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\nHIGHLIGHTSThe creation, utilisation, conversion, and exchange of thermal energy are all covered under the thermal engineering subject of heat transfer. Heat transfer plays a major role in engineering and industrial sectors like food packaging, food additive manufacturing, electronic cooling, microturbine, etc. Scientists across the world have tried to explore the impact of heat transfer on fluid past an expandable surface due to its exciting applications in industries like polymer production, paper production, crystal glass manufacturing, etc. This article has unique exploration, and it emphasises interpreting the Cross fluid flow along stretching surface with convective heat transport analysis by using the Lie group methodology. We investigated the implication of inclined upper-convected Maxwell fluid magnetohydrodynamic (MHD) movement through a penetrable strained plate. To solve nonlinear differential equations and clearly determine their absolute invariants, the Lie group approach is introduced. For the numerical solution of non-linear ordinary differential equations with boundary conditions, the fourth-order Runge–Kutta procedure with shelling performance is utilised. Plots showing the impacts of motivated and non-motivated MHD are researched and examined for the alterations of many parameters, and statistical graphs are given to explain the physical values. It is evident that opposing behaviour occurs in connection to temperature captivation and generation parameters together with motivated and non-motivated MHD. Under an amplified, heat-generating parameter and Deborah number, the rate of heat transmission increases. The Lie group investigation of Cross liquid in the presence/absence of inclined and non-inclined has not been investigated yet in the available literature.Some glimpses from the present research are given as follows: The problem of 2D Cross fluid motion subjected to a stretchable surface is discussed in detail.Inclined MHD and heat generation phenomena are considered.Lie group symmetry is utilised.The stretching sheet is considered.Shooting scheme is utilised for the numerical solution of modeled PDEs.The problem of 2D Cross fluid motion subjected to a stretchable surface is discussed in detail.Inclined MHD and heat generation phenomena are considered.Lie group symmetry is utilised.The stretching sheet is considered.Shooting scheme is utilised for the numerical solution of modeled PDEs. [ABSTRACT FROM AUTHOR]

In solar heating, ventilation, and air-conditioning (S-HVAC), communications are designed to create new 3D mathematical models that address the flow of Sutterby hybridization nanofluids rotating in front of slippery and expandable seats. The heat transfer investigation included effects such as copper (Cu) and aluminum alloys (AA7075) nanoparticles as well as thermal radiation. The activation energy and magneto effects were used to investigate mass transfer with fluid concentration. The limiting terms used were Maxwell's speed and Smoluchowksi's temperature slippage. With the use of fitting changes, numerically expressed partial differential equations (PDEs) strength, energy, and fixation can be reduced to ordinary differential equations (ODEs). To solve ODEs without dimensions, MATLAB's Keller box numerical technique was used. Copper–aluminum alloys/sodium alginate (Cu-AA7075/C6H9NaO7) is intended to address the performance analysis of the present study. Physical attributes, for example, surface drag coefficients, heat moves, and mass exchanges are mathematically processed and displayed as tables and figures when a variety of different factors differ. The field of temperature is increased by increasing the volume fraction of copper and graphene oxide nanoparticles, while the mass fraction field is increased by increasing the activation energy. When thermal radiative flowing upsurges by 55%, the heat transfer rate is boosted by 98% while the mass transfer rate is boosted by 86%. [ABSTRACT FROM AUTHOR]

Sun based energy is the chief source of heat from the sun, and it utilizes in photovoltaic cells, sun-based power plates, photovoltaic lights and sun-based hybrid nanofluids. Specialists are currently exploring the utilization of nanotechnology and sun-based radiation to further develop flight effectiveness. In this analysis, a hybrid nanofluid is moving over an expandable sheet. Analysts are presently exploring the utilization of nanotechnology and sunlight-based radiation to further develop avionics productivity. To explore the heat transfer rate phenomenon, a hybrid nanofluid stream is moving towards a trough having a parabolic type shape and is located inside of solar airplane wings. The expression used to depict the heat transfer phenomenon was sun based thermal radiation. Heat transfer proficiency of airplane wings is evaluated with the inclusion of distinguished effects like viscous dissipation, slanted magnetic field and solar-based thermal radiations. The Williamson hybrid nanofluid past an expandable sheet was read up for entropy generation. The energy and momentum expressions were solved numerically with the utilization of the Keller box approach. The nano solid particles, which are comprised of copper (Cu) and Graphene oxide, are dispersed utilizing SA (Sodium alginate) as an ordinary liquid (GO). A huge number of control factors, for example, temperature, shear stress, velocity, frictional element along with Nusselt number are investigated in detail. Intensification of thermal conduction, viscous dissipation and radiation improve the performance of airplane wings subjected to heat transmission. Hybrid nanofluid performance is much better than the ordinary nanofluid when it comes to heat transmission analysis. [ABSTRACT FROM AUTHOR]

Sun based energy is the chief source of heat from the sun, and it utilizes in photovoltaic cells, sun-based power plates, photovoltaic lights and sun-based hybrid nanofluids. Specialists are currently exploring the utilization of nanotechnology and sun-based radiation to further develop flight effectiveness. In this analysis, a hybrid nanofluid is moving over an expandable sheet. Analysts are presently exploring the utilization of nanotechnology and sunlight-based radiation to further develop avionics productivity. To explore the heat transfer rate phenomenon, a hybrid nanofluid stream is moving towards a trough having a parabolic type shape and is located inside of solar airplane wings. The expression used to depict the heat transfer phenomenon was sun based thermal radiation. Heat transfer proficiency of airplane wings is evaluated with the inclusion of distinguished effects like viscous dissipation, slanted magnetic field and solar-based thermal radiations. The Williamson hybrid nanofluid past an expandable sheet was read up for entropy generation. The energy and momentum expressions were solved numerically with the utilization of the Keller box approach. The nano solid particles, which are comprised of copper (Cu) and Graphene oxide, are dispersed utilizing SA (Sodium alginate) as an ordinary liquid (GO). A huge number of control factors, for example, temperature, shear stress, velocity, frictional element along with Nusselt number are investigated in detail. Intensification of thermal conduction, viscous dissipation and radiation improve the performance of airplane wings subjected to heat transmission. Hybrid nanofluid performance is much better than the ordinary nanofluid when it comes to heat transmission analysis. [ABSTRACT FROM AUTHOR]

In this research study, numerical and statistical explorations are accomplished to capture the flow features of the dynamics of ethylene glycol-based hybrid nanofluid flow over an exponentially stretchable sheet with velocity and thermal slip conditions. Physical insight of viscous dissipation, heat absorption and thermal radiation on the flow-field is scrutinized by dissolving the nanoparticles of molybdenum disulfide (MoS2) and graphene into ethylene glycol. The governing mathematical model is transformed into the system of similarity equations by utilizing the apt similarity variables. The numerical solution of resulting similarity equations with associated conditions are obtained employing three-stages Lobatto-IIIa-bvp4c-solver based on a finite difference scheme in MATLAB. The effects of emerging flow parameters on the flow-field are enumerated through various graphical and tabulated results. Additionally, to comprehend the connection between heat transport rate and emerging flow parameters, a quadratic regression approximation analysis on the numerical entities of local Nusselt numbers and skin friction coefficients is accomplished. The findings disclose that the suction and thermal radiation have an adverse influence on the skin friction coefficients and heat transport rate. Further, a slight augmentation in the thermal slip factor causes a considerable variation in the heat transport rate in comparison to the radiation effect. [ABSTRACT FROM AUTHOR]

Substantial efforts are underway to improve the recovery factor from existing oil reserves to meet the ever‐growing global oil demand. Surfactants are known to increase oil recovery through reducing interfacial tension (IFT) and/or altering the rock wettability. The selection of surfactants for high‐salinity high‐temperature oil fields is a challenging task owing to poor thermal stability, precipitation, and adsorption of surfactants on reservoir rocks. Sulfobetaine‐based polyoxyethylene zwitterionic surfactants have shown excellent thermal and surface properties. However, their solubility in high‐salinity brines becomes poor particularly with a long hydrophobic tail (>C17). Recently, we synthesized such types of surfactants by incorporating ethylene oxide (EO) units into the hydrophobic tail, which improved the solubility in formation water (213,734 ppm) and seawater (SW) (57,643 ppm). In this work, we investigated the IFT, thermal stability, rheological behavior, and foaming properties of two polyoxyethylene zwitterionic surfactants having different degrees of ethoxylation. Aging experiments exhibited excellent thermal stability and no change in the chemical structure was detected. The surfactant with lesser EO units (EASB‐1a) showed a lower IFT compared to the surfactant with higher EO units (EASB‐1b). Rheological studies revealed that the addition of both surfactants reduced the viscosity of the acrylamide copolymer. However, the effect of EASB‐1a was more prominent compared to that of EASB‐1b. The surfactant with a higher degree of ethoxylation showed lower adsorption compared to the surfactant with a lesser degree of ethoxylation. Both surfactants showed excellent foamability and foam stability compared to the commercial surfactants. Excellent thermal stability, water solubility under harsh reservoir conditions, foaming properties, and lower adsorption make them a suitable choice for high‐temperature, high‐salinity reservoirs. [ABSTRACT FROM AUTHOR]

The impact of thermal radiation on viscous dissipative boundary layer flow of heat absorbing magneto-nanofluid over a permeable exponentially stretching sheet with Navier's velocity and thermal slips has been analyzed. The prevailing mathematical equations are changed to nonlinear ordinary differential equations using the appropriate similarity variables and then the equations are numerically solved by Runge-Kutta scheme of fourth order together with the shooting technique. Three kinds of water based nanofluids having aluminum oxide, copper and titanium oxide as nanoparticles are considered for this investigation. The consequence of relevant flow parameters on nanofluid velocity, temperature distribution, wall velocity gradient and local Nusselt number are displayed by means of various graphs. In addition, analysis of quadratic regression estimation on the numerical data of coefficient of skin friction and local Nusselt number has been presented to verify the relationship among the controlling physical parameters and transfer rate parameters. Our result reveals that the velocity and temperature distribution profiles are lower for Cu-water nanofluid followed by Al2O3 and TiO2 water base nanofluids in the regime of boundary layer. The thermal radiation and viscous dissipation have tendency to augment the Cu-water temperature over the stretching sheet. [ABSTRACT FROM AUTHOR]

Abstract: High‐temperature/high‐salinity (HTHS) reservoirs contain a significant fraction of the world's remaining oil in place and are potential candidates for enhanced oil recovery (EOR). Selection of suitable surfactants for such reservoirs is a challenging task. In this work, two synthesized zwitterionic surfactants bearing a saturated and an unsaturated tail, namely 3‐(N‐stearamidopropyl‐N,N‐dimethyl ammonium) propanesulfonate and 3‐(N‐oleamidopropyl‐N,N‐dimethyl ammonium) propanesulfonate, respectively, were evaluated. The surfactant with the unsaturated tail showed excellent solubility in synthetic seawater (57,643 ppm) and in formation brine (213,734 ppm). However, the unsaturated surfactant with a saturated tail showed poor solubility, and therefore it was not evaluated further. The thermal stability of the synthesized unsaturated surfactant solution in seawater was evaluated by heating the solution at 90 °C in a sealed aging tube for 2 weeks. The thermal stability of the unsaturated surfactant was confirmed by FTIR and NMR analysis of the aged samples at such harsh conditions. The critical micelle concentration (CMC) of the synthesized unsaturated surfactant in seawater was 1.02 × 10−4 mol L−1, while the surface tension at CMC was 30 mN m−1. The synthesized unsaturated surfactant was able to reduce the oil–water interfacial tension to ~10−1 mN m−1 at different conditions. A commercial copolymer of acrylamide and 2‐acrylamido‐2‐methylpropane sulfonic acid (AM‐AMPS) was tested for EOR applications in HTHS conditions. The addition of the synthesized unsaturated surfactant to the AM‐AMPS copolymer increased the viscosity of the system. The increase in oil recovery by injecting the unsaturated surfactant solution and the surfactant–polymer mixture in solution was 8 and 21%, respectively. The excellent properties of the synthesized unsaturated surfactant show that surfactants with an unsaturated tail can be an excellent choice for HTHS reservoirs. [ABSTRACT FROM AUTHOR]

Objective. To compare the efficacy and cost-effectiveness of simple nonadherent dressings with other more expensive dressing types in the treatment of venous leg ulcers. Study Design. Retrospective cohort study. Location. The leg ulcer clinic at the University Hospital of South Manchester. Subjects and Methods. The healing rates of twelve leg ulcer patients treated with simple nonadherent dressings (e.g., NA Ultra) were compared with an equal number of patients treated with modern dressings to determine differences in healing rates and cost. Main Outcome Measures. Rate of healing as determined by reduction in ulcer area over a specified period of time and total cost of dressing per patient. Results. Simple nonadherent dressings had a mean healing rate of 0.353 cm2/week (standard deviation ± 0.319) compared with a mean of 0.415 cm2/week (standard deviation ± 0.383) for more expensive dressings. This resulted in a one-tailed p value of 0.251 and a two-tailed p value of 0.508. Multiple regression analysis gave a significance F of 0.8134. Conclusion. The results indicate that the difference in healing rate between simple and modern dressings is not statistically significant. Therefore, the cost of dressing type should be an important factor influencing dressing selection. [ABSTRACT FROM AUTHOR]

The Society of Vascular Surgery and the International Society of Cardiovascular Surgery identify three types of acute limb ischaemia to inform prognosis and management. Type 1 limb ischaemia is non-limb-threatening and is currently managed conservatively. We describe three cases of Type 1 limb ischaemia with femoropopliteal occlusion that were managed differently. The first case was initially managed conservatively but resulted in an adverse outcome following worsening of ischaemia. Overall, the cases managed with earlier intervention had good outcomes suggesting that conservative management alone may not be sufficient despite resolution of symptoms. The trend in other vessel diseases such as NSTEMI and TIA is towards earlier intervention, for example, PCI and CEA. It is likely that acute limb ischaemia has a similar natural history to these conditions. It is time to consider earlier revascularisation in selected patients with non-limb-threatening ischaemia. [ABSTRACT FROM AUTHOR]

Due to its application in the industry, heat transport is of crucial relevance. A novel form of nano-fluid known as the hybrid nanofluid helps to increase the thermal transfer capacity of regular fluids and has a larger thermal exponent. The two-part nanoparticle in a standard fluid is connected to the hybrid nanofluids. This study examines the hybrid nanofluid flowing properties and thermal transport passing through a slippy surface. There will be an examination of the forms of Inclined magnetic field, viscous dissipation, inclined joule heating, and thermal radiative impacts. The controlled equations are numerically solved using a numerical methodology, that is the finite difference procedure. This examination has included the hybrid tangent hyperbolic nanofluid which consists of the rich viscous non-Newtonian fluid (CH 2 OH) 2 (ethylene glycol) of the genre of dual different sorts of nano-solid particles i.e., copper (Cu) and silicon dioxide (SiO 2). It is worth noting that the heat transmission level of SiO 2 -Cu/(CH 2 OH) 2 which has been steadily increasing compared with the typical nanofluid (Cu-(CH 2 OH) 2). The entropy system is amplified to the Inclined magnetic field, radiative heat flux, Eckert and Weissenberg numbers by assimilation of nanoparticles ratio. Furthermore, SiO 2 -Cu/(CH 2 OH) 2 tangent hyperbolic hybrid nanofluid combinations hold an upper hand in the main aspects of heat transfer efficiency while compared to the Cu-(CH 2 OH) 2 tangent hyperbolic nanofluid. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to report the complication of perforation of the superior vena cava (SVC) leading to cardiac tamponade after the insertion of a Trapease IVC filter in the SVC position. A 29-year-old man was hit by a motor vehicle and sustained numerous injuries including a left skull fracture, intracerebral hemorrhage, and left open tibial shaft fracture. During his hospitalization, he developed an extensive symptomatic right upper extremity deep venous thrombosis involving the brachial, axillary, subclavian, internal jugular, and brachiocephalic veins. Owing to an intracerebral bleed, anticoagulation was contraindicated. Therefore, a Trapease filter (Cordis Inc.) was placed in the SVC via the left subclavian vein. Four hours later, the patient became hypotensive with associated tachycardia and tachypnea. Computed tomography of his chest revealed a hematoma around the SVC, a moderate amount of fluid within the pericardium, and a moderate-sized right pleural effusion. The patient was taken to the operating room and a pericardia! window was performed. Approximately 500 cc of blood was evacuated from the pericardium and immediate improvement in vital signs was noted. The patient was discharged from the hospital 2 weeks later and at 6-month follow-up had made a full recovery. This is the first case of SVC perforation leading to cardiac tamponade after the insertion of a Trapease filter. Owing to the rigid structure of the filter and associated motion of the SVC and pericardium, the Trapease filter may be contraindicated in the SVC. [ABSTRACT FROM AUTHOR]

Understanding the intricate interplay between variable fluid properties such as slip and thermal conductivity when flowing over porous surfaces is of utmost importance for a wide range of engineering applications. This investigation delves into this uncharted territory, connecting the analytical capabilities of HAM (Homotopy Analysis Method) to reveal captivating insights into the impact of these variables on the dynamics of Casson nanofluid flow. Besides, we documented the flow aspects which include thermal radiation, heat source, variable wall thickness and chemical reaction. We alter the partial differential flow-related conditions into nonlinear ordinary ones employing the similarity transformation approach. Then, using a popular semi-analytical technique known as the Homotopy Analysis Method (HAM), we were able to untangle them. This method yields to power series solutions to nonlinear differential equations. To illustrate the impact of the velocity, temperature and concentration profiles, parametric research has been done using tables and diagrams. In the limiting sense, the numerical results of our methodology are in great association with the outcomes of previous research. Finally, it is noted that higher values of the velocity slip parameter cause an enhancement in fluid velocity, while escalating values of the thermal slip parameter cause a decline in temperature distribution. [ABSTRACT FROM AUTHOR]

The key objective of this analysis is to examine the flow of hydromagnetic dissipative and radiative graphene Maxwell nanofluid over a linearly stretched sheet considering momentum and thermal slip conditions. The appropriate similarity variables are chosen to transform highly nonlinear partial differential equations (PDE) of mathematical model in the form of nonlinear ordinary differential equations (ODE). Further, these transformed equations are numerically solved by making use of Runge-Kutta-Fehlberg algorithm along with the shooting scheme. The significance of pertinent physical parameters on the flow of graphene Maxwell nanofluid velocity and temperature are enumerated via different graphs whereas skin friction coefficients and Nusselt numbers are illustrated in numeric data form and are reported in different tables. In addition, a statistical approach is used for multiple quadratic regression analysis on the numerical figures of wall velocity gradient and local Nusselt number to demonstrate the relationship amongst heat transfer rate and physical parameters. Our results reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. Finally, we have compared our numerical results with those of earlier published articles under the restricted conditions to validate our solution. The comparison of results shows an excellent conformity among the results. [ABSTRACT FROM AUTHOR]

In this article, we discuss an analytical method to solve physical equations occurring in acoustic waves. We acquire an approximate solution to the generalized fractional perturbed Zakharov-Kuznetsov (ZK) equation via the Residual power series method (RPSM). Three problems are considered to demonstrate the validity, efficiency and accuracy of the proposed method. The RPSM solution agrees very well with the results those obtained by q-homotopy perturbation transform method (q-HPTM) and the exact solution. The final results are shown through 3D graphs, 2D graphs and numerical tables. The results demonstrate the quality and power of the presented method. Fractional derivatives in the manuscript are defined in the Caputo’s sense whose order varies from 0 to 1. For mathematical computation Mathematica 10 is used. [ABSTRACT FROM AUTHOR]

The current article investigates the influence of radiation as well as gyrotactic microbes in the flow of micropolar nanoliquids through a channel. Flow is assumed to be symmetric across a channel having permeable walls. The work also focuses on the change in mass transport rate and density distribution of motile microbes across flow regimes in a porous channel. The governing nonlinear partial differential equations of the present problem are transformed into ODEs through dimensionless variables. The coupled nonlinear ODEs are numerically addressed by utilizing the quasi-linearization technique. Impacts of the pertinent parameters on the fluid flow are analyzed and demonstrated through tables as well as figures by using the powerful tool MATLAB. The velocity profiles escalate near both walls with an enhancement in Reynolds number. Moreover, an enhancement in values of heat radiation parameter causes declination in the fluid temperature. An evaluation of the comparison with existing results reveals an excellent harmony. The nanofluids possess marvelous characteristics subject to heat transport as compared to other ordinary fluids. We intend to elaborate the interaction of micropolar nanofluids with the microbes in a symmetric channel flow. [ABSTRACT FROM AUTHOR]

The key attention of this paper is to explore the heat and mass transport in oscillatory hydromagnetic Titanium alloy water nanofluid flow within two vertical alternatively non‐conducting and conducting walls enclosing Darcy‐Brinkman porous medium. Motional induction is considered because it is sufficiently strong in comparison to Ohmic dissipation. Hall phenomenon is considered because the electromotive force induced due to revolving of fluid particle about the magnetic field lines is significant. Suitable physical laws (constitutive and field equations) are used to derive the equations leading the flow model. An analytical approach is followed to extract the solutions of the flow model. The quantities of physical interest such as wall shear stress (WSS), rate of heat transport rate (RHT) and rate of mass transport rate (RMT) at the walls are obtained from the extracted solutions. The physical insight into flow manners is discovered from the graphs and tables generated from the numerical computation of the solutions. It is important to note from the study that the volume concentration of nanofluid and magnetic diffusion produce resistivity in the flow and tends to slow down the fluid flow. Magnetic diffusion weakens the strength of the primarily motional induced magnetic field. [ABSTRACT FROM AUTHOR]

Hydration of shale formation by water‐based drilling fluids leads to several problems, such as the collapse of boreholes, tight holes, and stuck pipe, which may impede further drilling and time loss in rectifying the problems, leading to heavy economic losses. This study reports the development of new gemini cationic surfactants as shale‐swelling inhibitors. These gemini surfactants are structurally similar but differ in terms of the spacer group. Saturated butyl group (GS1) and unsaturated 2‐butenyl (GS2) and 2‐butynyl (GS3) were introduced as spacer groups of gemini surfactants. To assess the performance of new gemini cationic surfactants, two reliable clay sources were considered. The first clay is from an unconventional formation and the second clay is sodium bentonite. The inhibition characteristics of gemini surfactants were evaluated using dynamic swelling, hot rolling, rheology, and filtration experiments. Different formulations based on commercially available solutions for shale‐swelling inhibitors were applied and compared with cationic shale inhibitors. It was observed that the new gemini cationic surfactants with different spacers (saturated and unsaturated) reduced the shale swelling by different percentages. The GS2 surfactant, containing an unsaturated double bond proved to be a good swelling inhibitor as compared to GS1 and GS3. It also showed acceptable performance compared with the common shale inhibitor (KCl) used in the industry. The addition of surfactant has less impact on the rheological properties as compared to KCl. The filtration properties of the base mud were unchanged when surfactants were used. However, the commercial inhibitor, KCl, significantly increased the filtration volume that is associated with the disintegration of the clay. In summary, unlike commercial inhibitors, the synthesized surfactants reduced the clay swelling without affecting the other properties of the drilling fluids. [ABSTRACT FROM AUTHOR]

• The thermal performance of steady hydromagnetic flow of Ti 6 Al 4 V-H 2 O nanofluid within two arbitrarily electrically conductive walls enclosing Darcy-Brinkman porous medium is explored in the article. • The energy dissipations due to drag forces arises from Darcy-Brinkman porous medium and presence of magnetic field (viscous and Joule heating) together with Hall effect on flow nature is also examined. • The flow model is solved by analytical approach and the velocity field, motional generated magnetic field and temperature field are derived in two special cases i.e., (i) in the case of the Hartmann flow (c = 0) and (ii) Hartmann-Couette flow (c = 1). • An interesting outcome of the study is the appearance of flow reversal in the direction of normal flow when c = 1. The drag force due to Darcy-Brinkman porous medium and upper wall conductivity significantly raise the normal flow near the opposite wall while these significantly reduces the normal flow in the area nearby the same wall. The primary purpose of the investigation is to explore the thermal performance of steady hydromagnetic flow of Ti 6 Al 4 V-H 2 O nanofluid within two arbitrarily electrically conductive walls enclosing Darcy-Brinkman porous medium. The energy dissipations and Hall effect on flow performance are also examined. The equations of the flow model are derived from the field and constitutive equations connecting electric and magnetic fields. The flow model is solved by an analytical approach, and the mathematical expressions for flow field such as velocity field, motional generated magnetic field, and temperature field are derived in two particular cases, i.e., (i) in the case of the Hartmann flow (c = 0) and (ii) Hartmann-Couette flow (c = 1). The quantities of physical interests like wall shear stress, the critical value of the Grashof number, mass flux, and heat transport rate are also derived. The governing parameters for the numerical computation are chosen for the range of h c = 0.25 ≤ h c ≤ h c = 0.75 , Da = 0.02 ≤ D a ≤ D a = 2 , ψ l , ψ u = 0.01 ≤ ψ l , ψ u ≤ ψ l , ψ u = 100 , Pr = 0.03 ≤ Pr ≤ Pr = 7.0 and Er = 0.05 ≤ E r ≤ E r = 2.0. An interesting outcome of the study is the appearance of flow reversal in the direction of normal flow when c = 1. It is further confirmed from the numerical results that the Darcy-Brinkman drags and upper wall conductivity significantly raise the normal flow near the lower wall. At the same time, while this substantially reduces the normal flow in the area nearby the upper wall. [ABSTRACT FROM AUTHOR]

Among several aspects, the one contributing towards the difficulty of groundwater quality evaluation is the large diversity of contamination sources. As contaminants comprising various compounds move from the soil to the water table, they will travel through several hydrologic zones. In constant unidirectional flow fields, a mathematical study of simultaneous adsorption and dispersion of a solute inside homogeneous and isotropic permeable media is described. The solute is adsorbed at a rate proportionate to its concentration in the dispersion systems, which are susceptible to input concentrations that fluctuate exponentially with time. The advection–dispersion equation (ADE) was solved numerically in this work to analyze the pollutants transport bearing in mind the coefficient of distribution and permeability by considering pollutant input concentrations. The solution is derived using the Laplace transform and Duhamel's theorem with moving coordinates. For specified medium and fluid characteristics, mathematical methods are created to forecast the concentration of pollutants in adsorbing porous media. [ABSTRACT FROM AUTHOR]

The aim of this paper is to highlight the impact of thermophoretic particle deposition (TPD) and heat source/sink on the steady two-dimensional laminar motion of Casson hybrid-type nanoliquid through a nonlinear stretched surface. Ordinary differential equations (ODEs) are created by taking a collection of partial differential equations (PDEs) and simplifying them using an appropriate similarity component. The reduced ODEs are then evaluated using the shooting method and Runge–Kutta–Fehlberg's fourth and fifth orders. Finally, tables and graphs are used to display the numerical data. It is seen that the fluid velocity step-downs when the porous parametric quantity and solid nanoparticle values increase. Heat distribution is enhanced with an enhancement in the heat source/sink constraint. Concentration goes down with an enhancement in thermophoretic constraint. The use of nanoparticles improves heat dispersion but reduces concentration in the linear case while increasing axial velocity in the nonlinear scenario. [ABSTRACT FROM AUTHOR]

In the current study, a vertical, 3D-heated plate is used to replicate the generation of heat energy and concentration into Prandtl liquid. We discuss how Dufour and Soret theories relate to the equations for concentration and energy. In order to see how effectively particles, interact with heat and a solvent, hybrid nanoparticles are used. It does away with the phenomena of viscous dissipation and changing magnetic fields. The motivation behind the developed study is to optimize solvent and heat storage uses in the biological and industrial domains. This article's major goal is to explore the aspects of thermal energy and mass transfer that influence how nanoparticles, hybrid nanoparticles, and 3D melting surface sheets behave. Variable thermal efficiency and variable mass transfer are combined. The system of generated PDEs (difference equations) includes the concentration, velocity, and heat energy equations. The numerical calculations are done for Silver (Ag), Molybdenum Disulfide (MoS2) nanoparticles with Ethylene glycol (C2H6O2) as the base fluid using a boundary layer approach to the mathematical formulation. The system of ODEs is formulated through transformations in order to find a solution. A Galerkin finite element algorithm (G-FEA) is adopted to analyze various aspects versus different parameters. It has been found that motion into hybrid nanoparticles is reduced by motion into nanoparticles. Additionally, differences in heat energy and solvent particle sizes are associated with modifications in magnetic, Dufour, Eckert, and Soret numbers. In contrast to hybrid nanostructures, the output of thermal energy is usually observed to be substantially higher. The magnetic field parameter decreases the particle velocity. In contradiction to the Eckert number, bouncy parameter, and magnetic parameter set values, the maximum quantity of heat energy is obtained. variable thermal conductivity's function. The 3D heated vertical surface convective heat transfer of nanofluids and hybrid nanofluids under the impact of a heat source, thermal radiation, and viscous dissipation has not yet been studied, as far as the authors are aware. [ABSTRACT FROM AUTHOR]

Researchers across the world have tried to explore the impact of non-Newtonian liquid flowing via an extendable surface with the inclusion of various effects due to its industrial and engineering applications like polymer production, paper production, filament extrusion from a dye, etc. This study investigates the behavior of stagnation point flow of Carreau liquid attached with inclined magnetic effect and spectral relaxation approach is utilized here for the numerical outcome. In this study, a few other vital features are attached like the quadratic multiple regression model for Nusselt number evaluation, passive control of nanoparticles, viscus heating thermophoresis, Brownian motion, and mixed convection, etc. Velocity disbursement visibility is analyzed by placing an inclined magnetic field. Physical model generates collection of partial differential equations (PDEs) and these PDEs are moved into ordinary differential equations by a similarity transformations scheme. Further for numerical process, spectral relaxation method is used. Growth in K causes a reduction in velocity because this parameter K creates the impedance to flowing resulting in confines the movement of liquid in restricted the plate. Direct relation is found between Ec and the energy file. In the case of S > 1, physically it is a representation of Joule and viscous dissipations. This article is novel in its sense that the influence of oblique magnetic force and second order velocity slippage on Carreau nano liquid and its numerical computation with help of the spectral relaxation method has never been done before. Furthermore, the quadratic multiple regression model has been employed to find the heat transition rate in the status of the Nusselt number. [ABSTRACT FROM AUTHOR]

Interpreting the complex interaction of nanostructured fluid flow with a dipole in a duct, with peripherally uniform temperature distribution, is the main focus of the current work. This paper also sheds light on the changes in the Nusselt number, temperature profiles, and velocity distributions for the fully developed nanofluid flow in a vertical rectangular duct due to a dipole placed near a corner of the duct. A finite volume approach has been incorporated for the numerical study of the problem. It is interesting to note the unusually lower values of the Nusselt number for the higher values of the ratio Gr/Re. Due to the nanostructure in the fluid, an enhancement in the Nusselt number has been noted, which is strongly supported by the magnetic field caused by the dipole. However, as the duct shape is transformed from rectangular to square, the Nusselt number is reduced remarkably. Further, as the dipole is brought nearer to the duct corner, the Nusselt number increases significantly. On the other hand, the flow reversal in the middle of the duct has been noted at higher values of the ratio Gr/Re. The dipole is noted to have a low impact on the reversal flow as well as on the temperature distribution. [ABSTRACT FROM AUTHOR]

Thermal performance of magnetically driven Casson nanofluid over a nonlinear stretching sheet under the influence of entropy, activation energy and convective boundary conditions was analyzed numerically, employing the quasi-linearization method (QLM). The collective behavior of thermophoretic diffusion and Brownian motion along with special effects of viscous dissipation, thermal radiation, heat generation and joule heating are considered in the energy equation for the flow problem. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and maintain the symmetry of the flowing structure. The governing highly nonlinear coupled differential equations of velocity, temperature, concentration and entropy are simulated through an iterative scheme encoded with MATLAB programming language. The geometric model is, therefore, described using a symmetry technique. A comparative analysis of linear and nonlinear stretching in sheets is presented via graphs and tables regarding pertinent dimensionless parameters. It is worth noting that the Nusselt number and Sherwood number decrease at relatively higher rates with growing values of activation energy in the case of nonlinear stretching. Moreover, the entropy generation rate near the stretching surface decreases due to the strong effects of Brownian motion and thermophoretic diffusion while it goes on improving far off the stretching surface. [ABSTRACT FROM AUTHOR]

Highlights: What are the main findings? The problem of 2-D Prandtl nanofluid past a moving wedge is investigated in detail; Tri-hybrid nanoparticles are considered here; Heat and mass transmission evaluations are conducted in the presence of endothermic/exothermic chemical reactions; The moving wedge is considered; What is the implication of the main finding? LobattoIIIA scheme is implemented for the numerical solution of modeled PDEs. Heat transfer is a vital fact of daily life, engineering, and industrial mechanisms such as cryogenic systems, spaceborne thermal radiometers, electronic cooling, aircraft engine cooling, aircraft environmental control systems, etc. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and keeps the symmetry of the flowing structure. Purpose: In this attempt, the effect of endothermic/exothermic chemical reactions accompanied by activation energy on a ternary hybrid nanofluid with the geometry of a wedge is taken into consideration. The mathematical form of PDEs is obtained by Navier–Stokes equations, the second law of thermodynamics, and Fick's second law of diffusion. The geometric model is therefore described using a symmetry technique. Formulation: The MATLAB built-in Lobatto III A structure is utilized to find the computational solution of the dimensionless ODEs. All computational outcomes are presented by graphs and statistical graphs in order to check the performance of various dimensionless quantities against drag force factor and Nusselt quantity. Finding: the addition of tri-hybridizing nanomolecules in the standard liquid improves the thermic performance of the liquid much better in comparison to simple hybrid nanofluids. Wedge angle parameter α brings about a decrement in fluid velocity and augmentation in thermal conductivity ϵ , thermal radiation R d , thermophoresis parameter N t and endothermic/exothermic reaction Ω , and fitted rate constant n accelerates the heat transmission rate. Novelty: The effect of tri-hybridizing nanomolecules along with endothermic/exothermic reactions on the fluid past a wedge have not been investigated before in the available literature. [ABSTRACT FROM AUTHOR]

The study of hydromagnetic mixed convection flow of viscoelastic fluid caused by a vertical stretched surface is presented in this paper. According to this theory, the stretching velocity varies as a power function of the displacement from the slot. The conservation of energy equation includes thermal radiation and viscous dissipation to support the mechanical operations of the heat transfer mechanism. Through the use of an adequate and sufficient similarity transformation for a nonlinearly stretching sheet, the boundary layer equations governing the flow issue are converted into a set of ordinary differential equations. The Keller box technique is then used to numerically solve the altered equations. To comprehend the physical circumstances of stretching sheets for variations of the governing parameters, numerical simulations are made. The influence and characteristic behaviours of physical parameters were portrayed graphically for the velocity field and temperature distributions. The research shows that the impact of the applied magnetic parameter is to improve the distribution of the viscoelastic fluid temperature and reduce the temperature gradient at the border. Temperature distribution and the associated thermal layer are shown to have improved because of radiative and viscous dissipation characteristics. Radiation causes additional heat to be produced in liquid, raising the fluid's temperature. It was also found that higher velocities are noticed in viscoelastic fluid as compared with Newtonian fluid (i.e., when K = 0). [ABSTRACT FROM AUTHOR]

The present work investigates heat transmission and stable MHD (magneto-hydrodynamic) mixed convective flowing in a ventilated porous enclosed space with a heated elliptic inner cylinder filled with MWCNT (multi-wall carbon nanotube)/CMC (carboxymethylcellulose) nanofluid. The enclosure is surrounded by a homogeneous magnetic field. By employing Galerkin finite element method (GFEM), the governing equations are confirmed. Simulations are performed for various ranges of pertinent parameters such as power law index (between 0.8 and 1.4), Hartmann number (between 0 and 100), elliptic cylinder inclination (between 0∘ and 90∘), and Richardson number (between 0.1 and 100). The numerical findings are given in bounds of isotherms, Nusselt numbers, and streamlines, which are critical governing factors for heat convective and enclosure flow. The data demonstrate that average Nusselt numbers Nu avg increases when Richardson number Ri and porosity ratio, increases. Hartman number works with the induced Lorentz force to make fluidity dominates the lower-level fluidity in the enclosure which reflects in isothermal displays. Even if the higher power law indexing operates against the fluidity by triggering shear force, it appears to be constructive in terms of heat transmission. [ABSTRACT FROM AUTHOR]

A mathematical model of 2D-double diffusive layer flow model of boundary in MHD Maxwell fluid created by a sloping slope surface is constructed in this paper. The numerical findings of non-Newtonian fluid are important to the chemical processing industry, mining industry, plastics processing industry, as well as lubrication and biomedical flows. The diversity of regulatory parameters like buoyancy rate, magnetic field, mixed convection, absorption, Brownian motion, thermophoretic diffusion, Deborah number, Lewis number, Prandtl number, Soret number, as well as Dufour number contributes significant impact on the current model. The steps of research methodology are as followed: a) conversion from a separate matrix (PDE) to standard divisive calculations (ODEs), b) Final ODEs are solved in bvp4c program, which developed in MATLAB software, c) The stability analysis part also being developed in bvp4c program, to select the most effective solution in the real liquid state. Lastly, the numerical findings are built on a system of tables and diagrams. As a result, the profiles of velocity, temperature, and concentration are depicted due to the regulatory parameters, as mentioned above. In addition, the characteristics of the local Nusselt, coefficient of skin-friction as well as Sherwood numbers on the Maxwell fluid are described in detail. [ABSTRACT FROM AUTHOR]

• Flow problem of Maxwell nanofluid with Fourier's and Fick's laws is analyzed. • Cattaneo-Christov heat flux and Buongiorno models are considered. • Heat source (sink) and thermal radiative heat flux is taken into consideration. • COMSOL program in collaboration with the Galerkin finite element method is utilized. • The concentration is boosted by the activation energy increment. The generation, utilization, adaptation, and transmission of thermal energy are all included in the controller topic of heat transport. Engineering and manufacturing disciplines include nutrition processing, the construction of food herbs, electric refrigeration, microturbines, and other fields rely heavily on heat transport. Because of the fascinating possibility in productions including the fabrication of polymers, papers, crystal glasses, and other materials, academics tried to probe the impact of heat transfer on liquid via an expandable sheet. To conduct our inquiry, we built a symmetric system connecting the properties of bio convection into an extended Maxwell nanofluid (MNF) using Fourier and Fick equations in a symmetrical stretchable slippage. Consideration has been given to the Cattaneo-Christov fluxing model. According to a Cattaneo-Christov connection (CCC), the Buongiorno occurring is likewise used for a symmetrical movement of nanofluids (NFs) in the Maxwell liquid. The regulator scheme that governs PDE was converted into ODE for the numerical solution utilizing similarity conversions. Galerkin finite element technique (GFEM) is created using the COMSOL application to produce mathematical conclusions for non-linear equations. In contrast to the updated Fourier-Fick scenarios, we saw higher temperatures and concentrations for Fourier-settings to calculate the current Biot quantity and general MNF factor, the heat outline is elevated. There is currently no information in the available literature on GFEM research of Maxwell nanofluid (MNF) in the occurrence of temperature producing, radiation temperature fluxing, and Cattaneo-Christov mass and temperature fluxing. [ABSTRACT FROM AUTHOR]