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Abstract Variable viscosity, activation energy and microgravity effects on Darcy nanofluid for the thermal performance improvement in thermal energy storage systems through stretching flat plate solar collector is the focus of this research. Thermal energy storage (TES) can be improved though solar collectors, phase change materials and photovoltaic cells using nanofluid in the base liquid. To increase the reaction rate in nanoparticles, the activation energy and solar radiations are used for the efficiency of TES. The viscosity of nanofluid improves the heat and mass transmission. Due to solar radiations, nanofluid plays prominent role in TES applications such as heat exchangers, electronic cooling devices and solar power generation through solar plate collector. Solar energy based mathematical model is developed to execute the frequency of oscillating heat transfer in TES numerically. Primitive and Stokes coefficients are used for feasible programming. Finite difference analysis is performed to display oscillatory thermal energy using Gaussian-elimination matrix scheme. Steady velocity, surface temperature and concentrations are plotted and utilized in oscillatory formula to perform oscillatory skin friction, oscillatory heat transfer and oscillatory mass transfer along π⁄4 angle. Fluid velocity enhances but temperature and concentration variation decreases as viscosity decreases. High amplitude in velocity, temperature and concentration is sketched as activation energy and microgravity increases. Steady heat and mass transmission enhances as thermophoretic and Brownian motion enhances. Amplitude and frequency of oscillations in heat transport, skin friction and mass transport enhances as Prandtl and Schmidt component enhances. In validation of results, the 0.00064% percentage error for heat transport and 0.00102% percentage error for mass transmission are deduced.

Abstract This study investigates the thermal behaviour of unsteady hybrid nanofluid flow on an infinite vertical plate. The investigation takes into account parameters such as magnetohydrodynamics and radiation effects, as well as the stratified medium. The systems of equations were solved by employing the explicit finite difference approach of Dufort-Frankel method. The main motivation of the study is to compare the performance of water, magnetic oxide, and multi-wall carbon nanotubes as working fluids. Additionally, velocity, temperature, and concentration outlines are visualized through plots, elucidating the fluid behaviour. Tables are provided for the Skin friction, Nusselt number, and Sherwood number, offering comprehensive insights crucial for optimizing performance in engineering applications ranging from thermal management systems to renewable energy technologies. The main finding of this study indicates that the quantitative result reveals that the temperature outline escalates among increasing values of radiation. In contrast, the outlines of a velocity and concentration show a decrease as the values of magnetohydrodynamics increase. In addition, multi-walled carbon nanotubes consume a larger outcome on temperature. A statistical study displays that the thermal stream rate of magnetic oxide-multi-wall carbon nanotubes-water increases from 1.7615 percentages to 7.4415 percentages, respectively, when the volume fraction of nanoparticles rises from 0.01 to 0.05. Future research is important to understanding hybrid nanofluid flows and their applications in thermal engineering systems such as energy systems, nuclear reactors, biomedical applications, electronics cooling, solar thermal systems, chemical processing, and other heat transfer applications where improved thermal performance is crucial.

Abstract The interplay of exchange rates among nations significantly influences both international and domestic trade, underscoring the pivotal role of the foreign exchange market (Forex) in a country's economic landscape. Forex fluctuations have a significant impact on the everyday lives of both government agencies and the public population, directly influencing a country's prosperity or misfortune. This work proposes an advanced fuzzy time series model that incorporates domain universe sub-partitioning, parameter adjustment optimization methodologies, and interval forecasting methods. We utilized this model to examine annual exchange rate patterns between the Pakistani rupee (PKR) and the US dollar (US$), comparing its forecast accuracy to that of other models. Our proposed methodology outperformed existing methodologies in terms of forecasting precision, providing stakeholders with valuable insights for making informed, data-driven business decisions that benefit both individual firms and the country overall.

Abstract The diabetes mellitus model (DMM) is explored in this study. Many health issues are caused by this disease. For this reason, the integer order DMM is converted into the time delayed fractional order model by fitting the fractional order Caputo differential operator and delay factor in the model. It is proved that the generalized model has the advantage of a unique solution for every time t. Moreover, every solution of the system is positive and bounded. Two equilibrium states of the fractional model are worked out i.e. disease free equilibrium state and the endemic equilibrium state. The risk factor indicator, R0 is computed for the system. The stability analysis is carried out for the underlying system at both the equilibrium states. The key role of R0 is investigated for the disease dynamics and stability of the system. The hybridized finite difference numerical method is formulated for obtaining the numerical solutions of the delayed fractional DMM. The physical features of the numerical method are examined. Simulated graphs are presented to assess the biological behavior of the numerical method. Lastly, the outcomes of the study are furnished in the conclusion section.

Abstract Within fluid mechanics, the flow of hybrid nanofluids over a stretching surface has been extensively researched due to their influence on the flow and heat transfer properties. Expanding on this concept by introducing porous media, the current study explore the flow and heat and mass transport characteristics of hybrid nanofluid. This investigation includes the effect of magnetohydrodynamic (MHD) with chemical reaction, thermal radiation, and slip effects. The nanoparticles, copper, and alumina are combined with water for the formation of a hybrid nanofluid. Using the self-similar method for the reduction of Partial differential equations (PDEs) to the system of Ordinary differential equations (ODEs). These nonlinear equation systems are solved numerically using the bvp4c (boundary value solver) technique. The effect of the different physical non-dimensional flow parameters on different flow profiles such as velocity, temperature, concentration, skin friction, Nusselt and mass transfer rate are depicted through graphs and tables. The velocity profiles diminish with the effect of magnetic and slip parameters. The temperature and concentration slip parameters reduce the temperature and concentration profile respectively. The higher values of magnetic factor lessened the skin friction coefficient for both slip and no-slip conditions. An elevation in the thermal slip parameter reduced the boundary layer thickness and the heat transfer from the surface to the fluid. The Nusselt number amplified with the climbing values of the radiation parameter. The mass transfer rate depressed with the solutal slip parameter. Comparison is made with the published work in the literature and there is excellent agreement between them.

Abstract The focus of present study is to incorporate the variable viscosity and temperature slip impact on heating rate and induced magnetic gradient along the moving non-conducting wedge under magnetic field. In industrial and engineering procedures, the impact of induced magnetization improves the efficiency of thermal systems to main the heating rates. The similarity transformations and stream functions are applied to reduce the governing equations into ordinary form. During this transformation, the pertinent parameters such as wedge parameter, moving parameter, Prandtl factor, viscosity parameter and temperature-slip parameter is obtained. These parameters play a prominent role on the physical values of fluid velocity, induced magnetic field and temperature distributions. The skin friction, Nusselt coefficient and induced magnetic gradient are incorporated through these parameters. The numerical values are executed by using the Keller box analysis with Newton–Raphson technique. It is depicted that the maximum slip in fluid velocity and temperature distribution is obtained for each values of thermal-slip parameter. It is noticed that maximum magnitude in induced magnetic field is reported for each wedge factor. The maximum velocity slip and temperature slip is observed for each choice of moving parameter. It is reported that the maximum variation in heating rate and induced magnetic gradient is obtained for magnetic force and viscosity parameter. The enhancing behavior of skin friction is observed for maximum values of Prandtl number.

In this paper, we study the boundedness of the commutator of the rough fractional Hausdorff operator on grand-variable-Herz-Morrey spaces when the symbol functions belong to bounded mean oscillations (BMO) space.

Abstract This research examines pseudoparabolic nonlinear Oskolkov-Benjamin-Bona-Mahony-Burgers (OBBMB) equation, widely applicable in fields like optical fiber, soil consolidation, thermodynamics, nonlinear networks, wave propagation, and fluid flow in rock discontinuities. Wave transformation and the generalized Kudryashov method is utilized to derive ordinary differential equations (ODE) and obtain analytical solutions, including bright, anti-kink, dark, and kink solitons. The system of ODE, has been then examined by means of bifurcation analysis at the equilibrium points taking parameter variation into account. Furthermore, in order to get insight into the influence of some external force perturbation theory has been employed. For this purpose, a variety of chaos detecting techniques, for instance poincaré diagram, time series profile, 3D phase portraits, multistability investigation, lyapounov exponents and bifurcation diagram are implemented to identify the quasi periodic and chaotic motions of the perturbed dynamical model. These techniques enabled to analyze how perturbed dynamical system behaves chaotically and departs from regular patterns. Moreover, it is observed that the underlying model is quite sensitivity, as it changing dramatically even with slight changes to the initial condition. The findings are intriguing, novel and theoretically useful in mathematical and physical models. These provide a valuable mechanism to scientists and researchers to investigate how these perturbations influence the system’s behavior and the extent to which it deviates from the unperturbed case.

The Phan–Thien–Tanner non-Newtonian model of fluid flow is considered to mathematically model the cilia governed flow inside human body. The collective action of cilia generates a rhythmic motion in form of metachronal wave travelling along the wall of channel. We used the necessary assumptions to non-dimensionalize this complex problem and exact solutions are obtained for the cilia governed flow problem. The graphical results are also incorporated to further discuss these solutions in detail. The wavy movements developed because of rhythmic actions of cilia are evident in pressure gradient graphs. Further, a parabolic flow pattern is also observed in this ciliated channel flow problem. Streamlines disclose the trapping phenomenon and the multiple pumping regions can be seen in intrigued pressure rise graphical solutions. Cilia-generated peristaltic flow is very important for mucus clearance in the respiratory tract, ovum transit in the reproductive system, nutrient digestion, fluid circulation in the brain, and pathogen removal in different tissues.

The significance of heat transfer during a reversible esterification process in a magnetohydrodynamic boundary layer Casson fluid flow along a vertical stretching plate is examined. The multi-slip conditions are considered in a porous medium. The presence of chemical process requiring an activation energy is considered in the analysis. The study also investigates the hydromagnetic boundary layer Casson fluid flow alongwith partial slip conditions across a vertical stretching plate. The incorporation of multi-slip constraints in a porous medium, alongside magnetic fields and other parameters, highlights its relevance in diverse engineering fields such as thermal engineering, polymerization, and biodiesel industries. Understanding the characteristics of such fluids under complex conditions is vital for optimizing heat and mass transfer in industrial applications, making this investigation timely and valuable. The nonlinear differential set of equations are solved numerically involving Runge-Kutta based shooting approach of fourth order and the results are verified with the bvp4c tool and the findings are explored using graphical plots. The predominance of significant factors on flow configurations are analyzed and presented in graphs and tables. A comprehensive analysis is provided on the effects on velocity, concentration, and temperature of diverse parameters such as reaction rate constant, magnetic parameter, suction parameter, mass Grashof number, Prandtl number, Casson parameter, thermal radiation parameter and slip parameters. The tabular representation of the adverse effects of drag coefficient, rate of mass transfer and Nusselt number on flow configurations for various significant parameters is presented. It is inferred that for the case of reversible and irreversible flows, the shear stress rate escalates by 29% when the magnetic parameter elevates from 0.5 to 1.5 and about 35% when the Casson parameter elevates from 0.5 to 1.5. For the suction parameter, the coefficient of drag increased by 27% and 26% for irreversible and reversible flows respectively. When the reaction rate increases from 0.5 to 1.5, the rate of shear stress elevates by 0.5% and 0.02% for irreversible and reversible flows in order. The Nusselt number decreased about 7% and 8% when the magnetic parameter and Casson parameter rises from 0.5 to 1.5 respectively, for irreversible and reversible flows. It is noteworthy that the previous studies are in precise agreement with the present investigation.

Obesity is a risk factor for several chronic diseases, including type 2 diabetes, heart disease, and high blood pressure. Developing models of obesity and its complications allows for close monitoring of these epidemics, informing the creation of effective control strategies. This research focuses on presenting an endemic model of obesity and its health complications, taking into account, social factors and relationships among people in society. The term epidemic is related to the influence of the health lifestyle of obese people on healthy individuals. The transmission of obesity and its complications is through peer pressure to consume fast food and acquire bad eating habits from relatives and friends. So, in our model, the effect of these factors is expressed with parameters [Formula: see text]. We demonstrate theoretically the asymptotic local stability of disease-free equilibrium and the asymptotic local stability of endemic equilibrium, proving the existence and uniqueness of the solution to the obesity model and its complications. To confirm the model's theoretical results, we conduct numerical simulations to study the impact of variation in social factor parameters on the diseases studied.

Vegetation concrete is increasingly being used for slope stabilization in highways, green roofing in urban developments, and erosion control in coastal areas due to its sustainable solutions for enhancing landscape aesthetics, mitigating pollution, and protecting the environment. However, the environmental and economic impacts of different mix proportions, particularly concerning CO2 emissions, remain insufficiently explored. This study aimed to identify the optimal mix proportions of vegetation concrete through laboratory testing that minimize CO2 emissions while ensuring compatibility with plant growth and cost-effectiveness. The vegetation concrete mix were prepared using different quantities of biochar (5 %, 10 %, and 15 %) and cement content (4 %, 8 %, and 12 %) by weight to evaluate their impact on porosity, unconfined compressive strength (UCS), alkalinity, plant compatibility, cost-effectiveness, and CO2 emissions from raw materials. The results indicate that increasing the biochar content from 0 % to 15 % led to a 16 % reduction in porosity and a 92 % increase in UCS of vegetation concrete. Similarly, increasing the cement content from 0 % to 12 % resulted in an 11 % decrease in porosity and a substantial 200 % increase in the UCS of vegetation concrete. Moreover, the addition of 5 % biochar had a beneficial effect on plant growth, however, increasing the biochar content beyond this level adversely impacted plant development. Based on laboratory test results, the recommended optimal mix for vegetation concrete includes a mix of 5 % biochar, 8 % low-alkaline sulfoaluminate cement, 6 % sawdust, and 6 % ferrous sulfate. The analysis of CO2 emission of the materials studied showed that cement contributed the most to CO2 emissions, followed by biochar, sawdust, water, and soil. Notably, the utilization of sulfoaluminate cement led to a 31.8 % reduction in CO2 emissions compared to Portland cement, while also lowering the overall cost of vegetation concrete by 24.7–33.8 %. This research underscores the necessity of scientifically establishing relationships between the composition of plant-based concretes and their environmental and economic performance. In summary, this study identifies optimal mix proportions for vegetation concrete, leveraging low-alkaline sulfoaluminate cement and biochar to minimize CO2 emissions, enhance landscape aesthetics, and ensure compatibility with plant growth, thus emphasizing its potential as a sustainable and cost-effective construction material.

The article exposes the use of the Runge-Kutta Fehlberg method of order five, a rarely studied methodology, to address the complexity involved in solving fuzzy hybrid differential equations. The study focuses on evaluating the reliability and accuracy of this method in contrast to recognized procedures, providing a thorough analysis of its performance. The article assesses the effectiveness of the RK-Fehlberg scheme by comparing its results with exact solutions, using thorough analysis and well-supported examples. This comparison analysis highlights the potential of the method to provide more accuracy compared to classic methods like Euler, improved, or modified schemes. The article demonstrates the strength and effectiveness of the method by using numerical examples. This not only helps improve computational techniques for solving fuzzy hybrid systems but also highlights the wide range of applications and reliability of the Runge–Kutta Fehlberg method in mathematical modeling and analysis.

The current research explores the useful impact of artificial neural networks (ANN) back-propagation along Levenberg-Marquardt Method (ANN-BLMM), for findng the influence of dimensionless numbers on the flow distribution pertaining magnetohydrodynamics (MHD) Jeffery–Hamel fluid amid two plates which are enclined at angles 2α. We have employed a numerical approach, ANN-BLMM to assess various aspects of our data, including testing, training, validation, Mean Square Errors (MSE), performance, and fitting. The methodology being used has been tested and validated through comparison with other results obtain numerically, showing extreme level of accuracy. Moreover, we have confirmed our findings through error histograms and regression tests. We used OHAM for the data set. Furthermore, we have also explored the influence of Reynolds number (R) on both flow and pressure distribution, visually representing our findings through graphical analysis. We have discussed about the nature and variations of velocity profiles within MHD Jefery–Hamel flow (MHDJHF), taking into account various values of Ha and Re in both convergent and divergent channels. It was discovered that a significant stabilizing influence of an increase in the magnetic field intensity was observed for both diverging and converging channel geometries and as the Hartman numbers rise, so does the fluid velocity. The absolute error is reduced to 10–2 to 10–6.

This work aims to study heat transfer analysis in a squeezing flow problem of nanofluid. The flow between pistons and nozzles in an automobile engine is one industrial application where the knowledge of the squeezing flow plays a crucial role. The applied magnetic field has a longitudinal inclined angle that ranges from zero to ninety degrees. In addition, viscous dissipation, chemical reaction, and suction injection are taken into consideration. Graphene nanoparticles with transformer oil are considered for Tiwari-Das Model. The transformed system of nonlinear ODEs is solved using the differential transform method. The numerical findings of the skin friction coefficient, the Nusselt and the Sherwood numbers are assessed with previously available works for accuracy. The graphical findings for relevant parameters of all profiles are analyzed. It becomes apparent that the velocity and heat transfer in compressing flows are significantly influenced by the angle of the inclination of the magnetic field. The temperature of the nanofluid and the rate of the heat transfer are both improved in the existence of the viscous-dissipation and thermophoresis. The findings show that the temperature rises with increased Prandtl and Eckert numbers. Furthermore, when Brownian movements of nanoparticles take place, the rate of mass transfer decreases.

Abstract Toxoplasma infection in humans is considered due to direct contact with infected cats. Toxoplasma infection (an endemic disease) has the potential to affect various organs and systems (brain, eyes, heart, lungs, liver, and lymph nodes). Bilinear incidence rate and constant population (birth rate is equal to death rate) are used in the literature to explain the dynamics of Toxoplasmosis disease transmission in humans and cats. The goal of this study is to consider the mathematical model of Toxoplasma disease with harmonic mean type incident rate and also consider that the population of humans and cats is not equal (birth rate and the death rate are not equal). In examining Toxoplasma transmission dynamics in humans and cats, harmonic mean incidence rates are better than bilinear incidence rates. The disease dynamics are first schematically illustrated, and then the law of mass action is applied to obtain nonlinear ordinary differential equations (ODEs). Analysis of the boundedness, positivity, and equilibrium points of the system has been analyzed. The reproduction number is calculated using the next-generation matrix technique. The stability of disease-free and endemic equilibrium are analyzed. Sensitivity analysis is also done for reproduction number. Numerical simulation shows that the infection is spread in the population when the contact rate $$\beta_{h}$$ β h and $$\beta_{c}$$ β c increases while the infection is reduced when the recovery rate $$\delta_{h}$$ δ h increases. This study investigates the impact of various optimal control strategies, such as vaccinations for the control of disease and the awareness of disease awareness, on the management of disease.

The dynamical behavior of the Lakshamanan-Porsezian-Daniel (LPD) model with applications in nonlinear optics is uncovered in this paper. The incorporation of spatio-temporal dispersion into the model, addressing the internet bottleneck issue, is emphasized. A planar dynamical system (DS) is accounted for by applying the Galilean transformation to the considered model. All types of phase portraits are plotted based on specific values of parameters. For the generation of quasi-periodic and chaotic patterns, Acos⁡(Ωτ) with strength and frequency components is added. The resulting quasi-periodic and chaotic orbits are also plotted. Various bifurcation and chaos detecting tools, such as time series analysis, Poincare maps, Lyapunov exponent, bifurcation diagrams, and sensitivity, are employed to examine the behavior of the obtained dynamical system under proposed initial conditions. The Hamiltonian function is calculated and plotted for the unperturbed dynamical system. Multi-stability phenomena demonstrate the coexistence of multi-stable orbits in their dynamic features. The dynamics of pulse propagation are found to be significantly impacted by the spatio-temporal dispersion.

Abstract Recent results demonstrate the dynamical peculiarities of the quantum chaos within the hybrid systems by chaotic parameters and probe the pattern formation under the influence of condensation. The complex dynamic behavior of the considered systems was determined with numerical simulation and presented an efficient technique that studied fractional systems comprising chaos-coherence fractions. The findings divulge the peculiar association between the coherence structure and the correlations at finite relative momenta. Thus the present study helps to explore the partially chaos hybrid systems in order to stimulate the experimental applications of nonlinear phenomena. The coherent-chaotic parameters can be measured by examining the chaos peculiarities that possess explicit relations with the condensations to demonstrate the environs of the physical systems. We investigate the influence of the multiplicities, chaos, momentum and temperature of the nonlinear system on the coherent-chaotic normalized correlations. The chaotic parameters are suppressed considerably with the coherence fraction and it appears numerically zero at maximum condensation and one at ideal chaos emissions. We procure that the meaningful parameters decrease significantly with the multiplicity of the nonlinear systems and increase with the momentum in the specified regimes. The identical multiplicity leads to contemplating the coherence and thus the normalized chaotic parameters within its spectacular influences exhibit significance worth contemplating in earnest. The findings underscore the significance of cogitating correlations in deciphering the nonlinear system characteristics and bestowing extraordinary perceptiveness into the convoluted essence of complex systems. The contemplated methodology can be applied to evaluating and analyzing the nonlinear systems and such an innovative approach computes the problems of celestial mechanics, heartbeats and chemical reactions in engineering and medical fields.

Microorganism motility holds significant importance in the realm of biomedical research. It contributes to the investigation of bacterial infections, microbial pathogenesis, and the formulation of strategies for combating antimicrobial resistance. Motile microorganisms embody a multifaceted and dynamic facet of microbial existence, exerting influence on ecosystems, human health, and advancements in technology. The significance of the current investigations is to develop a steady 3D computational model for the magnetic field hydrodynamics micropolar nanofluid along with the Buongiorno model which incorporates Brownian motion and thermophoretic diffusion effects to describe the heat transfer enhancement of micropolar nanofluid. The influence of thermal radiation on convective boundary conditions is also considered here. Similarity transformations are employed to convert an equation of motion into an ordinary differential equation. The final shape of ODEs is solved numerically with the aid of MATLAB software. Graphical results against convergence parameters like the influence of magnetic parameter, velocity ratio parameter, Prandtl number, micropolar parameter, porosity parameter thermophoretic number, Brownian motion, bio-convective Schmidt number, Peclet number thermal radiation parameter is demonstrated on velocity, temperature, concentration, motile and angular profiles. The default values of physical parameter used our analysis are: 0.2≤M≤0.5, 0.2≤λ≤0.6, 0.2≤K≤0.5, 0.0≤K1≤2.0, 1.0≤Sb≤1.4, 0.1≤σ≤0.9 0.1≤Nr≤0.9, 0.3≤Nt≤1.8, 1.5≤A≤3.5, 0.0≤B≤2.0; 0.0≤Nb≤2.0, 0.5≤γ≤2.5, 0.0≤S≤0.8, 1.0≤Sc≤1.8, 0.0≤D≤2.0, 0.1≤Pe≤0.5.The novelty of the present model is validated with the previously published data and found an excellent agreement. Our obtained results signifies that a rise in the mass and temperature convective parameter causes the velocity profile to grow, but a rise in the porosity and magnetic parameter causes it to decrease. The temperature profile increases with a rise in, thermophoretic parameter, and magnetic parameter, whereas it decreases with a rise in temperature exponent and Prandtl number. This research brings esteemed insights the micropolar nanofluids make them attractive options for a variety of uses in a range of sectors, such as manufacturing, energy, electronics, and healthcare.

Abstract This article establishes various fixed-point results and introduces the idea of an extended b-suprametric space. We also give several applications pertaining to the existence and uniqueness of the solution to the equations concerning RLC electric circuits. At the end of the article, a few open questions are posed concerning the distortion of Chua’s circuit and the formulation of the Lagrangian for Chua’s circuit.

Abstract Most of the countries in the world are affected by the coronavirus epidemic that put people in danger, with many infected cases and deaths. The crowding factor plays a significant role in the transmission of coronavirus disease. On the other hand, the vaccines of the covid-19 played a decisive role in the control of coronavirus infection. In this paper, a fractional order epidemic model (SIVR) of coronavirus disease is proposed by considering the effects of crowding and vaccination because the transmission of this infection is highly influenced by these two factors. The nonlinear incidence rate with the inclusion of these effects is a better approach to understand and analyse the dynamics of the model. The positivity and boundedness of the fractional order model is ensured by applying some standard results of Mittag Leffler function and Laplace transformation. The equilibrium points are described analytically. The existence and uniqueness of the non-integer order model is also confirmed by using results of the fixed-point theory. Stability analysis is carried out for the system at both the steady states by using Jacobian matrix theory, Routh–Hurwitz criterion and Volterra-type Lyapunov functions. Basic reproductive number is calculated by using next generation matrix. It is verified that disease-free equilibrium is locally asymptotically stable if $${R}_{0}1$$ R 0 > 1 . Moreover, the disease-free equilibrium is globally asymptotically stable if $${R}_{0}1$$ R 0 > 1 . The non-standard finite difference (NSFD) scheme is developed to approximate the solutions of the system. The simulated graphs are presented to show the key features of the NSFD approach. It is proved that non-standard finite difference approach preserves the positivity and boundedness properties of model. The simulated graphs show that the implementation of control strategies reduced the infected population and increase the recovered population. The impact of fractional order parameter $$\alpha$$ α is described by the graphical templates. The future trends of the virus transmission are predicted under some control measures. The current work will be a value addition in the literature. The article is closed by some useful concluding remarks.

Abstract The main goal of this study is to establish common fuzzy fixed points in the context of complete b-metric spaces for a pair of fuzzy mappings that satisfy F-contractions. To strengthen the validity of the derived results, non-trivial examples are provided to substantiate the conclusions. Moreover, prior discoveries have been drawn as logical extensions from pertinent literature. Our findings are further reinforced and integrated by the numerous implications that this technique has in the literature. Using fixed point techniques to approximate the solutions of differential and integral equations is very useful. Specifically, in order to enhance the validity of our findings, the existence result of the system of non-linear Fredholm integral equations of second-kind is incorporated as an application.

Motile microorganisms play a central role in ecosystems in both natural habitats and laboratory settings. Their contribution to nutrient cycling is crucial and their impact on human health can be significant. Furthermore, they are promising in various biotechnological applications. Ongoing studies of microbial motility represent a dynamic and evolving field of research with profound implications for our understanding of biology, ecology, and environmental science. The thermal properties of the base material are extremely advanced and enable a wide range of industrial, technical and process applications due to their thermal radiation, variable heat transfer properties and activation energy. Researchers are still working hard to find renewable energy sources that are both economical and environmentally friendly. In this regard, the past decade has seen growing interest in the potential of nanoparticles as renewable energy sources. The current study aimed to learn more about the rheological properties of thixotropic nanofluids on the surface of Riga surrounded by rotating bacteria. For this, theoretical investigations have been performed on 3D magneto-hydrodynamic micropolar-based Casson nanofluid on the surface of Riga surrounded by rotating bacteria. The influence of thermal radiation, activation energy and heat generation are considered in the present scenario. The rheology of Brownian motion, micro rotation and thermophoresis also accounted for. Classical equations of motion in the form of PDEs are transformed into ODEs by applying similarity variables. The converted ODEs are then solved with the help of a shooting algorithm using Bvp4c MATLAB software. From an engineering point of view, the impression of physical flow parameters dimensionless profiles is demonstrated graphically and in the form of tables. The outcomes show that enhancing the porosity parameter significantly reduces the velocity profiles while the opposite behaviour is noted for the viscoelastic parameter. Moreover, temperature and concentration fields are boosted by thermophoresis and concentration exponents. Present results are validated with the existing ones. The current study has the potential to improve the stability achieved by the bioconvection of nanomaterials.

Abstract Furin primarily localizes to the trans‐Golgi network (TGN), where it cleaves and activates a broad range of immature proproteins that play critical roles in cellular homeostasis, disease progression, and infection. Furin is retrieved from endosomes to the TGN after being phosphorylated, but it is still unclear how furin exits the TGN to initiate the post‐Golgi trafficking and how its activity is regulated in the TGN. Here three membrane‐associated RING‐CH finger (MARCHF) proteins (2, 8, 9) are identified as furin E3 ubiquitin ligases, which catalyze furin K33‐polyubiquitination. Polyubiquitination prevents furin from maturation by blocking its ectodomain cleavage inside cells but promotes its egress from the TGN and shedding. Further ubiquitin‐specific protease 32 (USP32) is identified as the furin deubiquitinase in the TGN that counteracts the MARCHF inhibitory activity on furin. Thus, the furin post‐Golgi trafficking is regulated by an interplay between polyubiquitination and phosphorylation. Polyubiquitination is required for furin anterograde transport but inhibits its proprotein convertase activity, and phosphorylation is required for furin retrograde transport to produce fully active furin inside cells.

The flow problem discussed in this research is an investigation of compressible viscous fluid in an unstable 2D MHD laminar driven vortex and stable boundary layer flow, passing a heated stretched sheet at varying speeds via a porous medium exposed to a magnetic field with viscous dissipation, thermal diffusion, thermal radiation, chemical reaction and Dufour effects. With the aid of similarity transformations, PDEs that come out in governing equations of this formulations are converted into non-linear sets of ODEs. Well-defined bvp4c technique used to numerically solve these converted equations. With use of various graphs, the consequences of different factors on the distributions of velocity, temperature and concentration were examined numerically and graphically. Physical parameters for this issue are also discussed.

A thermal case study on a non-Newtonian fluid flow field resulting from a moving surface under the combined influence of solutal and thermal stratifications in convective flow regimes is presented in the current attempt. A perpendicular magnetic beam and a non-uniform heat source/sink are the physical manifestations of the temperature flow regime. The physical problem is interpreted mathematically in terms of a non-linear coupled differential system. The eventual flow differential equations in this direction are non-linear and, hence, difficult to obtain the exact solutions. Here, the exact solutions of the reduced ordinary differential equations are developed in the form of confluent hypergeometric function for Jeffrey fluid flow. The surface quantities, namely wall temperature and concentration gradients, are assessed for several significant physical domains. It is observed that the thermal profile of Jeffrey fluid is enriched by the contributions of the elasticity of the fluid, while temperature stratification contributes to diminishing the temperature distribution in the flow domain. Further, the mass transfer rate at the surface is enriched with solutal stratification and the Schmidt number.

The Maxwell model of fluid flow in a rotating frame over a porous media is investigated in this paper. Binary chemical reactions and fluid movement under activation energy are both covered in this study. The impact of mass and heat transmission along the boundary layer is investigated in an equilibrium process. Using the method of similarity transformation, the controlling partial differential equations are changed into ordinary differential equations. The results are confirmed using the bvp4c Matlab built-in programme, and the altered equations are resolved utilizing a 4th order Runge Kutta based shooting method. Reversible and irreversible processes, activation energy, chemical reactions, Deborah numbers, and rotation parameters are some of the parameters for which the results are offered in tables and graphs. The prior objective of this study is to examine the impact of activation energy and chemical reactions on Maxwell fluid flow in an equilibrium setting. The concentration boundary layer for reversible flows is significantly finer than that of irreversible flows with the influence of activation energy, chemical reaction, and rotation factors. A reduced boundary layer thickness can improve the rates of heat and mass transmission in tremendous applications, such as exchangers of heat and chemical reactors. In this chemical process, sulphuric acid is utilized as a catalyst along with Maxwell fluid which affects the boundary layer reaction rate and selectivity. This is crucial for efficient catalytic process design. Controlling reaction rates using fluid elasticity and reaction kinetics is useful in operations that need accurate product production.

The current investigation formulated an efficient computing technique by incorporating the algorithm of Artificial Neural Network Levenberg Marquardt Method (ANNLMM) to approximate Soret and Dufour effects on Magnetohydrodynamic squeezing flow of Jeffrey fluid (MHDSFJF) in MATLAB environment. Due to its efficiency and flexibility, the applied neural network model can accurately predict the output results. In the ANNLMM, 80% of the data is used for training and 10% is set for both the testing and validation processes. The flow under consideration is mathematically formulated with the help of Navier Stokes Equations. The partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) by similarity variables. The effects of the physical parameters are discussed briefly. When the Hartmann number and Jeffrey fluid parameter increase, the concentration, temperature, and velocity profiles decreases. The temperature profile and heat transfer rate are improved by the effects of joule dissipation, Dufour numbers, and heat generation/absorption. On the other hand, as thermal radiation rises, the temperature profile decreases and the heat transfer rate increases. With an augment in Soret number, the mass transfer rate increases and the concentration profile slows down. Additionally, increasing chemical reactions, the mass transfer rate increases, but in convective chemical reactions, the contradiction is observed.

This study investigates the dynamic behavior of a two-phase dusty fluid under isothermal heating conditions, with implications for physiological fluid dynamics. The fluid, modeled as blood in contrast to a Casson fluid, flows within a channel formed by two inclined plates. One plate experience arbitrary wall shear stress, while the other undergoes oscillations. Magnetic field and porous medium effects are considered. Initially formulated as partial differential equations (PDEs), the problem is transformed into ordinary differential equations (ODEs) using similarity transformations. Analytical solutions for fluid velocity, dust particle velocity, and fluid temperature are obtained through the application of the Poincaré–Lighthill Perturbation Technique (PLPT). These solutions provide quantitative insights into the system's behavior. The numerical results are computed and graphically represented for various embedded parameters using Mathcad-15 software. The plots are prepared for velocity and temperature whereas the results for skin friction and Nusselt number are computed in tables. It is found from the results that skin friction increases with increasing inclination angle α=0,π6,π4. Here α=0 corresponds to the case of vertical channel. The results of Nusselt number indicated that with increasing Peclet number Pe = 5, 6, 7, the rate of heat transfer increases. The comparison between present work and published work is made and an excellent agreement is noted. This work can be extended in future for several other models of non-Newtonian fluids in different physical configurations.

Engineering technology is rapidly changing, and activation and binary chemical reactions have many uses in the fields of chemical engineering, processing food, and mobility and Geothermal reservoir, etc. Energy activation stimulates reactants with the least energy whenever a chemical transition occurs. The thermophysical features of viscoelastic fluids are based on internal energy change, which has been discussed for years. With this significance the current proposal focuses on the heat transfer process in reversible esterification reactions. The reversible chemical reaction and the activation energy with hydromagnetic movement of Casson fluid are considered. A complex multivariate partial differential equation set can be reduced to ordinary differential equations using appropriate variables. A numerical method is utilized to determine the solutions. In order to examine the outcomes of the concentration boundary layer utilizing the R-K-based shooting technique, the study primarily considers the reversible esterification process, which involves an ethanol-based reversible chemical reaction. Also, the bvp4c solver was employed to validate the results and appraise the precision of the R-K methodology. The temperature field, the momentum field, and the volumetric concentration of the esterification process are analysed in relation to a variety of numerical values. Graphical analysis considers the pertinent physical ramifications for temperature, velocity, and concentration contours. Explications that furnish a comprehension of the values accompany the tabular depictions of the heat transfer rate, local Sherwood number and skin friction. Reversible and irreversible flows differ considerably in the assessment of Sherwood number, local Nusselt number and rate of shear stress, when the inertial parameter, temperature difference parameter and activation energy are measured.

Abstact: Detailed investigation has been carried out to examine the behavior of squeezed fluid flow under the magnetic influence amid two infinitely extended disks arranged parallel to each other. Porosity is introduced in the lower disk to study the fluid flow characteristics. Applications in engineering and industrial processes, such as cooling systems and chemical reactors, where magnetic fields regulate fluid flow, need a thorough understanding of this phenomenon. The funamdental equations of Navier Stokes (N-S) Equations in the form of Partial Differential Equations (PDEs) are transformed into Ordinary Differential Equations (ODEs) with the help of similarity tranformation. For ensuring better accuracy MATLABs powerful tool is employed in the form of BVP4C technique, to compute the numerical solution. Fluid flow characteristics are discussed for the stated geometry. The velocity profile is discussed under variations of Non-dimensional parameters (Hartman Ha, Squeezed S, suction / injection A). Major findings of the current research revealed that the effect of the Hartmann Number on greatest value of velocity profile is more remarkable in the case of injection compared to suction. Moreover, Velocity profile exhibits a consistent increase as η rises in both scenarios without injection (A = 0) and with injection (A < 0). Current study opens new avenues in terms of exploration of fluid flow characteristics in context of simplicity, accuracy and verstality of numerical techniques.

The melting heat phenomenon in viscous nanofluid MHD flow over a stretching sheet with variable porosity and permeability was utilized. The behavior of magneto-viscous nanofluid flow was scrutinized using the concepts of machine learning and statistics. Thermal stratification, heat source, and activation energy in the solution of tween-20 nanoparticles and an ethyl-acetate base-type fluid are examined. Brownian and thermophoretic phenomena are included. Non-linear partial differential equations (PDEs) are converted into non-linear ordinary differential equations (ODEs) via von Karman similarity variables. Dataset is generated by the 4th-order Runge-Kutta numerical method for the artificial neural network. The ratio parameter and melting parameter enhance the velocity outline, while the melting parameter and thermal stratification parameter reduce the temperature outline. An increase in the concentration outline is seen with the activation energy parameter and Brownian motion parameter both increase the concentration outline. The system's performance using metrics like regression analysis, mean squared error, and error histograms is evaluated. The impact of these factors on significant results, such as the drag coefficient and heat transfer rate, is statistically investigated using multiple linear regressions. The integration of statistical and machine learning methods is deemed crucial for enhancing understanding of complex fluid dynamics in magnetic nanofluid flows.

Peristaltic movement of fluid flows has significant applications in biomedical engineering, medicine, human physiology, etc. Specifically, it is very useful to understand and cure the very common intestinal diseases in human beings. A number of theoretical and empirical models are used to analyze peristaltic movement. In this work, the peristaltic movement of nanofluid is modeled with a non-Newtonian Ellis fluid model in a curved channel with compliant wall properties. The effects of Brownian motion, thermophoresis, and nonlinear radiations are considered in the heat transfer for better thermal analysis. The mathematical modeling of the physical problem yields the nonlinear partial differential equations with boundary conditions. First, the governing partial differential equations are non-dimensionalized, and then the resultant system is simplified by using the assumptions of a small Reynolds number and long wavelength. Then the obtained boundary value problem of differential equations is solved with the built-in Mathematica command NDSolve. The accuracy and reliability of the adopted procedure are verified by comparing the computed results with the reported literature. The impacts of the pertinent parameters (Brownian motion, thermal radiation, mixed convection, and thermophoresis phenomenon) on thermal energy, velocity, concentration, heat transfer rate, and stress at the lower wall are analyzed both in qualitative and quantitative manners. This study revealed some interesting facts, such as the peristaltic-driven motion of nanoliquid is strongly influenced by wall properties (i.e., wall elasticity, mass density, and wall damping). In addition, the flow experienced more resistance in the case of larger wall damping, but larger wall elasticity and mass density provide favorable movement for fluid motion. In addition, mixed convection plays a vital role in heat transfer and nanoparticle concentration in the curved domain. In addition, the curved channel walls have a higher stress factor than straight-plane channels. The results of the current study are very useful to understand many biological phenomena, such as the peristaltic movement of liquid during dialysis, food movement through the intestine, etc.

This study aims to synthesize a ternary Fe3O4-NH2-APTES@rGO@SiO2 core–shell magnetic microspheres by modified Stöber technique to photodegrade aqueous phenol under UV-C light effectively. Results of the X-ray diffractogram of the as-synthesized Fe3O4-NH2-APTES@rGO@SiO2 core–shell magnetic microspheres showed the nanoparticles having an average size of 126.00 nm, comparable to 150.00 nm seen in the FESEM micrograph. These sizes were supported by the EDX and FTIR results which verified the presence of Fe3O4, rGO, and SiO2, and the TEM micrograph revealed them to be spherically shaped. Also, the thermally more stable microspheres than the pure individual components and binary nanocomposites were evident in their corresponding TGA thermograms.Similarly, the photoluminescence spectra of the Fe3O4-NH2-APTES@rGO@SiO2 microspheres supported their higher photodegrading ability as a consequence of an extended e-/h+ recombination rate. The microspheres were more effective in photo-catalytically degrading the highest amount of aqueous phenol (∼89 %) than Fe3O4-NH2-APTES@rGO (∼74 %), Fe3O4-NH2-APTES@SiO2 (∼78 %), and pure Fe3O4 (∼62 %), under an optimized condition of 0.2 g/350 mL catalyst loading and 50 ppm of initial phenol concentration. The enhanced photoactivity was ascribed to the high stability and specific surface of SiO2, the synergistic influence of Fe3O4, and the rGO sheet’s rapid electron transport·H2O2 enhanced phenol degradation to 94 %.

This research delves into Maxwell fluid flow's intricate fluid dynamics, as well as heat-mass transfer features over a porous horizontal plate. The investigation encompasses magnetohydrodynamics, heat generation, radiation, chemical reactions, and the influence of activation energy. Furthermore, the study integrates slip conditions for temperature, velocity, and concentration gradients at the interface between the fluid and solid surfaces. After formulating the governing equation with the abovementioned parameters, the partial differential equations are changed into ordinary ones through a similarity revolution. The results of the bvp4c solver in MATLAB provide significant insights into how various physical parameters interact and influence the flow dynamics and heat-mass transfer characteristics. This research's primary aim and objective is to comprehensively compare plots generated for different parameters under both no-slip and slip conditions by considering fixed values as Q = 0-0.3, Sc = 1–4, Ec = 0–1, Pr = 1–4, σ = 0–2, E = 0.1-0.7, λ = 0–2. The primary discoveries of this study indicate that with an increase in the power index, there is a decline in the concentration profile. In contrast, an increase in the activation energy leads to an elevation in this profile. An important revelation from this research is the significant decrease observed in the concentration profile as the activation energy parameter is raised.

This study delves into the intriguing interplay between activation energy, chemical reactions, no-slip effects, and radiation on the flow dynamics of a Maxwell fluid over a Riga plate nestled in a permeable medium. By initially formulating partial differential equations, which are then transformed into a set of ordinary differential equations using adept similarity transformations, we embark on a numerical journey aided by MATLAB. Unraveling the intricate tapestry of influences, we meticulously scrutinize the impact of activation energy, chemical reaction rates, no-slip parameters, and radiation on various flow characteristics. We explore the ramifications of velocity, energy distribution, skin friction, concentration profiles, and Nusselt number distributions through insightful plots. The essence of our findings reverberates throughout engineering and industrial domains, potentially reshaping practices and procedures. Our key revelations echo a narrative where heightened activation energy and adherence to no-slip conditions accentuate concentration profiles, contrasting the decrement induced by chemical reactions.

Abstract The impact of baffles on a convective heat transfer of a non-Newtonian fluid is experimentally studied within a square cavity. The non-Newtonian fluid is pumped into the cavity through the inlet and subsequently departs from the cavity via the outlet. Given the inherent non-linearity of the model, a numerical technique has been selected as the method for obtaining the outcomes. Primarily, the governing equations within the two-dimensional domain have been discretized using the finite element method. For approximating velocity and pressure, we have employed the reliable $${\mathbb{P}}_{2}$$ P 2 – $${\mathbb{P}}_{1}$$ P 1 finite element pair, while for temperature, we have opted for the quadratic basis. To enhance convergence speed and accuracy, we employ the powerful multigrid approach. This study investigates how key parameters like Richardson number (Ri), Reynolds number (Re), and baffle gap $${{\text{b}}}_{{\text{g}}}$$ b g influence heat transfer within a cavity comprising a non-Newtonian fluid. The baffle gap ( $${b}_{g}$$ b g ) has been systematically altered within the range of 0.2–0.6, and for this research, three distinct power law indices have been selected namely: 0.5, 1.0, and 1.5. The primary outcomes of the investigation are illustrated through velocity profiles, streamlines, and isotherm visualizations. Furthermore, the study includes the computation of the $${Nu}_{avg}$$ Nu avg (average Nusselt number) across a range of parameter values. As the Richardson number (Ri) increases, $${Nu}_{avg}$$ Nu avg also rises, indicating that an increase in Ri results in augmented average heat transfer. Making the space between the baffles wider makes heat flow more intense. This, in turn, heats up more fluid within the cavity.

Abstract As a first attempt, we obtain the boundedness of the rough fractional Hausdorff operator on variable exponent Herz-type spaces. The method used in this paper enables us to study the operator on some other function spaces with variable exponents.

Abstract The concept of graphical structures of extended suprametric space is introduced in this study and applied to supra-graphical contractive mapping. A recursive algorithm in connection with graphical notions can be employed in adaptive systems to construct a desired output function iteratively after specific conditions are first defined to ensure the existence of the solution by use of supra-graphical contractive mapping. After analyzing the historical context and relevant outcomes, we discuss the usage of graphical structures and supra-graphical contractive mappings in the conceptual frameworks of adaptive control and optimal control systems.

Abstract This article provides a comparison among the generalized Second Grade fluid flow described by three recently proposed fractional derivatives i.e. Atangana Baleanu fractional derivative in Caputo sense (ABC), Caputo Fabrizio (CF) and Constant Proportional-Caputo hybrid (CPC) fractional derivative. The heat mass transfer is observed during the flow past a vertical porous plate that is accelerated exponentially under the effects of the Magneto hydro dynamics. The effects of the heat generation and exponential heating in the temperature boundary layer and chemical reaction at the concentration boundary layer are also analyzed in this article. The flow model is described by three partial differential equations and the set of non-dimensional PDE’s is transformed into ODE’s by utilization of the integral transform technique (Laplace transform). For the better understanding of the rheological properties of the Second Grade fluid we used the CF, ABC and CPC operators to describe the memory effects. The analytical exact solution of the problem is obtained in the form of G-functions and Mittag Leffler functions. For the physical significance of flow parameters, different parameters are graphed. From this analysis it is concluded that the CPC is the most suitable operator to describe the memory effects.

Abstract SARS-CoV-2 and filovirus enter cells via the cell surface angiotensin-converting enzyme 2 (ACE2) or the late-endosome Niemann-Pick C1 (NPC1) as a receptor. Here, we screened 974 natural compounds and identified Tubeimosides I, II, and III as pan-coronavirus and filovirus entry inhibitors that target NPC1. Using in-silico, biochemical, and genomic approaches, we provide evidence that NPC1 also binds SARS-CoV-2 spike (S) protein on the receptor-binding domain (RBD), which is blocked by Tubeimosides. Importantly, NPC1 strongly promotes productive SARS-CoV-2 entry, which we propose is due to its influence on fusion in late endosomes. The Tubeimosides’ antiviral activity and NPC1 function are further confirmed by infection with SARS-CoV-2 variants of concern (VOC), SARS-CoV, and MERS-CoV. Thus, NPC1 is a critical entry co-factor for highly pathogenic human coronaviruses (HCoVs) in the late endosomes, and Tubeimosides hold promise as a new countermeasure for these HCoVs and filoviruses.

Considering the superior control characteristics and increased tuning flexibility of the Fractional-Order Proportional Integral Derivative (FOPID) controller than the conventional PID regulator, this article attempts to explore its application in the optimal design of the Automatic Voltage Regulator (AVR). Since FOPID has two additional tuning parameters (µ and ʎ) than its mentioned conventional counterpart, its tuning process is comparatively difficult. To overcome the stated issue, a self-regulated off-line optimal tuning method based on the Gradient-Based Optimization (GBO) algorithm is adopted in the current study. The optimal FOPID gains are obtained by minimizing the selected Fitness Function (FF) that is chosen as Integral Time Absolute Error (ITAE) in the current study. The simulations are performed using MATLAB/SIMULINK 2018a to test and compare the performance of the proposed GBO-based optimal AVR design based on the dynamic response, stability, and robustness evaluation metrics with some of the recently published metaheuristic optimization algorithm based optimal AVR designs in the literature. The results show that the proposed AVR design provides the most optimal dynamic response and enhanced stability among the considered AVR designs, thus proves its efficacy and essence.

Abstract Generation of fluid flow due to simultaneous occurrence of heat and mass diffusions caused by buoyancy differences is termed as double diffusion. Pervasive applications of such diffusion arise in numerous natural and scientific systems. This article investigates double diffusion in naturally convective flow of water-based fluid saturated in corrugated enclosure and containing hybrid nano particles composed of Copper (Cu) and Alumina (Al2O3). Impact of uniformly applied magnetic field is also accounted. To produce thermosolutal convective potential circular cylinder of constant radius is also adjusted by providing uniform temperature and concentration distributions. Finite element approach is capitalized to provide solution of utilized governing equations by utilizing Multiphysics COMSOL software. Wide-range of physical parameters are incorporated to depict their influence on associated distributions (velocity, temperature and concentration). Interesting physical quantities like Nusselt number, Sherwood numbers are also calculated against involved sundry parameters. It is note worthily observed that maximum strength of stream lines $${(\psi }_{max})$$ ( ψ max ) is 3.3 at $$\phi =0$$ ϕ = 0 and drops to 1.2 when $$\phi $$ ϕ is increased to 0.04. Furthermore, in the hydrodynamic case (Ha = 0), it is observed that the velocity field exhibits an increasing trend compared to the hydromagnetic case $$\left(Ha\ne 0\right),$$ H a ≠ 0 , which is proved from the attained values of stream-function i.e., $${|\psi |}_{max}=11$$ | ψ | max = 11 (in the absence of a magnetic field) and $${|\psi |}_{max}=3.5$$ | ψ | max = 3.5 (in the presence of a magnetic field). It is revealed from the statistics of Nusselt number that increase in volume fraction of nano particles from 0 to 0.4, heat flux coefficient upsurges up to 7% approximately. Since, present work includes novel physical aspects of thermosolutal diffusion generated due to induction of hybrid nanoparticles in water contained in corrugated enclosure, so this study will provide innovative thought to the researchers to conduct research in this direction.

An innovative technique to improve heat transmission is the use of nanofluids. Nanofluids have a significant thermal conductivity for better heat transport. For the thermal behavior of a porous polymer sheet, activation energy assessment is a useful technique for the advancement of the thermal properties of polymers. The governing model is developed for the numerical and physical analysis of heat transfer of porous polymer sheets. The present model is converted into a smooth format for the accuracy of results. The Keller box and Newton–Raphson approaches are used to calculate the thermal properties numerically. The novelty of this research is the depiction of the temperature distributions and heat transfer of chemically reacting thermophoretic nanomaterials along porous polymer stretching sheets. It is noted that the velocity and temperature of thermophoretic nanoparticles decreases and nanoparticle concentration increases as activation energy increases. It is noted that the velocity of nanoparticles increases and concentration decreases as the temperature difference increases. The enhanced heating transfer with maximum thermophoretic transportation was depicted under maximum reaction and activation energy. It is observed that the mass transfer of nanomaterials increases as the Brownian motion of thermophoretic nanomaterials enhances.

The objective of this research is to explore the mass and heat transmission characteristics of magnetohydrodynamic Powell-Eyring fluid through an absorptive flat surface, as the effects of mass diffusion and radiation. The validation process involves assessing the accuracy and reliability of the outcomes obtained from solving the ordinary differential equations derived from the governing partial differential equations using Lie symmetry scaling. Source parameters are integral to the validation process, ensuring the robustness and credibility of the obtained results. The percentage increase or decrease in these parameters is systematically analysed to understand their impact on the mass and heat transmission characteristics of the magnetohydrodynamic Powell-Eyring fluid. The validation also involves a comparison of the calculated quantities, such as heat transfer rate, skin friction factor, and mass transmission rate, against established theoretical expectations. This scrutiny ensures that the numerical solution, implemented through the Runge-Kutta Fehlberg method in MATLAB, aligns with the expected physical behaviour of the system under investigation. Furthermore, the presentation of results employs graphical representations and tabular formats (Graphs and Tables), facilitating a clear and concise visualization of the impact of varying physical constraints on flow characteristics.

In this work numerical solutions using finite difference method of hybrid nanofluids (TiO2–Cu/Water) over an inclined plate are obtained. The nanoparticles are taken of volume fraction of size less than or equal to 0.05. Heat and mass transfers are studied. Chemical reaction and viscous dissipation effect are also examined. The results are computed and plotted for various parameters such as radiation, chemical reactions, and magnetohydrodynamics. The results of skin friction, rate of heat and mass transfers are computed in tables for Prandtl number 6.2 which corresponds to water and discussed in details. The present results can be used for comparison in future research for other non-Newtonian fluids models.

Incised marine valleys (IVS) are hot topics in exploring the stratigraphic oil and gas-bearing plays. Multiple channelized sandstone lenses at varying depths [m], thicknesses [m], and porosities [%] constrain seismic impedance. The presence of hydrocarbon-bearing resources affects the seismic impedance (density (g/cc) and velocity (m/s)). Therefore, a quantitative prediction has been carried out for determining the thickness [m], porosity [%], and depths [m] of laterally distributed channelized sandstone lenses (SLS) for IVS, Indus offshore Basin (IOB), Pakistan, using 2-D instantaneous spectral porosity quantitative modelling (2DSSM), continuous wavelet transforms-based (CWT) 2-D instantaneous spectral density modelling (2DSSDM), and spectral decomposition tools. The 2DSSM remained limited in predicting the number of channelized sandstone lenses and their quantitative stratigraphic attributes. The 45-Hz-based processing of conventional 2DSSM has resolved the two channelized sandstone lenses of the stratigraphic trap. The deepest channelized sandstone lens has attained 1–6 m thickness with a lateral extent of 3 km, within the porosity range of 18–33 %. The highest confidence level for predicted petrophysical attributes such as 13 m-thick pay zones, −0.08, −0.067, and −0.07 acoustic impedances [g/c.c.*m/s], and 28 % porosities with R2 > 0.85 have validated interpretations. The response of 45-Hz CWT waveform-based inverted density and thickness simulations has predicted the highest thicknesses and lowest densities of reservoir sandstones within the meandering channel belt of the deepwater depositional system. The predicted densities and thicknesses for the coarse-grained sandstone lenses of point bars were 1.8–1.9 g/cc and 15 m, respectively. In the same way, the quantitative estimates of predicted density and simulated thickness have shown a strong coefficient correlation (R2 > 0.80), which confirms the presence of gas-bearing prospects within the IVS. The facies-controlled migration is thought to be the movement of the reservoir facies of the point bars and channelled sandstone-filled lenses to the side.

The process of drying agricultural products for food preservation is a difficult task that requires a significant amount of energy. The increasing cost and depletion of fossil fuels have led to the development of a food dryer that utilizes renewable energy sources. This research paper proposes the design and performance evaluation of an indirectly forced convection desiccant integrated solar dryer (IFCDISD) at the Solar Energy Research Lab at USPCAS-E, NUST Pakistan. Tomatoes were chosen as the test product due to their importance and widespread consumption. The drying process involves slicing the tomatoes and placing them on the IFCDISD rack, where a desiccant called calcium chloride (CaCl2) is integrated into the dryer. The experiments were conducted during both sunshine (SS) hours and Off-sunshine (OSS) hours. The IFCDISD operates using sunlight during SS hours and utilizes the absorbed heat of CaCl2 in OSS hours via a forced DC brushless fan powered by battery charged thro solar panel. The tomatoes were weighed before and after each drying mode, and the moisture removal was calculated. The results show that the dryer efficiency was 50.14 % on day 1, 66 % on day 2, and an overall efficiency of 58.07 %. The moisture content removal was 42.858 % on day 1, 22.9979 % on day 2, and an overall moisture content removal of 58.07 %. Moreover, the payback period is 5.1396 and the carbon mitigation was recorded as 2.0335, and the earned carbon credit was recorded as 11559.6.