors, and fibre optics. Using some free parameters related to the shape of hyperbolic functions, we determined the solutions. For the numerical values of the free parameters, we found a unique soliton solution, bell wave, bright and dark-kink wave, and periodic wave. We used MATHEMATICA 11.0 to provide a physical explanation of the solutions obtained to illustrate the behaviour of different solutions. The presented approach is essential and reliable as a smart optical soliton for nonlinear partial differential equations in nonlinear optics, fiber optics, and communication systems.
This research examines the rotating magneto-peristaltic flow of Williamson shear-thinning fluids within a porous asymmetric tapered channel, while accounting for the impacts of coupled cross-diffusion phenomena. This study integrates prior studies focused on specific transport mechanisms through a unified analytical framework. We derive closed-form solutions for the distributions of velocity, pressure, temperature, and solute concentration by employing lubrication approximation and an asymptotic perturbation expansion in low Reynolds number and long-wavelength circumstances. Computational findings indicate that an elevated Hartmann number causes a reduction in flow velocity by 15%–35%, attributed to the electromagnetic Lorentz resistance. Conversely, an increased Hall effect parameter and Darcy number contribute to a flow enhancement of 10%–20% through improved electromagnetic coupling and higher permeability of the porous material. A rise in the Weissenberg number enhances viscoelastic stress relaxation, resulting in intensification in velocity and a reduction in pressure gradient by approximately 18%–28%. The rise in temperature is ascribed to magnetic damping (Joule heating) and shear-induced viscous dissipation, in addition to cross-diffusion coupling between thermal and concentration fields. The main innovation involves the incorporation of Williamson non-Newtonian behavior, Hall-effect-modulated magnetohydrodynamic forcing, resistive heating, and rotation-induced Coriolis effects within complex geometrically designed porous asymmetric channels-phenomena that have previously been examined separately in earlier research. This analysis identifies distinct transitions in pumping zones and interrelated thermal-mass transport mechanisms that have not been previously recorded in the literature. Applications encompass biomedical peristaltic delivery systems, magnetically actuated microfluidic devices, and thermoelectric magnetohydrodynamic conversion units. Analytical solutions facilitate effective sensitivity analysis and optimization in engineering design, necessitating limited computational resources.
The present investigation presents a detailed qualitative computational analysis of the flow and thermodynamic behaviour of a Ternary-Hybrid-NanoFluid (THNF). The THNF, a mixture of water (the base fluid) with three types of nanoparticles, namely; Molybdenum Disulfide (MoS2); Silver (Ag); and Titanium Dioxide (TiO2) is assumed to have temperature dependent viscosity. The flow of the THNF is confined within a long horizontal microchannel and hence is assumed to be fully developed in the axial flow direction. The walls of the microchannel are assumed to be permeable, allowing for injection/suction flow in the vertical upward direction. Additionally, the microchannel is packed with a porous medium. The flow within the microchannel is subjected to a transverse magnetic field, thermal radiation, and exothermic reactions. A robust and efficient Semi-Implicit Finite Difference Algorithm (SIFDA) with demonstrable mesh-size and timestep-size convergence is employed to solve the resultant coupled system nonlinear governing equations in non-dimensional form. Qualitative results are given with respect to the dependence of solutions on the embedded dimensionless fluid-dynamical and thermophysical parameters. The main qualitative insights from the results include the following. THNFs offer better mitigation against the thermal runaway phenomena than either hybrid nanofluids or ordinary nanofluids. Both the flow velocity and THNF temperature decrease with increasing magnetic field strength. Similarly, both the flow velocity and THNF temperature decrease with increasing porous medium strength. The behaviour of the entropy generation at the walls with regards to variations in magnetic field and porous media strength mirrors that of the flow velocity and fluid temperature, specifically, the entropy generation decreases at the walls with increasing magnetic field strength or with increasing porous medium strength. In general, the qualitative behaviour of the flow velocity mirrors that of the THNF temperature, they either both increase or both decrease in response to increases in the values of the embedded parameters. The qualitative behaviour of the wall shear stress (and hence also of the entropy at the wall) mirrors that of the flow velocity. Similarly, the qualitative behaviour of the wall heat transfer rate (and hence also of the entropy at the wall) mirrors that of the THNF temperature.
The present investigation deals with the two-dimensional deformation in a semi-infinite thermoelastic semiconducting medium subjected to ramp-type heating in the presence of gravity field and initial stress. The medium is modelled as a coupled plasma-thermoelastic system, where the deformation is induced by a ramp-type heat source applied along the free surface. The governing equations, based on the thermoelastic semiconductor framework, account for ramp-type heating, thermal conduction, gravity field and initial stress, providing a comprehensive description of the medium’s behavior. By employing the normal mode analysis and eigenvalue approach, exact expressions for displacement components, stress distributions, temperature profiles, and carrier density are obtained. The numerical “simulations in Mathematica software illustrate how time, gravity field, and initial stress, thermoeleasting coupling, and ramp-type heating on the physical quantities is illustrated graphically and discussed in detail. A graphic comparison of our physical quantity accuracy results with earlier studies shows the significant influence of external conditions on ram-type heating phenomena. These findings highlight the complex interplay of multi-physical effects and offer insights for optimizing wave control in thermoelastic semiconductor medium and multifunctional materials, with potential applications in materials science, geophysics, and advanced engineering systems.
The gas-particle two-phase flow in solid annular aerospike nozzle rocket exerts a significant influence on the nozzle ablation and performance. However, the influence of nozzle contraction ratio on the two-phase flow characteristics in the throat region remains insufficiently explored. The analysis investigates the influence of the particle phase diameter, particle mass fraction, and nozzle contraction ratio on the flow field parameters of the nozzle throat region. For this purpose, numerical simulations employing the Euler-Lagrange method are conducted, and key performance indicators such as thrust efficiency, wall-adjacent temperature, and particle velocity are quantified. The results indicate that two-phase flow introduces performance loss; however, this loss can be mitigated to within 7% by selecting an appropriate nozzle contraction ratio (5.76 and 12.96). Additionally, the flow field parameters in the aerospike nozzle throat are influenced by the particle phase diameter, particle mass fraction, and nozzle contraction ratio. Among these factors, the temperature distribution is predominantly affected by the nozzle contraction ratio. Numerical results indicate that a nozzle with a contraction ratio of 12.96 can reduce the adiabatic wall-adjacent temperature from 2438 K to 1396 K. The velocity of the particle phase decreases as the diameter of the particle phase increases. These insights provide a reference for designing more efficient aerospike nozzles in solid rocket engines.
This study presents a novel nonlocal photo-thermoelastic framework that combines the Moore-Gibson-Thompson (MGT) heat conduction equation with an enhanced Green-Naghdi Type III (GN-III) model and the Guyer-Krumhansl (GK) nonlocal formulation. By integrating thermal relaxation, rate-dependent conductivity, and spatial nonlocality through a meaningful correlation length lq (representing the phonon/electron mean free path), the model addresses the unphysical infinite thermal wave speeds of classical Fourier theory, ensuring finite and causal propagation. The framework is employed to investigate the dynamics of thermal, elastic, and carrier density in a rotating semiconductor sphere subjected to thermal shock, uniform rotation, and an external magnetic field. Governing equations are numerically solved in the Laplace domain, leveraging L'Hôpital's rule to manage spherical singularities. Noteworthy findings indicate that nonlocality significantly alters the mechanical response, causing a sign reversal in central displacement from compressive to expansive and achieving a 977% increase in carrier recombination at the sphere's center—effects missing in local models. The full nonlocal MGT model predicts 20%–30% lower values for temperature, displacement, stress, and carrier density compared to classical photo-thermoelasticity, with contributions from thermal relaxation, rate-dependent conductivity, and nonlocal spatial averaging. The study provides a robust tool for optimizing high-performance semiconductor devices, such as rotating MEMS gyroscopes and laser diodes, where accurate predictions of photo-induced effects are essential.
Small axial turbines for geo-solar Brayton cycles require stator designs that are efficient and robust, yet systematic guidance on how detailed stator airfoil geometry influences performance in this power range remains limited. This study quantifies the sensitivity of stator and stage performance to fourteen geometric parameters defining the stator airfoil and derives practical design guidance for small-scale geo-solar Brayton cycles in the 20–70 kW range. A reference axial turbine stage is first generated using mean-line design, followed by three-dimensional blade modelling and meshing using BladeGen and TurboGrid. Steady-state, three-dimensional compressible flow simulations are performed in ANSYS CFX employing the SST k-ω turbulence model. Each stator geometric parameter is varied individually within realistic bounds while all other parameters are held at baseline values. Stator losses, stator efficiency, and total-to-total stage efficiency are evaluated across a range of pressure ratios (PR = 2–4). Numerical accuracy is ensured through grid refinement, y-plus control, and comparison with independent experimental data from the literature. The results show a clear hierarchy of geometric influence. Four parameters, namely trailing edge wedge angle, trailing edge thickness, and two parameters governing the rear suction side contour, dominate performance, causing up to 5% variation in stator efficiency and about 2% variation in stage efficiency at higher pressure ratios. At PR = 3, the best configuration increased stator efficiency from 88.36% to 92.31% and total to total stage efficiency from 83.46% to 85.32%. Reducing the rear suction side parameter F13 from 50 to 20 mm increased stage efficiency from 82.70% to 85.76% at PR = 2 and reduced the nozzle loss coefficient from 0.757 to 0.377. Overall, most efficiency variation is governed by a small subset of geometric features, indicating that near optimal performance can be achieved with simplified stator geometries when these key parameters are selected carefully.
With the increasing thrust-to-weight ratio demands of modern aeroengines, afterburner ignition performance requirements have become more stringent. To broaden the ignition boundary and enhance ignition capability under extreme conditions, a high-energy jet plasma igniter was developed and its ignition characteristics examined. Analysis focused on the ignition process, ignition delay, and ignition boundary. Results confirmed a two-stage ignition process: the self-ignition process of the igniter and the process of igniting the fuel-air mixture in the afterburner with the jet flame of the igniter. The durations of these stages constitute the total ignition delay. The experimental results show that the igniter has a wide working range and can successfully ignite between 0.63 and 16.91 excess air coefficient, covering the inlet velocity of the combustion chamber from 5.56 to 52.78 m/s. At Tin = 293 K and Win = 1000 m3/h, the ignition delay time in the second stage ranged from a minimum of 100.26 ms to a maximum of 314.99 ms. These results verified the significant advantages of the high-energy jet plasma igniter in effectively expanding the ignition boundary and improving ignition reliability.
The present study develops a high-fidelity numerical analysis of magnetohydrodynamic (MHD) transport phenomena in an Oldroyd-B hybrid nanofluid composed of blood as the base fluid with copper (Cu) and aluminum oxide (Al2O3) nanoparticles. The flow is induced by a nonlinear stretching surface situated inside a porous medium under the combined effects of thermal radiation, viscous dissipation, Joule heating, and finite thermal and solutal relaxation. The resulting nonlinear boundary-layer equations governing momentum, heat, and mass transfer are transformed into a coupled system of ordinary differential equations using similarity variables. The solutions are obtained with high accuracy using the overlapping spectral quasi-linearization method (OSQLM), which combines the advantages of quasi-linearization with the spectral accuracy of Chebyshev collocation on overlapping domains. A detailed parametric analysis is carried out to examine the effects of viscoelasticity, porous medium resistance, magnetic damping, nonlinear stretching, and nanoparticle concentration on the velocity, temperature, and concentration distributions. The hybrid nanofluid demonstrates enhanced thermal and mass transport characteristics compared with the conventional nanofluid due to its improved effective thermophysical properties. In particular, thermal relaxation significantly suppresses convective cooling, whereas increasing nonlinear stretching enhances the cooling effect. Mass transfer is found to depend strongly on the solutal relaxation parameter, Schmidt number, and power-law index. Furthermore, the hybrid nanofluid requires approximately 30%–40% lower nanoparticle volume fraction to achieve equivalent thermal performance, which is important for reducing biomedical toxicity concerns in practical applications. To complement the physics-based solver, an artificial neural network (ANN) surrogate model is developed using high-fidelity OSQLM data to rapidly predict engineering quantities. The ANN demonstrates excellent predictive performance with minimal error in estimating the skin friction coefficient, Nusselt number, and Sherwood number. The hybrid OSQLM-ANN framework provides an efficient computational tool for analysis, optimization, and real-time control of hybrid nanofluid transport in biomedical systems, porous media, and advanced thermal management applications.
This study explores the nonlinear dynamics of a nerve impulse neuron model governed by a partial differential equation (PDE) with beta-fractional derivatives, allowing the inclusion of nonlocal temporal dependence in the model formulation. The model exhibits rich dynamical behavior, including chaos, multistability, and chaos control, alongside the emergence of solitary and periodic wave solutions within the cell membrane. Through a suitable transformation, the PDE is transformed into an ordinary differential equation (ODE), which is further reduced to a planar dynamical system via the Galilean transformation. The stability of the system’s equilibrium points is assessed through eigenvalue analysis of the associated Jacobian matrix. Numerical solutions of the reduced integer-order ODE system are performed using a Runge-Kutta method, and chaotic dynamics are induced via a time-dependent periodic forcing term. Chaos is consistently identified using standard diagnostics, including phase portraits, time-series analysis, Lyapunov exponents, Poincaré maps, bifurcation diagrams, power spectra, return maps, and recurrence plots. The Pyragas time-delayed feedback control method is then applied to stabilize the system, resulting in stabilized periodic states. To explore wave solutions, variational and Hamiltonian approaches are employed to derive analytical expressions for bright, bright-dark, kinky-bright, and periodic wave solutions within the fractional-order framework. The influence of the fractional order on temporal dynamics and spatial wave propagation is illustrated through two- and three-dimensional graphical representations. These wave structures may be interpreted as mathematical analogs of excitation, inhibition, and rhythmic firing mechanisms in neuronal dynamics. The results provide new insights into the nonlinear features of the fractional neuron model, linking memory effects, nonlinear excitability to mathematically meaningful interpretations of neuronal firing and signal transmission.
This study investigates the magnetohydrodynamic (MHD) characteristics of hybrid nanofluid flow confined between concentric cylindrical surfaces. The governing momentum and energy equations are formulated and solved subject to appropriate boundary conditions to analyze fluid motion and heat transport mechanisms. Particular attention is given to the roles of the Darcy number and magnetic field strength in regulating flow behavior and thermal performance. Comparative assessments demonstrate the reliability of the results and reveal that hybrid nanofluids provide enhanced thermal effectiveness in restricted geometries. An increase in the Darcy number lowers resistance within the porous medium, leading to higher fluid velocities and improved heat transfer, which is beneficial for geothermal and subsurface energy applications. Variations in the shape factor influence the flow by reducing velocity while promoting a more uniform temperature distribution, thereby contributing to greater thermal stability in control and regulation systems. Intensifying the internal heat generation elevates temperature gradients and induces fluid expansion, strengthening heat transfer in systems such as cooling devices and nuclear reactors. Furthermore, higher magnetic field intensity suppresses fluid motion due to Lorentz forces. The increased wall shear stress caused by inertial factors causes the skin friction coefficient increase along with the Reynolds number. The thinner thermal boundary layer causes the Nusselt number to escalation with the Reynolds number. These findings offer valuable insights for the design and optimization of advanced thermal management systems, energy technologies, and industrial applications.
This study presents an analytical investigation of wave propagation in a magnetized, rotating, initially stressed microelongated thermoelastic layer within the framework of the Moore-Gibson-Thompson (MGT) heat conduction model, incorporating thermodiffusion and microstructural effects. The proposed formulation accounts for the coupled interactions between thermal, mechanical, magnetic, diffusive, and microelongational fields in a homogeneous and isotropic medium, providing a physically consistent multi-physics description of energy transport and wave dynamics. An exact analytical solution is obtained using the harmonic wave approach, enabling the derivation of bounded wave modes and characteristic propagation behavior in the half-space configuration. Numerical simulations are performed using aluminum-epoxy material properties to examine the influence of key parameters, including rotation, magnetic field intensity, and wave number, on temperature distribution, displacement components, stress fields, and chemical concentration. The results reveal strong thermo-rotational and magneto-thermoelastic coupling effects, demonstrating that increasing rotation enhances thermal energy accumulation and significantly modifies mechanical and diffusive responses. Stable finite solutions are obtained throughout the domain, and wave attenuation is shown to arise not only from intrinsic material dissipation mechanisms but also from boundary-induced energy loss effects. The proposed model provides a robust theoretical framework for understanding coupled wave phenomena in microstructured thermoelastic materials, with potential relevance to advanced engineering, energy systems, and microstructured material applications.
This work presents an advanced theoretical model for magneto-photothermal wave propagation in microtemperature hydro-poroelastic semiconductor media subjected to ramp-type thermal heating, explicitly accounting for fractional-order non-Fourier heat conduction, Hall current effects, and variable thermal conductivity. Unlike classical formulations that assume constant thermal properties, the present model incorporates a temperature-dependent thermal conductivity via the Kirchhoff transformation, enabling a realistic description of nonlinear heat diffusion under rapid thermal loading. A fractional-order time derivative is introduced in the heat conduction equation to capture thermal memory and anomalous diffusion, while Hall current effects are included in the electromagnetic coupling, leading to modified current density and Lorentz force expressions under strong magnetic fields. The governing system couples elastic deformation, microtemperature evolution, pore-fluid pressure, carrier density, and electromagnetic fields within a unified framework. Analytical solutions are obtained using the normal mode analysis technique, yielding closed-form expressions for the primary field variables and associated stresses. Numerical simulations are performed for porous silicon (PSi) as a representative hydro-poroelastic semiconductor material, using thermophysical, mechanical, electrical, and microtemperature properties reported in the literature. The parametric analysis spans physically relevant ranges of the fractional thermal order (0 < α≤ 1), Hall parameter, and thermal conductivity variation coefficient, allowing systematic investigation of memory effects, electromagnetic coupling, and nonlinear heat transport. The Hall parameter introduces additional damping and directional coupling, whereas ramp-type heating intensifies near-surface transient responses. The model reduces to the classical magneto-photothermal hydro-poroelastic theory in the limiting cases of constant thermal conductivity, integer-order heat conduction, and vanishing Hall current, confirming its generality. The proposed framework provides new physical insight into coupled wave phenomena in semiconductor materials and is relevant to the design of advanced optoelectronic, sensing, and energy-harvesting devices operating under rapid thermal loading and strong magnetic environments.
This study investigates magnetohydrodynamic (MHD) flow of a tangent hyperbolic nanofluid (HNF) over a stretching surface, incorporating thermal radiation, chemical reactions, and Soret-Dufour effects within a Darcy-Forchheimer porous medium. The governing partial differential equations (PDEs) are first converted into ordinary differential equations (ODEs) using appropriate similarity transformations. The MATLAB bvp4c algorithm is used to solve and generate a dataset for the Levenberg-Marquardt backpropagation artificial neural network (LMBP-ANN) numerically. The ANN model is trained, tested, and validated using comprehensive datasets generated for various fluid parameters, with accuracy assessed through regression analysis, error histograms, and curve fitting. The dataset was divided into three subsets, training, validation, and testing, 80%, 10%, and 10%. Key findings reveal that the velocity profile declines with increasing the value of the Hartmann number, Weissenberg number, and power-law index but rises with buoyancy parameters and the Deborah number. The temperature profile is enhanced by the Hartmann number, Brownian motion, power-law index, thermophoresis, Dufour number, and thermal radiation, while being reduced by the Prandtl number. The solute concentration profile decreases with the Schmidt number but increases with the Soret number. The numerical results for skin friction, Nusselt number, and Sherwood number are presented in tabular form.
This study presents a comprehensive investigation of micropolar nanofluid flow through a vertically rotating channel embedded in a resistive porous medium under the combined influence of magnetic, thermal, and electrical effects. The analysis also includes the use of fuzzy uncertainty modelling where the volume fraction of nanoparticles of 0%–3.5% is modelled using triangular fuzzy numbers, thus being able to give the realistic range of parameter variations as compared to other deterministic models. The combined effects of Hall current, Joule heating, and thermal radiation are systematically studied to explain their influence on the primary and secondary flows, microrotation, and thermal fields. A two-parameter homotopy analysis method (HAM) is employed to obtain highly accurate semi-analytical solutions and to effectively control convergence. Comparative evaluations between crisp and fuzzy solutions reveal notable sensitivity of the flow and heat transfer characteristics to uncertainty in nanoparticle concentration. Furthermore, analyses of skin friction coefficients and Nusselt numbers confirm the robustness and reliability of the proposed fuzzy-HAM approach in capturing uncertainty-driven magneto-thermal transport phenomena in micropolar nanofluids within porous rotating systems.
In this work the Carreau-Yasuda nanofluid is used to coat the wire in pressure type die. The properties of the liquid are considered temperature dependent in this study. This study involves theoretical results and data is collected with suitable numerical scheme Runge-Kutta-Fehlberg method. This numerical data is further utilized to check the parametric sensitivity of coated thickness and heat transfer rate with Surface Methodology (RSM). In order to do this, we formulated Analysis of Variance (ANOVA) tables and establish correlations between our results and the input parameters. The wire-coated thickness (R) is more sensitive to variable thermal conductivity; the wire-coated thickness decreases with increasing the values of variable viscosity. The current analysis reveals that the heat transfer rate (Nur) is very less sensitive to thermophoretic effects at a low level as we input the higher value of the thermophoretic the depth of the heat transfer rate (Nur) starts reducing. It is observed that heat transfers rate (Nur) decreases 215.29% and 8.45% by increasing thermophoretic parameter (Nt) and Brownian motion (Nb) from 0 to 1 and Nb from 0.1 to 1 respectively. Increasing the values of variable viscosity parameter from 0 to 3, the radius of coated thickness, shear stress and heat transfer rate decreases 8.59%, 96.1% and 129.15% respectively.
This work presents the first comprehensive framework to simultaneously incorporate spatial nonlocality and temporal phase-lag effects for coupled heat and mass transport in a cylindrical configuration. The model introduces two distinct nonlocal length scales, for thermal conduction and mass diffusion, respectively, alongside dual relaxation times, overcoming the scale limitations of classical continuum theories. A dual-phase-lag thermoelastic diffusion model is derived by generalizing the Lord-Shulman theory through nonlocal reformulations of Fourier’s and Fick’s laws. This formulation ensures finite signal speeds and captures the size-dependent response essential at micro- and nanoscales. The theory is applied to an infinitely long solid cylinder subjected to a transient surface load: a Gaussian-modulated cosine thermal pulse and an exponentially decaying chemical potential. Under axisymmetric conditions, all field quantities depend only on radial position and time. The governing equations are solved analytically via the Laplace transform, with solutions in the transformed domain expressed using modified Bessel functions. Time-domain results are recovered through numerical inversion based on a Fourier-series expansion. Results demonstrate that nonlocal and phase-lag parameters significantly dampen mechanical fields (displacement and stress) while amplifying and smoothing thermal and diffusive fields (temperature and concentration). The interplay between thermal and diffusive nonlocalities produces synergistic damping and enhanced penetration depths, effects unattainable with local or single-phase-lag models. This advanced framework provides a critical predictive tool for the design and analysis of micro- and nano-scale systems, including MEMS, semiconductor devices, energy-storage media, and biomedical implants, where coupled thermo-diffusive-mechanical interactions dictate performance and reliability.
The present study investigates the flow and heat transfer behavior of couple stress nanofluids under active control zero mass flux at the boundary mechanisms and sensitivity analysis of it. It focuses on three-dimensional couple stress nanofluid flow, incorporating non-Fourier thermal along with non-Fick mass flux models (combined fluxes) within a second-degree slip model framework. Its aim is to explore the influence of magnetohydrodynamic effects and velocity slip conditions on the heat and mass transfer characteristics of couple stress nanofluids. This work aims to deliver a holistic insight into the ways these factors alter fluid flow and heat transfer mechanisms. The initial set of coupled nonlinear partial differential equations is transformed into higher-order nonlinear ordinary differential equations using similarity transformation then solved by Galerkin finite element method. The numerical results are verified through grid independence tests, confirming consistency. The presence of couple-stress effects introduces higher-order momentum derivatives; however, the interaction between these microstructural effects and second-order slip boundary conditions remains largely unexplored. From a numerical standpoint, many previous investigations rely on traditional solution techniques that face limitations when dealing with strongly nonlinear, higher-order systems. In contrast, finite element method based sensitivity analyses for such coupled nonlinear models are notably limited in the existing literature. The findings reveal that velocity increases with the couple stress parameter, mixed convection, and buoyancy parameter, while it decreases with increasing magnetic. The velocity and temperature profiles decrease with lower first-order slip (γ) and temperature relaxation time δe whereas higher second-order slip (δ) and concentration relaxation time δc lead to increased velocity and concentration profiles. Moreover, 62.07% of the results show an increase in key metrics, while 37.93% show a decrease. Furthermore, the elevated values of the coefficient of determination, R2=99.1%, and adjusted R2=98.7%, highlight the model's excellent capability in accurately predicting the thermal characteristics of the system. Using sensitivity analysis Nt is the most influential factor with a strong positive sensitivity, indicating that increasing thermophoresis significantly enhances the sensitivity of Nux. The numerical results are verified through grid independence tests, confirming consistency. Additionally, to ensure the reliability of the results, a detailed comparison with existing literature confirms that the present results are in strong concordance with previous investigations. The findings have potential applications in heat transfer, microfluidics, energy storage, lubricant production, machinery longevity, and biofluid dynamics, including blood flow, and thermal management.
