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These days, innovation in nanostructures, which are distinguished by their exploratory use in a variety of biological applications, is a result of the advancement of nanotechnology. Over the last few decades, advances in nanoscience, nanotechnology, and thermal engineering have culminated in the multidisciplinary topic of nanofluid technology. Novel features found in nanofluids have the potential to be applied in a wide range of fields, including biotechnology, information technology, food and agriculture, national security and defense, aerospace, the plastics and textile industries, energy and the environment, cosmetics, and health and medicine. In this analysis, energy and mass transport rate of nanoliquid with micro-rotation impacts have been discussed. Furthermore, Soret impact, radiations, and stagnation motion are discussed in detail. The boundary layer equations are converted into (ODE's) ordinary differential equations and elucidated the results numerically employing the Keller box technique. We established the enhancement in the temperature profile against the growth of thermal radiation parameter. Further, the increment in Soret factor presents concentration profile increases. The impact of Brownian motion on nanoparticles enhanced the temperature profile. This study will help to control the cooling process in industry and engineering applications. [ABSTRACT FROM AUTHOR]

The ferromagnetic flow of Maxwell nanoliquid past a stretching surface is the focus of this endeavor. The flow is modeled in a porous medium obeying Darcy's law and is also subjected to the effects of magnetic dipole, nonlinear radiative heat flux, and activation energy. Using proper transformation, the governing system of partial differential equations (PDEs) transforms into ordinary differential equations (ODEs). The solution process employs a shooting approach. For nanofluid concentration, temperature, velocity, skin fraction, Sherwood number, and Nusselt number, the effects of relevant non-dimensional flow parameters and numbers are explored. The results show that the porosity, elastic, and ferromagnetic parameters all reduce nanofluid velocity. The nanofluid temperature drops as the ferromagnetic and Prandtl numbers increase, while the nanofluid temperature rises to enhance the temperature ratio and radiative heat parameters. The nanofluid concentration profile rises due to the non-dimensional activation energy and falls as the Schmidt number increases. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

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 FROM AUTHOR]

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 FROM AUTHOR]

This study examines the flow dynamics and heat transfer characteristics of Maxwell fluid in a channel influenced by magnetohydrodynamics (MHD), Joule heating, thermal radiation, and boundary layer suction/blowing effects. The governing partial differential equations (PDEs) for momentum, energy, and concentration are transformed into ordinary differential equations (ODEs) using similarity transformations. The boundary value problem (BVP) is solved numerically using the bvp4c solver in MATLAB, yielding accurate solutions for velocity, temperature, and concentration profiles under various parameters. Key findings reveal that the porous parameter decreases the velocity profile but increases the temperature profile for both suction and blowing effects. Additionally, the MHD, Deborah, and Eckert numbers significantly influence the velocity and temperature profiles differently under these conditions. This study highlights the crucial role of integrating MHD, thermal, and boundary control effects to optimize performance and efficiency in engineering systems involving Maxwell fluids, with applications in polymer processing, biomedical engineering, electronics cooling, oil recovery, and chemical processing. [ABSTRACT FROM AUTHOR]

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 and endemic equilibrium is locally asymptotically stable if R 0 > 1 . Moreover, the disease-free equilibrium is globally asymptotically stable if R 0 < 1 and endemic equilibrium is globally asymptotically stable if 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 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 FROM AUTHOR]

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 FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We embarked on an investigation with potential implications for studying blood flow within the cardiovascular system; keeping this application in mind, this investigation aims to provide numerical evaluations for a complex problem involving MHD flow, chemical reactivity, and energy transfer of a Maxwell fluid within a channel. The governing equations for momentum, concentration, and energy are renovated into ODEs for concentrated analysis using a similarity transformation. Dimensionless velocity, temperature, and concentration fields corresponding to steady motions of Maxwell fluid over a channel are numerically recognized using the bvp4c inbuilt software in MATLAB. We validated our results with existing work to check the gained results and got an excellent agreement. The impression of physical parameters on fluid motion is plotted and debated. The quantitative outcome of this study is that the Deborah number surges, and both velocity and temperature experience enhancement while the concentration within the fluid diminishes. This knowledge can be applied to various fields, such as material processing, biomedical engineering, and environmental sciences, to optimize processes and design systems accordingly. The outcomes and key findings of this study indicate that concentration distribution declines with the introduction of a chemical reaction and a complex Schmidt number. Additionally, the quantitative results of this learning are that the impression of the magnetic parameter is observed, resulting in reduced velocity and temperature profiles, while concentration profiles exhibit an increase across the entire domain. Furthermore, the rise in the Reynolds number corresponds to an escalation in the temperature outline. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Combined effects of magnetic field and porous media on non-Newtonian fluid flow are investigated in this work. Here, sodium alginate (C6H9NaO7) is used as a counter-example to Casson fluid, which is regarded as a non-Newtonian fluid. The fluid (along a vertical plate) experiences quadratic translational motion. This work considers the natural or free convection phenomenon. Based on accurate initial and boundary conditions, the problem is initially represented in terms of linear partial differential equations. The Laplace transform method (LTM) is applied to solve the post-transformation problem, and precise solutions are established for temperature and fluid velocity in terms of special functions (error and complementary error functions). Entropy generation (EG) and Bejan number (BN) analytical results are established in the presence of MHD and porosity effects. Expressions are provided for both the skin friction coefficient and the rate of heat transfer. Numerical solutions and graphs are obtained using the finite difference approach. The results of the investigation demonstrated that MHD and porosity have a significant impact on not only the flow analysis but also EG and BN. With a higher Hartmann number, it is discovered that the magnitude of the EG is greater than the BN, but the BN is changed in a more powerful way. According to the porosity effect, entropy generation decreases as a medium becomes more porous, while the BN rises. [ABSTRACT FROM AUTHOR]

Alloys A A 7072 and A A 7075 are significant with thermal, physical, and mechanical characteristics; these are extensively used in manufacturing of spacecraft, aircraft parts. and bio nanoscience applications. The main interest of the present work is numerical and analytical investigation of heat transfer in MHD Jeffery-Hamel flow of a hybrid nanofluid with nanoparticle shapes (i.e., spherical, cylinder, and platelet) and mixture base fluid ( H 2 O - C 2 H 6 O 2 ( 50 % - 50 % )). Hybrid nanofluid containing alloys A A 7072 and A A 7075 as the nanoparticles is considered. The solution of the studied problem has been presented using a new analytical method (Daftardar-Jafari method). The obtained results in particular cases are compared to those gained by the HAM-based Mathematica package BVPh 2 and by the Runge–Kutta-Fehlberg 4th–5th order (RKF-45) for validation. The effect of diverse parameters for instance is as follows: external magnetic field H a ∈ 0 - 500 , Reynolds number R e ∈ 50 - 150 , opening of the channel α ∈ ± 2 ∘ - ± 6 ∘ , hybrid nanoparticles φ A A 7072 + A A 7075 ∈ 0 - 6 % , Hartmann number H a ∈ 0 - 150 , and nanoparticle shapes (i.e., spherical, cylinder, and platelet) on dimensionless velocity and temperature profiles, as well as on the behavior of skin friction coefficient and Nusselt number. The results indicate that the skin friction coefficient and Nusselt numbers decrease with the increasing nanoparticle shapes. In addition, the study's findings were found to be in exceptional agreement with existing literature results. [ABSTRACT FROM AUTHOR]

The utilization of viscoelastic fluid is prevalent in various industries such as medical sector, food, petrochemical, and polymer due to its ability to reduce turbulent drag, exhibit elastic turbulence, and other notable characteristics. This aspect has consistently captured the attention of researchers. In the present study, the aim is to report the results associated with the Couette flow of viscoelastic rotating dusty nanofluids between rotating porous plates. Furthermore, in the present study, transformer oil is used as a base fluid, because to its numerous applications in power engineering and industrial sciences. Transformers are one of the crucial elements that requires high-level condition monitoring to ensure continuous power supply. Therefore, an effort is made to improve the critical features of the transformer oil by suspending nanodiamond and aluminum oxide nanoparticles, because the creation of transformer oil with desirable dielectric and thermal properties is in high demand due to its essential role in development. The governing equations for the above flow regime is modeled and formulated in terms of partial differential equations. A definite method (Poincare Light-Hill technique) is then used to solve the non-dimensional partial differential equations. The impact of different parameters on the temperature and velocity profiles are shown graphically. Nusselt number and Skin friction are computed and tabulated. The nanofluid velocity is observed to decline with raising suction parameter and magnetic field. It is noteworthy that the transformer oil's heat transfer rate is improved by 27.58 % for A l 2 O 3 nanoparticles and 31.27 % for nanodiamond particles, when the A l 2 O 3 and nanodiamond nanoparticles volume fraction is raised from 0.01 to 0.04 . This study has a wide range of applications in industrial science and engineering. This study also provides that how the nanofluids are using as a cooling agent. [ABSTRACT FROM AUTHOR]

This research investigates on the heat transfer and flow characteristics of nanofluid and hybrid nanofluid over a melting stretching/shrinking surface. The present study is inspired by the impactful application of hybrid nanofluid in industrial processes such as casting and welding. Specifically, the behavior of water-based hybrid nanofluid containing alumina oxide and Cu nanoparticles is analyzed, while influences of magnetohydrodynamics and thermal radiation are considered. Employing the Keller Box method, the governing equations are numerically solved. A comparison between the hybrid and alumina oxide/water-based nanofluid is presented. Key parameters, including the melting, stretching/shrinking factors, magnetic influences, Nusselt number, and skin friction are examined and presented through graphical and tabular representations. The findings underscore the enhanced heat transfer efficiency exhibited by hybrid nanofluid relative to regular nanofluid. It is observed that the heat transfer rate decreases with an increase in the melting parameter and is inversely impacted by the stretching/shrinking parameters. This research provides insights into the heat transfer behaviors in hybrid and regular nanofluid across melting boundaries, useful for their practical applications. [ABSTRACT FROM AUTHOR]

The current research paper investigates analytical study of steady incompressible viscous two-dimension, couple stress boundary layer flow for hybrid nanofluids with the influence of viscous dissipation and thermal radiation. The three types of nanoparticles ( T i O 2 , A g , G O ) are considered and engine oil is taken as base fluid. We used the proper transformations to change a set of PDEs into nonlinear ODEs. The authors solved this set of equations using the homotopy analysis approach (HAM). The results are planned with the aid of graphs involving the magnetic field, nanoparticle volume concentration, couple stress parameter, Eckert number, thermal radiation parameter, and Prandtl number. The influence of various temperature and velocity parameters is intended. The structures of flow features, such as temperature and velocity profiles, are simulated and evaluated using a physical description in response to changes in developing factors. [ABSTRACT FROM AUTHOR]

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 β h and β c increases while the infection is reduced when the recovery rate 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

The investigation focused on a Maxwell fluid's convective double diffusive flow, considering the influences of chemical reaction radiation on a permeable moving horizontal plate. Factors like heat generation, Newtonian heating conditions, and the effect of MHD were also included in this study. The governing equations, presented as partial differential equations, are then transformed into ordinary differential equations (ODEs) via similarity transformation approach. MATLAB's built-in software, BVP4C, was considered to solve the resulting system of ODEs. The obtained solutions were presented as graphical representations illustrating the flow field, energy conservation, and concentration behaviours for different parameter combinations. The targeted parameter here is to be taken as a Newtonian heating condition on the boundary, so the critical discovery from this study is the increase in nondimensional temperature contour and Nusselt number profile as the Newtonian heating effect value increased. The Sherwood number profile rose as the chemical reaction effect value increased. We have rigorously validated our work by comparing it to existing research, and the results have demonstrated a remarkably high degree of alignment. Consequently, we can confidently assert that our code is accurate and effectively aligned with this field's existing body of knowledge. This validation process reinforces the reliability and validity of our work, underlining its robustness and correctness. [ABSTRACT FROM AUTHOR]

The current research paper investigates semi numerical study of steady incompressible viscous two-dimension, boundary layer flow for hybrid nanofluids with the influence of viscous dissipation and dynamic viscosity. The three types of nanoparticles ( T i O 2 , A g , G O ) are considered, and engine oil is taken as a base fluid. To convert a collection of PDEs to nonlinear ODEs, we applied appropriate transformations. The authors used the Homotopy analysis approach (HAM) to solve this set of equations. The influence of different parameters on temperature, and velocity is intended, and the results are planned with the help of graphs, involving the magnetic field, nanoparticle volume concentration, dynamic viscosity, Eckert's number, and Prandtl's number. From the current analysis, we see that the magnetic field, nanoparticle volume concentration, and dynamic viscosity are inversely related to the velocity field; similarly, the Prandtl number is inversely related to the temperature field, and the Eckert number is directly related to the temperature profile. A physical description is used to simulate and evaluate the structures of flow features such as temperature and velocity profiles in response to changes in developing factors. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

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 FROM AUTHOR]

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 (ψ max ) is 3.3 at ϕ = 0 and drops to 1.2 when 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 H a ≠ 0 , which is proved from the attained values of stream-function i.e., | ψ | max = 11 (in the absence of a magnetic field) and | 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. [ABSTRACT FROM AUTHOR]

This study is numerically executed to investigate the influence of heat generation or absorption on free convective flow and temperature transport within a wavy triangular enclosure filled by the nanofluid taking the Brownian effect of nanoparticles. The water (H2O) is employed as base fluid and copper (Cu) as nanoparticles for making effective Cu–H2O nanofluids. The perpendicular sinusoidally wavy wall is cooled at low temperature while the horizontal bottom sidewall is heated non-uniformly (sinusoidal). The inclined wall of the enclosure is insulated. The governing dimensionless non-linear PDEs are executed numerically with the help of the Galerkin weighted residual type finite element technique. The numerically simulated results are displayed through average Nusselt number, isothermal contours, and streamlines for the various model parameters such as Hartmann number, Rayleigh number, heat generation or absorption parameter, nanoparticles volume fraction, and undulation parameter. The outcomes illustrate that the temperature transport rate augments significantly for the enhancement of Rayleigh number as well as nanoparticles volume fraction whereas reduces for the increment of Hartman number. The heat transfer is significantly influenced by the size, shape, and Brownian motion of the nanoparticles. The rate of heat transport increases by 20.43% considering the Brownian effect for 1% nanoparticle volume. The thermal performance increases by 8.66% for the blade shape instead of the spherical shape of nanoparticles. In addition, heat transfer is impacted by the small size of nanoparticles. The thermal transport rate increases by 35.87% when the size of the nanoparticles reduces from 100 to 10 nm. Moreover, the rate of heat transmission increases efficiently as the undulation parameter rises. It is also seen that a crucial factor in the flow of nanofluids and heat transmission is the heat generation/absorption parameter that influences temperature distribution, heat transfer rates, and overall thermal performance. [ABSTRACT FROM AUTHOR]

The aim of present work is to apply the Caputo–Fabrizio fractional derivative in the constitutive equations of heat transfer. Natural convection flow of an unsteady second grade fluid over a vertical plate with exponential heating is discussed. The generalized Fourier law is substituted in temperature profile. A portion of the dimensionless factors are utilized to make the governing equations into dimensionless structures. The solutions for temperature and velocity profiles of Caputo–Fabrizio model are acquired through the Laplace transform method. These solutions are greatly affected through the variation of different dimensionless variables like Prandtl number, Grashof number, and second-grade fluid parameter. Finally, the influence of embedded parameters is shown by plotting graphs through Mathcad. From the graphical results it is concluded that, the temperature of the fluid decreases with the increasing values of the Prandtl number and Second grade fluid parameter and increases with the passage of time. The velocity of the fluid increases with increasing values of the Grashof number, second grade parameter and time while decreases with increasing values of fractional parameter and Prandtl number. [ABSTRACT FROM AUTHOR]

This present research article investigates the exact analytical solution for the mathematical model of the generalized Casson fluid flow by using the new fractional operator with Rabotnov exponential kernel i.e. Yang–Abdel–Cattani operator. The impacts of heat source, magnetic hydrodynamics and chemical reactions on the flow of fractional Casson fluid through a vertical flat plate are studied in this article. For the sake of a better interpretation of the rheological behavior of Casson fluid we have used the new operator of fractional order with exponential kernel of Rabotnov known as Yang–Abdel–Cattani operator of fractional derivative. By making use of the technique of Laplace transform we have find the exact analytical solution of the problem in the Mittag–Leffler's form, for all the three governing equations i.e. Velocity, energy and concentration equation. It has been noticed from the literature that it is challenging to obtain analytical results from fractional fluid model derived by the various fractional operators. This article helps to address this issue by providing analytical solutions for fractionalized fluid models. To analyze the physical importance of different fluid parameters such as Schmidt number, Prandtl number, MHD and alpha on the heat, mass and momentum class are presented through graphs. The concentration of the fluid decreases with Schmidth number and temperature of the fluid decreases with the increasing Prandtl number. The velocity of the fluid decreases with increasing MHD effects and increases with increasing Alpha. The Yang–Abdel–Cattani operator of fractional order can describe the memory effects more suitably than the other fractional operators. [ABSTRACT FROM AUTHOR]

The terms susceptibility, exposure, infectiousness, and recovered all have some inherent ambiguity because different population members have different susceptibility levels, exposure levels, infectiousness levels, and recovery patterns. This uncertainty becomes more pronounced when examining population subgroups characterized by distinct behaviors, cultural norms, and varying degrees of resilience across different age brackets, thereby introducing the possibility of fluctuations. There is a need for more accurate models that take into account the various levels of susceptibility, exposure, infectiousness, and recovery of the individuals. A fuzzy SEIR model of the dynamics of the measles disease is discussed in this article. The rates of disease transmission and recovery are treated as fuzzy sets. Three distinct numerical approaches, the forward Euler, fourth-order Runge-Kutta, and nonstandard finite difference (NSFD) are employed for the resolution of this fuzzy SEIR model. Next, the outcomes of the three methods are examined. The results of the simulation demonstrate that the NSFD method adeptly portrays convergent solutions across various time step sizes. Conversely, the conventional Euler and RK-4 methods only exhibit positivity and convergence solutions when handling smaller step sizes. Even when considering larger step sizes, the NSFD method maintains its consistency, showcasing its efficacy. This demonstrates the NSFD technique's superior reliability when compared to the other two methods, while maintaining all essential aspects of a continuous dynamical system. Additionally, the results from numerical and simulation studies offer solid proof that the suggested NSFD technique is a reliable and effective tool for controlling these kinds of dynamical systems.The convergence and consistency analysis of the NSFD method are also studied. [ABSTRACT FROM AUTHOR]

In this article, the ratio-dependent prey-predator system perturbed with time noise is numerically investigated. It relates to the population densities of the prey and predator in an ecological system. The initial prey-predator models only depend on the time and a couple of the differential equations. We are considering a model where the prey-predator interaction is influenced by both space and time and the need for a coupled nonlinear partial differential equation with the effect of the random behavior of the environment. The existence of the solutions is guaranteed by using Schauder's fixed point theorem. The computation of the underlying model is carried out by two schemes. The proposed stochastic forward Euler scheme is conditionally stable and consistent with the system of the equations. The proposed stochastic non-standard finite difference scheme is unconditionally stable and consistent with the system of the equations. The graphical behavior of a test problem for different values of the parameters is shown which depicts the efficacy of the schemes. Our numerical results will help the researchers to consider the effect of the noise on the prey-predator model. [ABSTRACT FROM AUTHOR]

This study focuses on investigating the energy and mass transfer characteristics of a hybrid nanofluid by comparing its performance with that of the base fluid using the finite difference method. Viscous dissipation, thermal radiation, Newtonian heating conditions, and radiation, along with MHD, are considered on the infinite vertical plate for framing the governing equations. The finite difference technique is employed to numerically solve the governing equations of heat transfer in a computational domain. The key goal of this research is to evaluate the effect of nanoparticle concentration, size, and thermal conductivity on the energy transfer characteristics of the hybrid nanofluid. To accomplish this, a comprehensive parametric analysis is conducted, considering various combinations of nanoparticle volume fractions, sizes, and thermal conductivities. The performance of the hybrid nanofluid is then compared to that of the base fluid to assess the potential enhancements in heat transfer. The solution of the study provides valuable insights into the heat transfer behavior of the hybrid nanofluid and its comparison with the base fluid. The findings demonstrate the impact of nanoparticle properties on energy transfer enhancement and reveal the optimum conditions for achieving improved thermal performance. Moreover, the study highlights the limitations and challenges associated with the use of hybrid nanofluids in practical applications, facilitating informed decision-making for their effective utilisation. [ABSTRACT FROM AUTHOR]

Advanced techniques are used to enhance the efficiency of the energy assets and maximize the appliance efficiency of the main resources. In this view, in this study, the focus is paid to the solar collector to cover thermal radiation through optimization and enhance the performance of the solar panel. Hybrid nanofluids (HNFs) consist of a base liquid glycol (C3H8O2) in which nanoparticles of copper (Cu) and aluminum oxide (Al2O3) are doped as fillers. The flow of the stagnation point is considered in the presence of the Riga plate. The state of the solar thermal system is termed viva stagnation to control the additional heating through the flow variation in the collector loop. The inclusion of entropy generation and Bejan number formation are primarily conceived under the influence of physical parameters for energy optimization. The computational analysis is carried out utilizing the control volume finite element method (CVFEM), and Runge–Kutta 4 (RK-4) methods. (FEATool Multiphysics) software has been used to find the solution through (CVFEM). The results are further validated through a machine learning neural networking procedure, wherein the heat transfer rate is greatly upgraded with a variation of the nanoparticle's volume fraction. We expect this improvement to progress the stability of heat transfer in the solar power system. [ABSTRACT FROM AUTHOR]

A lot of computational resources are required for time-dependent CFD simulations for the accurate prediction of the quantities of interest. To circumvent such difficulties, an artificial neural network (ANN) has been coupled with CFD simulations. Training and validation datasets have been generated by CFD and then are fed through ANN with optimal number of neurons and inner layers. A well-known benchmark problem for incompressible flows, namely, the flow around cylinder has been considered for the hybrid CFD network. The mathematical formulations are based on nonstationary Navier–Stokes equations incorporating the viscosity through power-law fluid constitutive model. The underlying ANN model consists of 3 input layers, 2 output layers, and 10 hidden layers. The network has been trained through one of the most efficient backpropagation algorithms, namely, Levenberg–Marquardt (LM) algorithm that provides second-order training speed. The obtained finite element results for drag and lift coefficients have been validated with the ANN predicted values through statistical measures represented by mean square error (MSE) and the coefficient of determination (R). For all cases, we have obtained a higher predictivity for drag coefficient C D and lift coefficient C L as MSE values approached zero and R values found to be close to unity. The agreement between the CFD results and the data predicted from ANN determined via the correlations is within less than ± 5% errors. It is concluded that ANNs may help to reduce the computing time and other resources required for time-dependent simulations. [ABSTRACT FROM AUTHOR]

Water plays a key role in the economic growth of an agricultural country. Pakistan is a farming country that uses almost 90% of its water resources for agriculture. Khyber Pakhtunkhwa (KPK) province of Pakistan has extensive surface water resources. In addition to using groundwater resources for irrigation, large parts of its flat plains are irrigated with the Kabul River surface water. Due to large population growth and unregulated small/local scale industries in the region, surface water quality deteriorates with time, which affects people's health when polluted surface water is used for irrigation purposes. This research investigates the surface water quality of Kabul River's different tributaries. It identifies the most critical and vulnerable locations regarding water quality using the weightage-based identification method and distance-based iteration method, respectively. The Bara River exhibited the most critical location, surpassing the threshold values by a considerable margin in at least seven water quality parameters. The maximum seven critical values determined against the Bara River using the weightage-based method, i.e., 17.5, 5.95, 7.35, 27.65, 1.75, 0.35, and 10.45 for total alkalinity, sodium, total hardness, magnesium, total suspended solids, biological oxygen demand (BOD), and turbidity. The Khairabad station, where the Kabul River meets the Indus River, was identified as vulnerable due to elevated levels of total suspended solids, hardness, sulfate, sodium, and magnesium using distance-based methods. The locations, i.e. Adezai, Jindi, Pabbi, and Warsak Dam, appeared critical and vulnerable due to the prevalence of small-scale industries on their bank and high population densities. All the results are finally compared with the interpolated values over the entire region using Kriging interpolation to identify critical and vulnerable areas accurately. The results from the distance and weightage-based methods aligned with the physical reality on the ground further validate the results. The critical and vulnerable locations required immediate attention and preventive measures to address the deteriorating water quality parameters by installing monitoring stations and treatment plants to stop further contamination of the particular parameter. [ABSTRACT FROM AUTHOR]

There are numerous contagious diseases caused by pathogenic microorganisms, including bacteria, viruses, fungi, and parasites, that have the propensity to culminate in fatal consequences. A communicable disease is an illness caused by a contagion agent or its toxins and spread directly or indirectly to a susceptible animal or human host by an infected person, animal, vector, or immaterial environment. Human immunodeficiency virus (HIV) infection, hepatitis A, B, and C, and measles are all examples of communicable diseases. Acquired immunodeficiency syndrome (AIDS) is a communicable disease caused by HIV infection that has become the most severe issue facing humanity. The research work in this paper is to numerically explore a mathematical model and demonstrate the dynamics of HIV/AIDS disease transmission using a continuous Galerkin–Petrov time discretization of a higher-order scheme, specifically the cGP(2)-scheme. Depict a graphical and tabular comparison between the outcomes of the mentioned scheme and those obtained through other classical schemes that exist in the literature. Further, a comparison is performed relative to the well-known fourth-order Ruge–Kutta (RK4) method with different step sizes. By contrast, the suggested approach provided more accurate results with a larger step size than RK4 with a smaller step size. After validation and confirmation of the suggested scheme and code, we implement the method to the extended model by introducing a treatment rate and show the impact of various non-linear source terms for the generation of new cells. We also determined the basic reproduction number and use the Routh-Hurwitz criterion to assess the stability of disease-free and unique endemic equilibrium states of the HIV model. [ABSTRACT FROM AUTHOR]

Better electrical insulation and thermal properties of vegetable oil with nanoparticles are crucial for its uses as a replacement for conventional previous lubricants used in heavy and light industries for cutting and machining. In this study, a magnetohydrodynamic (MHD) flow of a Brinkman-type nanofluid is used to investigate an infinite vertical plate with chemical reaction, heat radiation, and MHD flow. In order to improve the machining and cutting powers of regular vegetable oil, four distinct types of nanoparticles were selected to be the base fluid. The problem is modeled by coupled system partial differential equations (PDEs), and the results are generalized by the Caputo-Fabrizio fractional differential operator for the exponential non-singular kernel. In order to prepare nanofluids, four different types of nanoparticles, namely graphene oxide (GO), molybdenum disulfide (MoS2), titanium dioxide (TiO2), and aluminum oxide (Al2O3) are suspended separately in vegetable oil. The results of skin friction, the Nusselt number, and the Sherwood number are computed in various tables. It is found that GO nanoparticles, (followed by MoS2, TiO2, and Al2O3) are the materials that can heat transfer at the maximum rate. The heat transfer rate for GO is found to be the greatest with an enhancement up to 19.83% when 4% of nanoparticles are dispersed, followed by molybdenum disulfide at 16.96%, titanium dioxide at 16.25%, and alumina at 15.80%. [ABSTRACT FROM AUTHOR]

The thermophysical features of Casson fluid flow caused by a nonlinear permeable stretchable surface are assessed in the present study. The computational model of Casson fluid is used to define viscoelasticity, which is quantified rheologically in the momentum equation. Exothermic chemical reactions, heat absorption/generation, magnetic field and nonlinear volumetric thermal/mass expansion over the stretched surface are also considered. The proposed model equations are lessened by the similarity transformation to the dimensionless system of ODEs. The obtained set of differential equations are numerically computed through parametric continuation approach. The results are displayed and discussed via figures and tables. The outcomes of the proposed problem are compared to the existing literature and bvp4c package for the validity and accuracy purposes. It has been perceived that the energy and mass transition rate of Casson fluid increased with the flourishing trend of heat source parameter and chemical reaction respectively. Casson fluid velocity can be elevated by the rising effect of thermal, mass Grashof number and nonlinear thermal convection. [ABSTRACT FROM AUTHOR]

Heat transport in a 2D steady radiative boundary layer with Maxwell fluid flow and the influence of heat generation and MHD has been studied across a porous inclined vertical plate. Through similarity transformation, the mathematical modelling is converted to ODEs, and the built-in solver Bvp4c via MATLAB is used to solve. The linear movement of an inclined porous plate introduced the flow. The MHD (M), Prandtl number (Pr), radiation (Rd), Rayleigh number (Ra), local Nusselt number (Nux), angle of inclination (γ), and material relaxation time (β) have a considerable impact on the flow field as a result. The local Nusselt numbers and the skin friction coefficient are also given as numbers. The validation with the numerical solution is presented. The results are shown, and a thorough physical analysis has been done. The temperature of the fluid rises due to the greater electric field, increasing the heat transfer on the inclined plate. However, skin friction increases dramatically as the heat radiation parameter rises. The critical findings of this study are that the temperature profile increases and the velocity profile lower as the inclination angle increases. The Maxwell fluid parameter raises the velocity profile as well. [ABSTRACT FROM AUTHOR]

In the current analysis, we examine the heat transmission analysis of nanofluid (NF) movement impinging on a porous extending sheet. The influence of nonlinear thermal radiation (TR), buoyancy force, and slip at the boundary are also examined. The leading partial differential equations (PDEs) are altered to convectional differential equation (ODEs) by suitable transformation. The ODEs are then transformed to first order by introducing the innovative variables and elucidated numerically using bvph2. The Skin Friction (SF) and Nusselt number (NN) are elaborated in detail for Al2O3, Cu, and TiO2 nanoparticles. For validation of the code, ND-solve approach is also applied. The novelty of the current effort is inspect NF flow with heat transfer over extending sheet enclosing thermal and slip effect at the boundary numerically. The thickness of boundary layer increases as the temperature and radiation factors are increased. It is perceived that the fluid velocity decays with the growing values of volume fraction parameter. When permeability and velocity slip parameters are improved the velocity outline enhances. It is investigated that the temperature inside the fluid enhances as the values of velocity slip factor, permeability factor and Biot number are augmented. For the growing values of temperature ratio, volume friction, and thermophoresis factor the temperature is enhances. It is detected that the slip factor causes the friction factor to decrease. Furthermore, the existent study is associated with the preceding. [ABSTRACT FROM AUTHOR]

In this paper, we prove that any mean curvature flow translator Σ 2 ⊂ R 3 with finite total curvature and one end must be a plane. We also prove that if the translator Σ has multiple ends, they are asymptotic to a plane Π containing the direction of translation and can be written as graphs over Π . Finally, we determine that the ends of Σ are strongly asymptotic to Π and obtain quantitative estimates for their asymptotic behavior. [ABSTRACT FROM AUTHOR]

The aim of the present work is to apply the Caputo–Fabrizio fractional derivative to the heat transformation of unsteady incompressible second grade fluid. The effects of magneto hydro dynamic and radiation are analyzed. In governing equation of heat transfer nonlinear radiative heat is examined. Exponential heating phenomena is considered at boundary. Firstly, the dimensional governing equations with the initial & boundary conditions are converted into non-dimensional form. Exact analytical solutions are obtained for dimensionless fractional governing equations which consist of momentum and energy equations by using Laplace transform method. Special cases are investigated of the obtained solutions and it is noticed that some well-known results are achieved published in literature from these special cases. At the end, for graphical illustration the influences of different physical parameters like radiation, Prandtl, fractional parameter, Grashof numbers and Magneto hydro dynamic are checked graphically. [ABSTRACT FROM AUTHOR]

The present paper is dealt with a predator–prey model in which the growth of the prey population is influenced by the Allee effect while the predator species are contended with the prey population following the Crowley–Martin type response function. The proposed model is comprehensively analyzed in terms of stability and manifestation of bifurcation of the system. The system unveils the bi-stability together with the existence of a separatrix. In view of the eminence of spatial ecology, the dynamical complexity emanating from the induction of the Allee effect in prey species of a Crowley–Martin reaction–diffusion predator–prey model is also investigated profoundly. The results of numerical simulations reveal that the present system dynamics is motivated by both the Allee effect and diffusion-controlled pattern formation growth to hot spots, stripe-hot spot mixtures, stripes, labyrinthine, stripe-cold spot mixtures, and cold spots replication. The theoretical consequences of the spatiotemporal model under study are validated through numerical simulations. [ABSTRACT FROM AUTHOR]

Several scientists are interested in recent developments in nanotechnology and nanoscience. Grease is an essential component of many machines and engines because it helps keep them cool by reducing friction between their various elements. In sealed life applications including centralized lubrication systems, electrical motors, bearings, logging and mining machinery, truck wheel hubs, construction, landscaping, and gearboxes, greases are also utilized. Nanoparticles are added to convectional grease to improve its cooling and lubricating properties. More specifically, the current study goal is to investigate open channel flow while taking grease into account as a Maxwell fluid with MoS2 nanoparticles suspended in it. The Caputo-Fabrizio time-fractional derivative is used to convert the issue from a linked classical order PDE to a local fractional model. To determine the precise solutions for the velocity, temperature, and concentration distributions, two integral transform techniques the finite Fourier sine and the Laplace transform technique are jointly utilized. The resultant answers are physically explored and displayed using various graphs. It is important to note that the fractional model, which offers a variety of integral curves, more accurately depicts the flow behavior than the classical model. Skin friction, the Nusselt number, and the Sherwood number are engineering-related numbers that are quantitatively determined and displayed in tabular form. It is determined that adding MoS2 nanoparticles to grease causes a 19.1146% increase in heat transmission and a 2.5122% decrease in mass transfer. The results obtained in this work are compared with published literature for the accuracy purpose. [ABSTRACT FROM AUTHOR]

In this article, we developed a new higher-order implicit finite difference iterative scheme (FDIS) for the solution of the two dimension (2-D) time fractional Cable equation (FCE). In the new proposed FDIS, the time fractional and space derivatives are discretized using the Caputo fractional derivative and fourth-order implicit scheme, respectively. Moreover, the proposed scheme theoretical analysis (convergence and stability) is also discussed using the Fourier analysis method. Finally, some numerical test problems are presented to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this research article the heat transfer of generalized second grade fluid is investigated with heat generation. The fluid flow is analyzed under the effects of Magneto hydrodynamics over an infinite vertical flat plate. The Newtonian heating phenomenon has been adopted at the boundary. For this purpose the problem is divided into two compartments i.e. momentum equation and energy equations. Some specific dimensionless parameters are defined to convert the model equations into dimensionless system of equations. The solutions for dimensionless energy and momentum equations are obtained by using the Laplace transform technique. From obtained results by neglecting magneto hydrodynamic effects and heat source some special case are achieved which are already published in literature. The case for which the fractional parameter approaches to the classical order is also discussed and it has been observed that it is convergent. Finally, the influences of different physical parameters are sketched graphically. It has been observed that for increasing values of Prandtl number the velocity and temperature decreases, for increasing values of Grashof number the velocity of the fluid increases. Also it has been investigated that for increasing values of fractional parameter the velocity and temperature of the fluid increases. [ABSTRACT FROM AUTHOR]

Nanofluids are considered as smart fluids that can improve heat and mass transfer and have numerous applications in industry and engineering fields such as electronics, manufacturing, and biomedicine. For this reason, blood-based nanofluids with carbon nanotubes (CNTs) as nanoparticles in the presence of a magnetic field are discussed. The nanofluid traverses the porous medium. The nanofluids move on a vertical plate that can be moved. The free convection heat transfer mode is considered when the heat source and heat fluxes are constant. Convective flows are often used in engineering processes, especially in heat removal, such as geothermal and petroleum extraction, building construction, and so on. Heat transfer is used in chemical processing, power generation, automobile manufacturing, air conditioning, refrigeration, and computer technology, among others. Heat transfer fluids such as water, methanol, air and glycerine are used as heat exchange media because these fluids have low thermal conductivity compared to other metals. We have studied the effects of MHD on the heat and velocity of nanofluids keeping efficiency in mind. Laplace transform is used to solve the mathematical model. The velocity and temperature profiles of MHD flow with free convection of nanofluids were described using Nusselt number and skin friction coefficient. An accurate solution is obtained for both the velocity and temperature profiles. The graph shows the effects of the different parameters on the velocity and temperature profiles. The temperature profile improved with increasing estimates of the fraction parameter and the volume friction parameter. The velocity of the nanofluid is also a de-escalating function with the increasing values of the magnetic parameter and the porosity parameter. The thickness of the thermal boundary layer decreases with increasing values of the fractional parameter. [ABSTRACT FROM AUTHOR]

In this paper, we have been study a hybrid nanofluid over an exponentially oscillating vertical flat plate. Therefore the fractional derivatives definition of Caputo–Fabrizio approach is applied to transform the classical model for this hybrid nanofluid to fractional model. Together with an oscillating boundary motion, therefore the heat transfer is cause as a result of the buoyancy force produce due temperature differences between the plate and the fluid. The dimensionless classical model is generalized by transforming it to the time fractional model using Caputo–Fabrizio time fractional derivative. Exact analytical solutions are obtained by using Laplace transform method to the set of dimensionless fractional governing equations, containing the momentum and energy equations subjected to the boundary and initial conditions. Numerical computations and graphical illustrations are used to checked the results of the Caputo–Fabrizio time-fractional parameter, the second-grade parameter, the magnetic parameter and the Grashof numbers on the velocity field. An assessment for time spin-off is shown graphically of integer order versus fractional-order for these non-Newtonian hybrid nanofluid through Mathcad software. The fluid velocity increases for increasing the value of the fractional parameter, second-grade parameter and Grashof number. Also for increasing the values of the MHD parameter the fluid velocity decreases. [ABSTRACT FROM AUTHOR]

The process of thin films is commonly utilized to improve the surface characteristics of materials. A thin film helps to improve the absorption, depreciation, flexibility, lighting, transport, and electromagnetic efficiency of a bulk material medium. Thin-film treatment can be especially helpful in nanotechnology. As a result, the current study investigates the computational process of heat relocation analysis in a thin-film MHD flow embedded in hybrid nanoparticles, which combines the spherical copper and alumina dispersed in ethylene glycol as the conventional heat transfer Newtonian fluid model over a stretching sheet. Important elements such as thermophoresis and Brownian movement are used to explain the characteristics of heat and mass transfer analysis. Nonlinear higher differential equations (ODEs) were attained by transforming partial differential equations (PDEs) into governing equations when implementing the similarity transformation technique. The resulting nonlinear ODEs have been utilized by using the homotopy analysis method (HAM). The natures of the thin-film flow and heat transfer through the various values of the pertinent parameters: unsteadiness, nanoparticle volume fraction, thin-film thickness, magnetic interaction, and intensity suction/injection are deliberated. The approximate consequences for flow rate and temperature distributions and physical quantities in terms of local skin friction and Nusselt number were obtained and analyzed via graphs and tables. As a consequence, the suction has a more prodigious effect on the hybrid nanofluid than on the injection fluid for all the investigated parameters. It is worth acknowledging that the existence of the nanoparticles and MHD in the viscous hybrid nanofluid tends to enhance the temperature profile but decays the particle movement in the thin-film flow. It is perceived that the velocity and temperature fields decline with increasing unsteadiness, thin-film thickness, and suction/injection parameters. The novel part of the present work is to investigate the hybrid nanofluid including Cu–Al2O3 dispersed in Ethylene glycol as a base fluid in the presence of a magnetic field, which has not been investigated yet. So, in limiting cases the present work is validated with published work and found in excellent agreement as shown in Table 3. [ABSTRACT FROM AUTHOR]

The primary goal of this article is to analyze the oscillating behavior of Maxwell Nano-fluid with regard to heat and mass transfer. Due to high thermal conductivity of engine oil is taken as a base fluid and graphene Nano-particles are introduced in it. Coupled partial differential equations are used to model the governing equations. To evaluate the given differential equations, certain dimensionless factors and Laplace transformations are used. The analytical solution is obtained for temperature, concentration and velocity. The temperature and concentration gradient are also finds to analyze the rate of heat and mass transfer. As a special case, the solution for Newtonian fluid is discussed. Finally, the behaviors of various physical factors are studied graphically for both sine and cosine oscillation and give physical meanings to the parameters. [ABSTRACT FROM AUTHOR]

Gold nanoparticles are commonly used as a tracer in laboratories. They are biocompatible and can transport heat energy to tumor cells via a variety of clinical techniques. As cancer cells are tiny, properly sized nanoparticles were introduced into the circulation for invasion. As a result, gold nanoparticles are highly effective. Therefore, the current research investigates the magnetohydrodynamic free convection flow of Casson nanofluid in an inclined channel. The blood is considered as a base fluid, and gold nanoparticles are assumed to be uniformly dispersed in it. The above flow regime is formulated in terms of partial differential equations. The system of derived equations with imposed boundary conditions is non-dimensionalized using appropriate dimensionless variables. Fourier's and Fick's laws are used to fractionalize the classical dimensionless model. The Laplace and Fourier sine transformations with a new transformation are used for the closed-form solutions of the considered problem. Finally, the results are expressed in terms of a specific function known as the Mittag-Leffler function. Various figures and tables present the effect of various physical parameters on the achieved results. Graphical results conclude that the fractional Casson fluid model described a more realistic aspect of the fluid velocity profile, temperature, and concentration profile than the classical Casson fluid model. The heat transfer rate and Sherwood number are calculated and presented in tabular form. It is worth noting that increasing the volume percentage of gold nanoparticles from 0 to 0.04 percent resulted in an increase of up to 3.825% in the heat transfer rate. [ABSTRACT FROM AUTHOR]