Abstract This study examines entropy generation in the magnetohydrodynamic (MHD) electro-osmotic peristaltic flow of a nanofluid through an asymmetric microchannel saturated with a Darcy–Forchheimer porous medium, including Hall current, Joule heating, temperature-dependent thermal conductivity, and velocity and thermal slip. The electric double-layer potential is obtained from the Debye–Hückel-linearized Poisson–Boltzmann equation, and the lubrication-reduced momentum, energy, and nanoparticle-concentration equations are solved with the MATLAB bvp4c collocation solver, which is verified against an exact limiting solution and through mesh- and tolerance-independence tests. Increasing the Hartmann number from 1 to 3 lowers the peak axial velocity by approximately 34 %, whereas increasing the Darcy number from 0.05 to 0.5 raises it approximately fivefold and increases the channel-averaged entropy generation by 41–163 %. The Forchheimer drag alters the velocity by less than 6 % for Fr ≤2. Increasing the Joule heating parameter from 0 to 1 raises the peak temperature by 29–43 %. A variance-based (Sobol) sensitivity analysis shows that the Joule heating parameter dominates the peak temperature and the total entropy generation, the thermal Grashof and Darcy numbers dominate the volumetric flow rate, and Brownian diffusion controls the Bejan number. The results provide quantitative guidance for the design of electro-osmotic micropumps and biomedical microfluidic devices.
Abstract For a variety of applications, the flow of fluid that is induced by rotating disks has become a problem that is worth addressing. Nanofluids that flow over rotating disks display a complicated relationship between their behaviour, the viscosity of their fluid, and the inertia of their fluid properties. The applications including polymer-based treatment, reactive systems, accelerators, storage equipment, lubricating processes, nuclear reactors, a MHD-based generators, and microfluidics all require improvements in heat transfer and performance. These improvements are necessary. Within the scope of this investigation, an LMANN-numerical method is utilized to investigate a magnetised Boger nanofluid that undergoes heating by ohmic current while rotating. The Levenberg–Marquardt Artificial Neural Network(LMANN), in conjunction via a back propagation based artificial neural network, is utilised in order for investigating the steady, incompressible movement of a Boger nanofluid. The investigation focuses on mathematical modelling and characterization of Boger nanofluids flowing with a spinning disc. The bvp4c algorithm is utilized in order to acquire numerical solutions corresponding to the reduced equations. The bvp4c solver is then utilised in order to simulate the numerical behaviour that has been observed. The research investigates the impacts of relevant parameters on profiles of temperature, concentration, velocity, and motile microbes, as well as the Nusselt number and the Sherwood number. An artificial neural network that is driven by the Levenberg-Marquardt algorithm includes the additional feature of being able to simulate and forecast flow behaviour in an extremely efficient manner. A training dataset consisting of 70 % is followed by a validation dataset consisting of 15 % and a testing dataset including 15 %. Simulations using numerical data and the Levenberg–Marquardt Artificial Neural Network(LMANN) approach are in good agreement. For the purpose of evaluating and validating Levenberg–Marquardt Artificial Neural Network (LMANN) performance with relation to variations in physical parameters, the study made use of regression techniques, training process procedure (MSE) analyzing graphs. The utilization of this hybrid framework allows for the efficient management of heat management systems in industrial applications. When it comes to developing accurate predictive models, this study will be helpful to scientists and engineers who are interested in understanding flow characteristics and how they behave. Increasing the magnetic parameter from M = 0.5 to M = 2.0 changes the skin friction coefficient by 51.7 %, reflecting the retarding Lorentz force on the flow; increasing the Brownian-motion parameter from Nb = 0.5 to Nb = 2.0 reduces the local Nusselt number by 66.4 %, as enhanced nanoparticle motion raises the near-wall fluid temperature and weakens the wall temperature gradient. These results are relevant to the design of rotating-disk contactors, MHD-based pumps and generators, and spinning-disk bioreactors, where the present LMANN surrogate offers a computationally inexpensive route to predicting heat- and mass-transfer rates across operating conditions without repeatedly re-solving the full boundary value problem.
Abstract The objective of this study is to address the time-dependent movement of thermally radiative Casson nanofluid between two orthogonally moving disks. The Buongiorno nanofluid model is used to address the critical nanoparticle transport mechanisms, specifically Brownian movement and thermophoretic, which play a major contribution in affecting heat and solutal transfer properties. The modeled equations are transformed into a framework of non-linear ordinary differential equations by employing suitable similarity transformations and then solved using the bvp4c solver. The key outcomes reflected that an increment in the thermophoresis factor improves the fluid temperature but reduces the Nusselt number. A higher Brownian motion boosts both the nanoparticle concentration and Sherwood number. A greater activation energy leads to a temperature drop but an increase in concentration, whereas a higher reaction rate diminishes the concentration. When the thermophoresis parameter values ranged from 0 to 2, the heat transfer rate dropped by 31.87 %. The mass transfer rate reduced by 16.03 % when the activation energy constraint values are between 0 and 3. The numerical results are validated using a Bayesian neural network, which showed good agreement with the bvp4c solutions, with a mean squared error on the order of 10−9.
Abstract Reliable interpretation of sequential measurements requires methods that can distinguish meaningful changes in process relationships from routine variability. This requirement is particularly important for heat exchangers, where progressive fouling may alter the overall heat-transfer coefficient, its response to operating conditions, and the associated measurement variability. This study develops a data-driven profile-monitoring framework based on a double cumulative sum (DCUSUM) procedure for detecting changes in linear process profiles. The proposed DCUSUM3 chart simultaneously monitors the profile intercept, slope, and error variance, which represent the response level, sensitivity to the explanatory variable, and residual variability, respectively. Coding the explanatory variable enables independent estimation and monitoring of these characteristics using routinely collected measurements without requiring a detailed physical process model. Performance is evaluated through Monte Carlo simulations under zero-state and steady-state conditions using average, dispersion, median, percentile-based run-length measures, and conditional expected delay. The results confirm that the chart maintains the prescribed in-control performance and that its detection delay and run-length variability decrease systematically as individual or joint shifts increase. Comparisons with Shewhart, EWMA, CUSUM, and DEWMA profile charts demonstrate competitive detection across a broad range of changes, with particularly strong steady-state performance. Application to controlled shell-and-tube heat-exchanger measurements illustrate earlier identification of fouling-related profile changes, thereby supporting reliable condition assessment and timely maintenance decisions. An interactive Shiny application supports chart calibration, performance evaluation, and practical implementation.
Abstract This study aimed to develop a unified mathematical model that couples couple stress rheology, chemical reaction, thermal radiation, and non-Fourier heat conduction with the Buongiorno two-phase nanoparticle transport model for magnetohydrodynamic Jeffrey nanofluid flow over a moving vertical flat plate, addressing a gap left by previous works that treated these phenomena in isolation. The governing partial differential equations were transformed into ordinary differential equations and solved numerically using the bvp4c solver in MATLAB. Grid independence testing confirmed convergence beyond 200 mesh points, and relative errors remained below 0.1 % against established benchmark solutions. An artificial neural network trained with the Levenberg-Marquardt algorithm was used as a consistency check on the computed dataset; the network reproduced the bvp4c outputs with correlation coefficients close to unity and mean squared errors between 10–10 and 10–12. The results reveal that increasing the couple stress parameter and Deborah number both reduced fluid velocity, the former through heightened resistance to rotational deformation and the latter through stronger elastic memory effects. Temperature increased with thermal radiation and thermophoresis but decreased with the thermal relaxation parameter, since the fluid requires finite time to respond to boundary heating. Concentration declined with rising chemical reaction and Brownian motion parameters, reflecting accelerated species consumption and enhanced diffusive mixing respectively. The skin friction coefficient increased with the couple stress parameter, while the Nusselt number decreased as thermophoresis intensified. These findings provide practical design guidance for heat exchangers, drag control in maritime and aerospace applications, nanoparticle-based drug delivery, solar thermal collectors, and continuous casting processes, where accurate prediction of flow and transport behaviour directly influences operational efficiency and product quality.
