Analytical investigation of Carreau fluid flow through a non-circular conduit with wavy wall.

Peristaltic flow through an elliptic channel has vital significance in different scientific and engineering applications. The peristaltic flow of Carreau fluid through a duct with an elliptical cross-section is investigated in this work . The proposed problem is defined mathematically in Cartesian coordinates by incorporating no-slip boundary conditions. The mathematical equations are solved in their dimensionless form under the approximation of long wavelength. The solution of the momentum equation is obtained by applying perturbation technique ([Formula: see text] as perturbation parameter) along with a polynomial solution. We introduce a new polynomial of twenty degrees to solve the energy equation. The solutions of mathematical equations are investigated deeply through graphical analysis. It is noted that non-Newtonian effects are dominant along the minor axis. It is found that flow velocity is higher in the channels having a high elliptical cross-section. It is observed from the streamlines that the flow is smooth in the mid-region, but they transform into contours towards the peristaltic moving wall of the elliptic duct.

The baffle shape effects on natural convection flow and entropy generation in a nanofluid-filled permeable container with a magnetic field.

Enhancing heat transfer rates within enclosures is a topic of considerable interest since it has several technical applications. Most heat transfer research projects focus on increasing the heat transfer rates of thermal systems since this will raise the systems' total efficiency. The geometry of the enclosure might have a substantial impact on heat transfer rates. This research studies quantitatively the natural convection of a nanofluid in a complicated form geometry with many baffle configurations. The system's governing equations were addressed by the Galerkin Finite Element Method (GFEM). The main consideration was given to the effects of the following factors: The Darcy number (Da), which ranges from 10-2 to 10-5; the Hartmann number (Ha), which ranges from 0 to 100; the volumetric fraction (ϕ), which ranges from 0 to 0.08, and the Rayleigh number (Ra) (102 to 106). The results suggested that raising Ra increases heat transfer discharge, whereas raising Ha and Da decreases it. In terms of heat transmission, case 1 (the case with a wavenumber of 1 and the zigzag pointing outward) is determined to be the optimum cavity structure, as it obtained the highest mean Nusselt (Nuavg) number when compared to other cases. At the highest studied Ra number, growing (ϕ) from 0 to 0.8 improved Nuavg by 25%, while growing Da from 10-2 to 10-5 and Ha from 0 to 100 declined Nuavg by 57% and 48%, respectively. The reason for the improvement in the values of the (Nu) is due to the speed of fluid movement within the compartment. Also, the shape of fins plays a major role in strengthening and weakening thermal activity.

Nanoencapsulated phase change material in a trapezoidal prism wall under the magnetic field effect for energy storage purposes.

Recently, Nano-encapsulated phase change materials (NEPCM) have attracted the attention of researchers due to their promising application in thermal management. This research investigates magnetohydrodynamic mixed convection of NEPCM contained within a lid-driven trapezoidal prism enclosure containing a hot-centered elliptical obstacle. The upper cavity wall is moving at a constant velocity; both inclined walls are cold, while the rest of the walls are insulated. The Galerkin Finite Element Method was used to solve the system's governing equations. The influence of Reynolds number (Re 1-500), Hartmann number (Ha = 0-100), NEPCM volumetric fraction φ (0-8%), and elliptical obstacle orientation α (0-3π/4) on thermal fields and flow patterns are introduced and analyzed. The results indicated that the maximum heat transfer rate is observed when the hot elliptic obstacle is oriented at 90°; an increment of 6% in the Nu number is obtained in this orientation compared to other orientations. Reducing Ha from 100 to 0 increased Nu by 14%. The Maximum value of the Bejan number was observed for the case of Ha = 0, α = 90° and φ = 0.08.

Ulam-Hyers stability of tuberculosis and COVID-19 co-infection model under Atangana-Baleanu fractal-fractional operator.

The intention of this work is to study a mathematical model for fractal-fractional tuberculosis and COVID-19 co-infection under the Atangana-Baleanu fractal-fractional operator. Firstly, we formulate the tuberculosis and COVID-19 co-infection model by considering the tuberculosis recovery individuals, the COVID-19 recovery individuals, and both disease recovery compartment in the proposed model. The fixed point approach is utilized to explore the existence and uniqueness of the solution in the suggested model. The stability analysis related to solve the Ulam-Hyers stability is also investigated. This paper is based on Lagrange's interpolation polynomial in the numerical scheme, which is validated through a specific case with a comparative numerical analysis for different values of the fractional and fractal orders.

Corrigendum: Numerical study of perforated obstacles effects on the performance of solar parabolic trough collector.

[This corrects the article DOI: 10.3389/fchem.2022.1089080.].

Mathematical analysis of nonlinear thermal radiation and nanoparticle aggregation on unsteady MHD flow of micropolar nanofluid over shrinking sheet.

Significance of study: Typical liquids aren't great for engineering because of their low heat conductivity. To enhance heat transfer capabilities in industries as diverse as computers, pharmaceuticals, and molten metals, researchers and scientists have developed nanofluids, which are composed of nanoparticles distributed in a base fluid. Aim of study: Mathematical modeling of micropolar C u - H 2 O nanofluid driven by a deformable sheet in the stagnation area with nanoparticle aggregation, thermal radiation, and the mass suction action has been investigated in this paper. In this case, copper ( C u ) nanoparticles make up the nanofluid. Method: ology: We have used suitable transformations to arrive at a system of nonlinear ODEs, which we then solve numerically in MATHEMATICA using Runge-Kutta methods of the fourth order coupled with shooting approaches. Findings: Tables and graphs are used to examine the effects of immersed flow and display profiles of physical parameters of interest. This includes velocities, temperatures, skin friction, and Nusselt numbers. The average heat transfer rate increased to 17 . 725 % as the volume percentage of copper nanoparticles in micropolar nanofluid increased from 0.0 to 0.01 . Additionally, the results showed that the local Nusselt number of the micropolar nanofluid increased along with an increase in the unsteady and radiation parameters. However, its value is reduced in an undeniable fashion if a material parameter is present. The impact of radiation on the aggregation of nanoparticles is compared and contrasted with the effects of a non-radiative scenario, and the resulting fluctuations in Nusselt numbers are provided in tables. When the results of this study were compared to data that had already been published about some cases, a lot of agreement was found.

Numerical analysis of magnetohydrodynamics Casson nanofluid flow with activation energy, Hall current and thermal radiation.

In this study we analyzed the flow, heat and mass transfer behavior of Casson nanofluid past an exponentially stretching surface under the impact of activation energy, Hall current, thermal radiation, heat source/sink, Brownian motion and thermophoresis. Transverse magnetic field with the assumption of small Reynolds number is implemented vertically. The governing partial nonlinear differential equations of the flow, heat and mass transfer are transformed into ordinary differential equations by using similarity transformation and solved numerically by using Matlab bvp4c package. The impact of each of the Hall current parameter, thermal radiation parameter, heat source/sink parameter, Brownian motion parameter, Prandtl number, thermophoresis parameter and magnetic parameter on velocity, concentration and temperature, is discussed through graphs. The skin friction coefficient along the x-and z-directions, the local Nusselt number and the Sherwood number are calculated numerically to look into the inside behavior of the emerging parameters. It is witnessed that the flow velocity is a diminishing function of the thermal radiation parameter and the behavior has observed in the case of Hall parameter. Moreover, mounting values of Brownian motion parameter reduce the nanoparticle concentration profile.

On the Bioconvective Aspect of Viscoelastic Micropolar Nanofluid Referring to Variable Thermal Conductivity and Thermo-Diffusion Characteristics.

The bioconvective flow of non-Newtonian fluid induced by a stretched surface under the aspects of combined magnetic and porous medium effects is the main focus of the current investigation. Unlike traditional aspects, here the viscoelastic behavior has been examined by a combination of both micropolar and second grade fluid. Further thermophoresis, Brownian motion and thermodiffusion aspects, along with variable thermal conductivity, have also been utilized for the boundary process. The solution of the nonlinear fundamental flow problem is figured out via convergent approach via Mathematica software. It is noted that this flow model is based on theoretical flow assumptions instead of any experimental data. The efficiency of the simulated solution has been determined by comparing with previously reported results. The engineering parameters' effects are computationally evaluated for some definite range.

Fuzzy Control Modeling to Optimize the Hardness and Geometry of Laser Cladded Fe-Based MG Single Track on Stainless Steel Substrate Prepared at Different Surface Roughness.

Metallic glass (MG) is a promising coating material developed to enhance the surface hardness of metallic substrates, with laser cladding having become popular to develop such coatings. MGs properties are affected by the laser cladding variables (laser power, scanning speed, spot size). Meanwhile, the substrate surface roughness significantly affects the geometry and hardness of the laser-cladded MG. In this research, Fe-based MG was laser-cladded on substrates with different surface roughness. For this purpose, the surfaces of the substrate were prepared for cladding using two methods: sandpaper polishing (SP) and sandblasting (SB), with two levels of grit size used for each method (SP150, SP240, SB40, SB100). The experiment showed that substrate surface roughness affected the geometry and hardness of laser-cladded Fe-based MG. To predict and optimize the geometry and hardness of laser-cladded Fe-based MG single tracks at different substrate surface roughness, a fuzzy logic control system (FLCS) was developed. The FLCS results indicate that it is an efficient tool to select the proper preparation technique of the substrate surface for higher clad hardness and maximum geometry to minimize the number of cladding tracks for full surface cladding.

Analysis of Nonlinear Convection-Radiation in Chemically Reactive Oldroyd-B Nanoliquid Configured by a Stretching Surface with Robin Conditions: Applications in Nano-Coating Manufacturing.

Motivated by emerging high-temperature manufacturing processes deploying nano-polymeric coatings, the present study investigates nonlinear thermally radiative Oldroyd-B viscoelastic nanoliquid stagnant-point flow from a heated vertical stretching permeable surface. Robin (mixed derivative) conditions were utilized in order to better represent coating fabrication conditions. The nanoliquid analysis was based on Buongiorno's two-component model, which features Brownian movement and thermophoretic attributes. Nonlinear buoyancy force and thermal radiation formulations are included. Chemical reactions (constructive and destructive) were also considered since coating synthesis often features reactive transport phenomena. An ordinary differential equation model was derived from the primitive partial differential boundary value problem using a similarity approach. The analytical solutions were achieved by employing a homotopy analysis scheme. The influence of the emerging dimensionless quantities on the transport characteristics was comprehensively explained using appropriate data. The obtained analytical outcomes were compared with the literature and good correlation was achieved. The computations show that the velocity profile was diminished with an increasing relaxation parameter, whereas it was enhanced when the retardation parameter was increased. A larger thermophoresis parameter induces an increase in temperature and concentration. The heat and mass transfer rates at the wall were increased with incremental increases in the temperature ratio and first order chemical reaction parameters, whereas contrary effects were observed for larger thermophoresis, fluid relaxation and Brownian motion parameters. The simulations can be applied to the stagnated nano-polymeric coating of micromachines, robotic components and sensors.

Thermal transport of biological base fluid with copper and iron oxide nanoparticles in wavy channel.

The nanoparticles are frequently used in biomedical science for the treatment of diseases like cancer and these nanoparticles are injected in blood which is transported in the cardiovascular system on the principle of peristalsis. This study elaborates the effects of Lorentz force and joule heating on the peristaltic flow of copper and iron oxide suspended blood based nanofluid in a complex wavy non-uniform curved channel. The Brinkman model is utilized for the temperature dependent viscosity and thermal conductivity. The problem is formulated using the fundamental laws in terms of coupled partial differential equations which are simplified using the creeping flow phenomenon. The graphical results for velocity, temperature, streamlines, and axial pressure are simulated numerically. The concluded observations deduce that the solid volume fraction of nanoparticles reduces the velocity and enhance the pressure gradient and accumulation of trapping bolus in the upper half of the curved channel is noticed for temperature dependent viscosity.

Nonlinear Thermal Diffusion and Radiative Stagnation Point Flow of Nanofluid with Viscous Dissipation and Slip Constrains: Keller Box Framework Applications to Micromachines.

The radiated flow of magnetized viscous fluid subject to the viscous dissipation phenomenon is numerically studied. The radiative phenomenon is addressed with nonlinear relations. Further, analysis is performed by using the slip effects and convective thermal flow constraints. The transformed problem is numerically evaluated using the Keller Box method. The physical parameter effects, such as the magnetic parameter for the velocity profile, Prandtl number, Brownian motion parameter and Biot number for the energy profile and Lewis number, and the thermophoresis parameter for the concentration profile are discussed. The obtained results suggest applications in enhancing the heat transfer phenomenon, thermal system, energy generation, heat transmission devices, power generation, chemical reactions, etc.

Partial differential equations modeling of thermal transportation in Casson nanofluid flow with arrhenius activation energy and irreversibility processes.

The formation of entropy in a mixed convection Casson nanofluid model with Arhenius activation energy is examined in this paper using magnetohydrodynamics (MHD). The expanding sheet, whose function of sheet velocity is nonlinear, confines the Casson nanofluid. The final equations, which are obtained from the first mathematical formulations, are solved using the MATLAB built-in solver bvp4c. Utilizing similarity conversion, ODEs are converted in their ultimate form. A number of graphs and tabulations are also provided to show the effects of important flow parameters on the results distribution. Slip parameter was shown to increase fluid temperature and decrease entropy formation. On the production of entropy, the Brinkman number and concentration gradient have opposing effects. In the presence of nanoparticles, the Eckert number effect's augmentation of fluid temperature is more significant. Furthermore, a satisfactory agreement is reached when the findings of the current study are compared to those of studies that have been published in the past.

Comprehensive examination of radiative electromagnetic flowing of nanofluids with viscous dissipation effect over a vertical accelerated plate.

This research aims to establish the MHD radiating convective nanofluid flow properties with the viscous dissipation across an exponentially accelerating vertical plate. As the plate accelerates, its temperature progressively increases. There are two separate types of water-based nanofluids that include copper ([Formula: see text]) and titanium dioxide ([Formula: see text]) nanoparticles, respectively. The most crucial aspect of this investigation is finding a closed-form solution to a nonlinear coupled partial differential equations scheme. Galerkin finite element method (G-FEM) is used to figure out the initial managing equations. Utilizing graphs, the effect of the flow phenomenon's contributing variables as well as the influence of other factors is determined and depicted. In the part dedicated to the findings and discussion, the properties of these emergent parameters are described in more depth. Nonetheless, the thermal radiation and heat sink factors increase the thermal profile. In addition, the greater density of the copper nanoparticles cause the nanoparticle volume fraction to lessen the velocity delineation.

2D MHD Mixed Convection in a Zigzag Trapezoidal Thermal Energy Storage System Using NEPCM.

In a magnetic field, two-dimensional (2D) mixed convection is investigated within a zigzagged trapezoidal chamber. The lower side of the trapezoidal chamber is irregular, in particular, a zigzagged wall with different zigzag numbers N. The fluid particles move in the room due to the motion of the upper wall, while the porosity-enthalpy approach represents the melting process. The thermal parameters of the fluid are enhanced by what is called a nano-encapsulated phase change material (NEPCM) consisting of polyurethane as the shell and a nonadecane as the core, while water is used as the base fluid. In order to treat the governing equations, the well-known Galerkin finite element method (GFEM) is applied. In addition, the heat transfer (HT) irreversibility and the fluid friction (FF) irreversibility are compared in terms of the average Bejan number. The main results show that the melt band curve behaves parabolically at smaller values of Reynolds number (Re) and larger values of Hartmann number (Ha). Moreover, minimizing the wave number is better in order to obtain a higher heat transfer rate.

Recent Development of Heat and Mass Transport in the Presence of Hall, Ion Slip and Thermo Diffusion in Radiative Second Grade Material: Application of Micromachines.

This article describes the incompressible two-dimensional heat and mass transfer of an electrically conducting second-grade fluid flow in a porous medium with Hall and ion slip effects, diffusion thermal effects, and radiation absorption effects. It is assumed that the fluid is a gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. It is assumed that the liquid is opaque and absorbs and emits radiation in a manner that does not result in scattering. It is considered an unsteady laminar MHD convective rotating flow of heat-producing or absorbing second-grade fluid across a semi-infinite vertical moving permeable surface. The profiles of velocity components, temperature distribution, and concentration are studied to apply the regular perturbation technique. These profiles are shown as graphs for various fluid and geometric parameters such as Hall and ion slip parameters, radiation absorption, diffusion thermo, Prandtl number, Schmidt number, and chemical reaction rate. On the other hand, the skin friction coefficient and the Nusselt number are determined by numerical evaluation and provided in tables. These tables are then analysed and debated for various values of the flow parameters that regulate it. It may be deduced that an increase in the parameters of radiation absorption, Hall, and ion slip over the fluid region increases the velocity produced. The resulting momentum continually grows to a very high level, with contributions from the thermal and solutal buoyancy forces. The temperature distribution may be more concentrated by raising both the heat source parameter and the quantity of radiation. When one of the parameters for the chemical reaction is increased, the whole fluid area will experience a fall in concentration. Skin friction may be decreased by manipulating the rotation parameter, but the Hall effect and ion slip effect can worsen it. When the parameter for the chemical reaction increases, there is a concomitant rise in the mass transfer rate.

Modeling and Mathematical Investigation of Blood-Based Flow of Compressible Rate Type Fluid with Compressibility Effects in a Microchannel.

In this investigation, the compressibility effects are visualized on the flow of non-Newtonian fluid, which obeys the stress-strain relationship of an upper convected Maxwell model in a microchannel. The fundamental laws of momentum and mass conservation are used to formulate the problem. The governing nonlinear partial differential equations are reduced to a set of ordinary differential equations and solved with the help of the regular perturbation method assuming the amplitude ratio (wave amplitude/half width of channel) as a flow parameter. The axial component of velocity and flow rate is computed through numerical integration. Graphical results for the mean velocity perturbation function, net flow and axial velocity have been presented and discussed. It is concluded that the net flow rate and Dwall increase in case of the linear Maxwell model, while they decrease in case of the convected Maxwell model. The compressibility parameter shows the opposite results for linear and upper convected Maxwell fluid.

Numerical Computation for Gyrotactic Microorganisms in MHD Radiative Eyring-Powell Nanomaterial Flow by a Static/Moving Wedge with Darcy-Forchheimer Relation.

The intention of this study is to carry out a numerical investigation of time-dependent magneto-hydro-dynamics (MHD) Eyring-Powell liquid by taking a moving/static wedge with Darcy-Forchheimer relation. Thermal radiation was taken into account for upcoming solar radiation, and the idea of bioconvection is also considered for regulating the unsystematic exertion of floating nanoparticles. The novel idea of this work was to stabilized nanoparticles through the bioconvection phenomena. Brownian motion and thermophoresis effects are combined in the most current revision of the nanofluid model. Fluid viscosity and thermal conductivity that depend on temperature are predominant. The extremely nonlinear system of equations comprising partial differential equations (PDEs) with the boundary conditions are converted into ordinary differential equations (ODEs) through an appropriate suitable approach. The reformed equations are then operated numerically with the use of the well-known Lobatto IIIa formula. The variations of different variables on velocity, concentration, temperature and motile microorganism graphs are discussed as well as force friction, the Nusselt, Sherwood, and the motile density organism numbers. It is observed that Forchheimer number Fr decline the velocity field in the case of static and moving wedge. Furthermore, the motile density profiles are deprecated by higher values of the bio convective Lewis number and Peclet number. Current results have been related to the literature indicated aforementioned and are found to be great achievement.