The innovative aspect of the current study employs the Physics Informed Neural Network(PINN) with SHAP(Shapley Additive Explanations) analysis to understand the flow behavior of the trihybrid nanofluid between the two coaxial cylinders, the outer rotating cylinder with some fixed angular velocity including the inner stretching horizontal cylinder. The trinanofluid consists of gold(Au), copper(Cu), titanium(Ti) embedded as nanoparticles with blood as the base fluid. The flow in between the annular gap has a wide range of theoretical model in many fields like spacecraft thermal management, hypersonic vehicle leading edge cooling, satellite attitude control systems and bio medical diagnosis. To understand this crucial fluid flow which is applicable in rotating machinery, the internal cylinder surface incorporates the first- order slip condition, the Darcy-Forchheimer medium and the local thermal non-equilibrium model were considered. Transform the conservation of mass, Navier–Stokes, and energy equations into dimensionless ODEs by applying appropriate transformations, which were solved numerically using the ND-solver by following the shooting strategy in MATHEMATICA environment. These equations are constructed into residuals using the PINNs along with the initial and boundary conditions and it is validated by mean squared error(MSE) and regression value which are closely match the numerical results. The calculated outcomes of the Nusselt number for both phases, the skin-friction coefficient, and the Sherwood number were trained using Keras with the Adam optimizer, which exhibits the ANN data and regression, demonstrating the fit of the fluidic model with an accuracy of 95%. The response surface methodology and sensitivity analysis also included for the parameter studies. The angular velocity parameter shows the impact of 66.13% decrease and curvature parameter 21.23% increase in the skinfriction coefficient by discussing the SHAP analysis.

Improving thermal management through suspensions of Nano-Encapsulated Phase Change Materials (NE-PCM) in conventional fluids is essential for optimizing thermal system performance, as it influences flow behavior and thermal distributions in complex-shaped enclosures, which are crucial for enhancing system efficiency. In this context, the present article investigates the flow and thermal behavior of NE-PCM-H2O inside a closed enclosure, where all walls are sinusoidally designed to resemble a fan-like structure. The enclosure features varying undulation configurations, with the bottom wall heated, the top wall cooled, and the side walls exhibiting a linearly varying temperature. The NE-PCM consists of an n-nonadecane core encapsulated in a polyurethane shell, suspended in water. Experimental-based correlations for effective viscosity and thermal conductivity, as functions of suspension volume fraction, are employed to model the governing equations, which are then nondimensionalized and solved using the Galerkin Finite Element Method. The impact of the Rayleigh number (103 <= Ra & lowast; <= 5 x 104) and the non-dimensional fusion temperature (0.1 <= theta & lowast;f <= 0.9) on heat transfer is explored in the enclosure with varying undulations (0.3 <= A & lowast; <= 0.4), focusing on streamlines, isotherms, heat capacity ratio, and Nusselt numbers. Increasing the Rayleigh number from 103 to 5 x 104enhances the Nusselt number by 34.35%, 17.54%, and 5.98% forA* = 0.3, 0.35, and 0.4, respectively. Additionally, increasing A* from 0.3 to 0.4 raises the Nusselt number by 37.45%, 37.06%, and 8.43% for Ra* = 103, 104, and 5 x 104, highlighting the significant influence of both parameters on heat transfer. A sensitivity analysis of the fusion temperature parameter further reveals that the highest average Nusselt number is attained at theta & lowast;f 1/40.6, with enhanced heat-transfer performance occurring within the range 0.5 <= theta & lowast; f <= 0.7 for enclosures with higher undulation.

In this paper, the fractional-order Heimburg model is under consideration analytically. This model has applications in the fields of pharmacology, neuroscience, cardiology, Biomembranes, and nerves. The newly modified extended direct algebraic method is used to gain the different types of exact solitary wave solutions. These solutions are successfully obtained in the form of dark, singular, complex singular, dark-singular, periodic, and rational functions. Additionally, getting the necessary aspects in accordance with the requirements is stimulated by the soliton's velocity. The wave profiles of the developed dynamical structural system are used to demonstrate the sensitivity and chaotic analysis, where the nerves wave singularity is controlled by the soliton wave velocity and wave number parameters. Lastly, the physical behavior of some extracted solutions is drawn by selecting the different values of parameters in the form of 3-dim and their corresponding contour plots. This work demonstrates that the technique used is efficient and can be applied to identify suitable closed-form solitary solitons to the dynamic study of Biomembranes and nerves.

Enhancing natural convection with finned surfaces is essential yet challenging for effective thermal management in electronic devices, industrial cooling units, and heat-dissipation systems. This study investigates the thermal performance of four heated fin configurations-Bottom-Multi-Fin, Top-Multi-Fin, Left-Multi-Fin, and Right-Multi-Fin-placed inside a square enclosure filled with an incompressible viscous fluid, a set of configurations not previously examined in a unified framework. The walls opposite the heated fins are maintained at a cold temperature, while the adjacent walls are insulated, representing practical passive cooling conditions. The nondimensional governing equations are solved using the Galerkin finite element method to assess the influence of the Rayleigh number number (103 < Ra < 6 x 105) on flow structure, temperature distribution, and both local and average Nusselt numbers. Results show that the BottomMulti-Fin and Top-Multi-Fin configurations are conduction dominated and provide minimal enhancement in natural convection, even at high Rayleigh numbers. In contrast, the Left-MultiFin and Right-Multi-Fin configurations generate stronger buoyancy-driven circulation and significantly improve heat transfer. The Right-Multi-Fin arrangement delivers the highest cooling performance at elevated Rayleigh numbers, making it the most efficient orientation for natural convection applications.

This paper investigates how ester-based nanofluids flow between two parallel disks when subjected to micropolar effects. Compared to traditional Newtonian fluids, micropolar fluids which exhibit spin inertia and micro-rotation provide a more thorough knowledge of the behaviour of complicated fluids. The ester-based nanofluid, selected due to its exceptional thermal characteristics and favourable environmental effects, is examined with different micropolar parameters to evaluate their impact on heat transfer rates and flow dynamics. Initially, we created a mathematical model to explain the fluid dynamics of ester-based micropolar nanofluids between two parallel disks using the Navier-Stokes equations. The suggested mathematical problem is converted into a non-linear ordinary differential equation (ODE) using the similarity transformation technique. We then solved the governing equations numerically using MATLAB's built-in BVP4c method. Through numerical simulations, we explored the velocity distribution, micro-rotation profiles and temperature profiles within the disk system. The results reveal that micropolar effects significantly enhance the thermal conductivity and viscosity of the nanofluid, leading to improved heat transfer efficiency and altered flow patterns. Nanoparticles in porous disk flow increase velocity and micro-rotation profiles, resulting in a more streamlined flow. Nanoparticle volume fraction also increases temperature, reducing thermal boundary layer thickness and enhancing convective heat transfer.

This paper investigates the influence of chemical reactions and variable magnetic field on three dimensional Oldroyd B micropolar nanofluids subjected to exponentially stretching sheet in the presence of motile microbes. The study incorporates several significant physical phenomena, including Cattaneo-Christov heat, thermal radiation, chemical reaction kinetics, and Darcy-Forchheimer effects. A particularly novel aspect of PST (prescribed surface temperature) and PHF (prescribed heat flux) are taken into account. The governing nonlinear PDEs of Oldroyd B fluids with thermophoretic diffusion and Brownian motion are transformed in to nonlinear ODEs via similarity functions. The resulting set of nonlinear ODEs are solved numerically via MATLAB platform and compared the results with published literature through bvp4c built-in code for better agreement. The results of on different parameters like Peclet number, Forchheimer number, thermal relaxation time, chemical reaction, Prandtl number, Schmidt number, porosity parameter, heat source coefficient and magnetic parameter on Skin friction, Nusselt number, Sherwood number and motile density number are discussed in detail through graphs, tables and literature. It is declared that Skin friction coefficients decline for developed values of magnetic parameter M, porosity parameter K1.and viscoelastic parameter K2. The thermal boundary layer thickness decreases with growing value of Prandtl number. The findings have significant implications for industrial and engineering processes where heat transfer is major issue.

Ethylene glycol is extensively used in solar energy systems because of its thermo-physical properties; however, its toxicity presents health and environmental risks. To overcome this, non-toxic solutions such as propylene glycol or water-ethylene glycol blends are promoted, keeping system efficiency while enhancing safety and sustainability. This study proposes the integration of advanced machine learning (ML) and artificial intelligence (AI) with computational fluid dynamics (CFD) for the thermal analysis of a mixture comprising three distinct base fluids: Ethylene Glycol (EG)-water, Propylene Glycol (PG)-water, and EG with hybrid nanoparticles, aimed at minimizing toxicity and production costs in solar collector energy systems. The effect of non-Fourier heat flux on the Blasius–Rayleigh–Stokes variable (BSRV) flow of a hybrid nano-fluid across a plate is investigated numerically for this purpose. Hyper-parameter optimization is performed for four alternative AI training methods to determine the best suitable choice. Whereas for numerical simulation, the Keller-Box method (KBM), a modified finite difference methodology, is employed. Regression scores of 1 indicate an impeccable correspondence between numerical information and the predictions. Conclusively, a comparative analysis is presented to support our claim, which states that by using combination of PG-Water, similar heat transfer rate can be achieved, which is less harmful and also cost effective.

The convective heat transfer is one of the most important mechanism of heat transference for controlling the chaotic characteristics in porous media. A comparative study of thermal non-equilibrium model is proposed for fractal porous under the consideration of chaotic convection. A novel chaos control is focused between fractal porous and fractional porous by means of newly proposed differential and integral techniques. The sensitivity analysis for chaos expansion and uncertainty quantification for the flow in heterogeneous media have been perceived to the problem of chaotic convection through numerical simulations. In order to approximate the propagation of chaos, two types of simulations have been carried out in terms of chaotic attractors through fractal and fractional approaches. For examining a variety of chaos under the numerical simulations in which fractal domain is varied and fractional domain is fixed, fractal domain is fixed and fractional domain is varied, and both fractal as well as fractional domain are varied. Finally, it is observed that the fractional and fractal memory effects have caused by interactions between uncertain parameters and disclosed the microstructures on the permeability of porous media.

In this paper, we present optical recursively fractional SKμ−electroosmotic fractional recursivelySKμ−energy. Also, we have spacelike microfluidicsfractional SKμ− electroosmotic recursively tension energy. Moreover, we construct main Katugampola recursive-normal hyperbolic fractional KFα−tension field in hyperbolic space. Finally, we characterize spacelike radiative recursively fractional SKμ− phase in hyperbolic space.

A growing interest in researching mixed convective flow with the magnetic field has been seen recently. Numerous researchers have focused on problems related to flow within cavities or enclosures, considering various parameters and conditions. However, there seems to be a lack of research that incorporates Casson fluid in a staggered cavity to study heat and mass transfer and entropy generation. So, in this work we tried to conduct a numerical investigation to evaluate the characteristics of thermal performance and mass transport in a staggered cavity under the influence of magnetohydrodynamic conditions with different inclination angles using Casson fluid. The characteristic flow features are examined through non-dimensional parameters such as the Hartmann number (Ha), Lewis number (Le), inclination angle (γ), Reynolds number (Re), and Casson number (β). The findings have been shown as graphical representations, isotherm, isoconcentration, and streamlines. The average Nusselt number and Sherwood number have been plotted for various conditions. The mass concentration and temperature gradient have been shown for different values of Re, Ha, and Casson number. Key findings include a 37.4% increase in the Nusselt number and a 41.8% increase in the Sherwood number as Re increases from 10 to 1000. Similarly, entropy generation is maximized at 90° inclination, while heat and mass transfer rates decline by approximately 20% with higher Ha. It is found that Re and γ can amplify the phenomenon of heat and mass distribution, while the opposite trend is seen for Ha and β. Added to that, the thermal and mass transport performance decreases with the growth of Lewis number in the cavity. Entropy generation has been found to be higher at higher inclination angles for both constant Lewis and Hartmann numbers.

Power losses and voltage deviations in distribution power networks (DPNs) are high since they carry more power demand than transmission power networks. Also, voltage deviation beyond the allowable range causes voltage stability problems in the DPN. The power loss (PL) in the DPN should be kept at the minimum level for the economic operation of the electric grid. Integrating distributed generation (DG) in appropriate sites of the power networks can minimize the power losses and voltage drops. An integrated optimization approach is proposed in this paper, by combining an analytical and metaheuristic algorithm to optimize the placement and sizing of multiple DGs. The active power loss sensitivity (APLS) index is an analytical mathematical computation approach used to identify the optimal bus locations for DG placement. The modified ant lion optimization (MALO) algorithm is applied to optimize the ratings of the DG systems. The MALO algorithm is proposed by adopting the Lévy flights (LF) pattern in the random walk process (RWP). LF representation of RWPs enhances the exploration phase of the ALO algorithm and helps to obtain the near-optimal solution. The proposed integrated approach optimizes multiple units of photovoltaic (PV) and wind turbine (WT) units to minimize the multi-objective function, including AP loss and voltage deviation (VD) minimizations. The effectiveness of the proposed integrated approach is validated on the IEEE 69-bus, 85-bus, and 118-bus radial DPNs. Besides, the simulation study is extended for ant lion optimization (ALO), BAT, and artificial bee colony (ABC) algorithms-based techniques. The integrated approach has reduced the total AP loss of the IEEE 69-bus and 85-bus radial DPN from 225 kW to 70.51 kW and 316.12 kW to 162.80 kW, respectively, for the optimized three PV DG units allocation. Likewise, the total AP loss of the 118-bus radial DPN is cut down from 1296.3 kW to 432.3 kW after the optimized five PV DG units allocation. Meanwhile, the total AP LOSS of the 69-bus, 85-bus, and 118-bus radial DPNs is reduced to 4.78 kW, 53.87 kW, and 112.2 kW, respectively, after the optimized WT DG allocation. Additionally, the optimized inclusion of multiple DG units significantly minimized the VD of the DPNs. The minimum VD of the 69-bus, 85-bus, and 118-bus test systems is reduced from 0.0908 p.u., 0.1297 p.u., and 0.1312 p.u. to 0.0174 p.u., 0.0384 p.u., and 0.0201 p.u., respectively, for the multiple PV unit allocations. Similarly, the minimum VDs of the 69-bus, 85-bus, and 118-bus radial DPNs are minimized to 0.0048 p.u., 0.0190 p.u., and 0.0093 p.u., respectively, following the multiple WT DG unit allocations. The simulation findings of the APLS-MALO integrated approach are related to the various optimization techniques. The comparative study reveals that the proposed integrated approach gives a more effective and efficient solution than ALO, BAT, ABC, and other optimization techniques. Finally, the simulation findings of the APLS-MALO integrated technique are verified via the calculation of conventional statistical metrics and the conduction of a non-parametric Wilcoxon test.

In this article, we discuss the qualitative analysis and develop an optimal control mechanism to study the dynamics of the novel coronavirus disease (2019-nCoV) transmission using an epidemiological model. With the help of a suitable mathematical model, health officials often can take positive measures to control the infection. To develop the model, we assume two disease transmission sources (humans and reservoirs) keeping in view the characteristics of novel coronavirus transmission. We formulate the model to study the temporal dynamics and determine an optimal control mechanism to minimize the infected population and control the spreading of the novel coronavirus disease propagation. In addition, to understand the significance of each model parameter, we compute the threshold quantity and perform the sensitivity analysis of the basic reproductive number. Based on the temporal dynamics of the model and sensitivity analysis of the threshold parameter, we develop a control mechanism to identify the best control policy for eradicating the disease. We then conduct numerical experiments using large-scale numerical simulations to validate the theoretical findings.

The current study focuses on analyzing the two-dimensional bioconvective flow of a Williamson fluid over a porous curved stretching surface, by considering homogeneous-heterogeneous reactions and Darcy Forchheimer effect. The investigation explores the thermal properties of the flow under the impact of several factors such as Joule heating, thermal radiation, and heat generation/absorption. The surface boundary conditions are thermally stratified with a perpendicular magnetic field applied to the surface. By employing suitable transformations, the momentum and energy equations are converted into a system of nonlinear ordinary differential equations, which are subsequently solved numerically via the BVP4C approach on MATLAB. The results are presented graphically and tabular form, which reveals that fluid velocity decreases with increasing porosity and Williamson parameters. Similarly, fluid temperature decreases with higher thermal Prandtl numbers and stratification parameters. Additionally, the microorganism profile increases with the curvature parameter, while it shows a declining trend when the Peclet number and bio-convection Lewis number are increased.

This work aimed to improve the phase change material (PCM) of latent heat energy storage systems (LHTESS) performance. Thermal energy is accumulated and stored in LHTESS during the phase transition from solid to liquid. The primary limitation of this system lies in the inadequate heat conductivity of the phase change material, which is employed to achieve equilibrium by balancing energy demand and supply. Various augmentation strategies are employed to address this challenge. This study employs the method of dispersing nanoparticles in pure Phase Change Material (PCM) to produce Nano-Enhanced Phase Change Material (NEPCM) and incorporates uniquely shaped fins to expedite the melting process. Subsequently, the impact of volume fractions on the melting rate is analysed, and a parallel investigation is conducted between nanoparticle dispersion and fin addition. This work presents novel fin configurations that draw inspiration from the crystal structure of trapezoidal longitudinal fins. The effects of adding fins to different structures on the performance of LHTESS have been examined, focusing on improving energy storage capacity and charging speed. The dispersion of nanoparticles in PCM and its effectiveness is further investigated. In summary, the results show that irrespective of the pattern of the fin on the energy storage chamber, the use of a fin demonstrates to be a better option to improve the charging process in LHTESS than using nanoparticle dispersion. As a result of these two attributes, a higher storage capacity for energy and a faster melting rate are observable. Also, adding an optimized longitudinal fin with PCM would significantly speed up the melting rate more than LHTESS with regular extended fins compared to optimized regular fins.

The Troposkein wind turbine (TWT) is analyzed and developed from its inception. Classic aerofoils are investigated for wind turbines because of their low sensitivity to Reynolds Number. This study aims to determine the most efficient design for a TWT by adjusting the blade profile, number of blades, and aerofoils. Three comprehensive investigations have demonstrated that aerofoils based on the National Advisory Committee for Aeronautics (NACA)-633108 have a higher energy extraction capacity compared to other surfaces. In addition to these enhancements, the “Hybrid Concept” utilizes piezo-electric patches and solar panels to enhance the generation of electricity from TWT. The TWT model requires the use of substantial hybrid energy extraction procedures for energy results with an average power of 2 kW. The hybrid energy extraction functions are structurally facilitated by the combination of S-glass fibre composite and GY-70-based carbon fibre composite. Therefore, the utilization of hybrid energy extraction renders TWT a highly effective energy harvester.

Numerical and response surface (RS) analysis of the thermal performance of prismatic battery- operated cell is performed cooled by the forced flow of air considering conjugate condition at the cell-fluid interface. At the battery-air interface, where the heat flow continuity and temperature condition exist, the combined heat transfer condition is examined. Control volume-based code is developed where the Navier-stokes equation is solved by SIMPLE algorithm. The numerical work is endorsed by the experimental work specified in the literature. The effects of bcc (conduction-convection parameter - 0.06 to 0.1), Ar (Aspect ratio 10 to 30), volumetric heat generation (Sq - 0.1 to 1.0), and Re (Reynolds number - 250 to 2000) are investigated. The effect of the parameters mentioned above on temperature distribution (TeDi) along the axial direction (AD) in the battery cell (BC) and transverse TeDi in the fluid channel is investigated. The variations in temperature gradient and maximum temperature (MT) difference for different Sq, bcc, Re, and Ar are illustrated. The RS methodology is employed to analyze the MT of the battery. The MT difference obtained with increasing Sq and Re is quite significant. The MT difference obtained with an increase in bcc and Re is much less and the same is negligible with Ar. Re below 500 and bcc below 0.06 will cause a greater increase in MT, which acts as lower limits. Similarly, Re above 1250 and zeta cc above 0.08 do not help in the reduction of MT. For Sq = 0.7 and above, the temperature crosses its maximum permissible limit of the battery cell. The RS model developed gives an accuracy of 97 %, close to the numerical values. The RS analysis of MT indicates that Sq is the most influential parameter.

ABSTRACT Standard distributions must be improved to enhance their capacity for data modeling because they do not inherently suit all sorts of data sets in an acceptable manner. Due to this lack of previous ones, we developed a novel model employing the entropy‐transformed function. We utilized the inverse Weibull model to function as the reference model to assess the applicability of the entropy transformation. The distribution, referred to as the “Entropy‐Transformed Inverse Weibull Distribution” (ETIWL), is derived by applying the entropy transformation to the inverse Weibull model. The proposed distribution's core characteristics have been taken into account. The maximum‐likelihood approach is used to estimate the parameters of the given distribution. Four real data sets are used in this study with the thorough simulation analysis to see whether the proposed distribution is superior.

Many Engineering applications use multi-jet systems, such as aircraft propulsion units and spacecraft. A complex aerodynamic flow field occurs when multiple jets are close to each other. This study experimentally examines the supersonic jets' mean flow field and mixing characteristics from one, two, and three different convergingdiverging nozzles placed in close vicinity. The cross-wire is used as a passive control technique to investigate the impact of the control on the flow field and the core length. The nozzle is designed for Mach number M = 1.5, with an inter-nozzle positioning equal to twofold the nozzle exit diameter. The typical contact procedure and the triple jet's growth are discussed using cross-sectional contour patterns and transverse pressure profiles. The effect of leading parallel jets on local flow field features, comprising shock wave structure, supersonic core, and jet spread, is observed by measuring pressure beside the jet axes. Similarly, the flow spread rate declines when the quantity of jet flow increases- this is mainly owed to a decrease in attuning; subsequently, the jet decays more slowly, and the core length decreases. Schlieren's pictures of triple, twin, and single jets reveal that the core of the supersonic jet varies in triple and twin jets compared to single jets.

This research investigates the intricate thermal dynamics of Maxwellian nanofluids interacting with a sloping, porous, and heat-conductive melting surface under the influence of magnetic fields. The thermal and hydrodynamic behavior of Maxwellian nanofluids plays a significant role in optimizing heat transfer applications in engineering and industrial processes. This study aims to examine the influence of buoyancy, bioconvection on the Falkner-Skan flow of Maxwellian nanofluids over a sloping, melting surface. The analysis assumes a porous and thermally conductive wedge surface subjected to a stable magnetic field and incorporates the effects of Brownian motion, thermophoresis, and gyrotactic microorganisms. To simplify the governing equations, similarity transformations are applied, converting the partial differential equations into a set of ordinary differential equations. The resulting equations are solved numerically using MATLAB's robust bvp4c solver, ensuring validation through comparison with existing literature. The study reveals that parameters such as the magnetic field strength, Deborah number, and melting surface characteristics significantly enhance flow behavior and boundary layer thickness, whereas parameters like Prandtl number and thermophoresis diminish temperature profiles. The findings underscore the critical interplay between magnetic and thermal parameters, providing insights for improving heat management in advanced technological systems. These results have practical implications for designing efficient thermal systems in industries ranging from chemical engineering to bio-nanomaterial production.

This study investigates the convection effects of adding non-Darcy porous media to open enclosures with diagonally placed hot baffles near the open ports. The cold wall is fixed at the right side of the cavity. The remaining sidewalls are adiabatic. The fluid enters the enclosure from the inlet in the left vertical wall and leaves from an outlet at the right vertical wall. The finite difference method is employed to discretize the governing equations. The problem is analyzed for various parameters, Rayleigh number (104 <= Ra <= 106), length of heating baffles (15%<= hb <= 35%), porosity of the porous medium (0.4 <=& varepsilon;<= 0.8), Reynolds number (10 <= Re <= 100) and Darcy number (10-4 <= Da <= 10-2) at alternate configured vented cavities and the results are illustrated graphically. The observation shows maximum heat transfer attained at BT open enclosure regardless of various parameters. For Ra=106, considerable increase in the heat transfer occurs at the right sidewall when the porosity of porous medium increases. The impact of configurations on heat transfer along the right wall is negligible at low Reynolds numbers but becomes significant at high Reynolds numbers.