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Pharmaceutical fluid processing is a procedure of medication manufacturing, utilizing a particular kind of heat transfer in a biofluid designed to maintain the desired temperature for extended periods. Choosing a suitable fluid can have a positive effect on the operating efficacy of the system and lengthen the fluid's and system's life spans. As an outcome of this development, we investigate the influence of the partial slip and gyrotactic microorganisms on the peristaltic transport of a magnetohydrodynamic Ree–Eyring nanofluid via an aligned porous conduit with thermal radiation, energy generation, along with cross and double diffusion effects. By invoking suitable nondimensional parameters, the proposed dimensional governing equations are transformed into a system of dimensionless partial differential equations. The analytical solutions for the system of partial differential equations are obtained by incorporating the homotopy perturbation method. Further, tabular and graphical presentations are used to examine the characteristics of the various sundry parameters on the temperature, concentration, motile microorganism density, axial velocity, trapping, and other relevant flow quantities. The observations of this study indicate that the Darcy number and thermal Grashof number have the capability to enhance the velocity distribution of the Ree–Eyring nanofluid in the presence of bioconvection. The trapped bolus size and the skin friction coefficient increase noticeably because of an enhancement in the Ree–Eyring fluid parameter. Also, the Darcy number and the Hall current parameter increase the skin friction coefficient. Furthermore, validation of the results is carried out to examine the consistency between the current and the previous findings for some special cases and excellent agreements are found. [ABSTRACT FROM AUTHOR]

In this work, a dimensionless group-incorporating artificial neural network (DI-ANN) model is established to determine the relative influence of factors affecting single-track depth for laser-directed energy deposition (L-DED), specifically as it correlates with two types of porosity (keyhole mode and lack-of-fusion voids). The DI-ANN model's input features include process parameters, process signatures acquired from experiments, and multiphysics simulation-based dimensionless groups. Experimental data were acquired for SS316L straight single-track samples, prepared using a continuous-wave laser with a top-hat profile. The feature influence on single-track depth was analysed using Spearman's correlation coefficient before training the DI-ANN model, which was tested using 5-fold cross-validation. Laser power, scanning speed, powder feed rate, melt pool width, melt pool area, maximum temperature, maximum Marangoni number, mean and maximum Grashof number, and mean solidification time are selected for training the model. The predictive quality of this model for single-track depth is 6.1% mean absolute percent error (MAPE) and 11.7% maximum absolute percent error (MXAPE). Compared with recent literature, this study shows an approximately 30% improvement in the MAPE and a 70% improvement in MXAPE. The presented model can be used for process parameter optimisation for porosity reduction and be a valuable foundation for feedback control algorithms for heat penetration. [ABSTRACT FROM AUTHOR]

This article investigates the simultaneously developing pure turbulent mixed convective regime and compares the hydrodynamic and thermal features of both buoyancy-assisted and opposed flows in a vertical tube. Two-dimensional (2D) axisymmetric steady-state simulations were carried out for Reynolds number, 5,000–20,000; Grashof number, 1.25 × 106 to 108; and Richardson number, 0.05–0.25 for a length-to-diameter ratio of 150 with uniform heat flux boundary condition and water as the working fluid. Three Reynolds-averaged-Navier–Stokes turbulence models were compared and then the most suitable model was used for the simulations. At a given Richardson number, the friction factor and Nusselt number are lower in the case of buoyancy-assisting flow compared to buoyancy-opposing flows. Similar friction factors and heat transfer trends were obtained at a given Grashof number. At varying Grashof numbers and Richardson numbers keeping the Reynolds number constant, no discernible variations were observed for both flows. The entry length was also examined, and it has been found that the hydrodynamic and thermal entry lengths are restricted to a length-to-diameter ratio of 25 and 20 for assisting and opposing flows, respectively. Correlations were developed for both flows to quantify the friction factor, Colburn factor, and Nusselt number in terms of the Reynolds number. [ABSTRACT FROM AUTHOR]

This research paper examines the combined effects of thermal and mass stratification on unsteady flow past a vertical oscillating plate with periodic temperature variation and variable mass diffusion. The Laplace transform technique is introduced to deal with the linear coupled parabolic equations satisfying initial as well as boundary conditions and obtained solutions in closed form for concentration, temperature, and velocity. For example, to find the Laplace transform of an exponentially ordered piece wise continuous function n(t) $n(t)$, one can uses the formula L{n(t)}=∫0∞e−stn(t)dt=n¯(s) $L\{n(t)\}={\int }_{0}^{\infty }{e}^{-st}n(t)dt=\bar{n}(s)$, t being the time and s is a parameter. In this study, we explore the effects of different factors such as plate amplitude, plate frequency, thermal Grashof number, and the mass Grashof number on the concentration, velocity, and temperature profiles and shows them graphically. We see a decline in the fluid's velocity for thermal and mass stratification. Most interestingly, in presence of higher temperature gradient, as the frequency of the oscillations increases close to the plate surface, the fluid velocity declines. The reason behind this is that the flow system has a plate with very high fluctuations. We have found that the fluid's temperature goes up while the concentration goes down when there is a decrease in the thermal stratification and a rise in the mass stratification. [ABSTRACT FROM AUTHOR]

Ciliary‐driven flows manifest prominently in various physiological and biological phenomena, serving as micro mixers in cilia‐based actuators, regulating flow in small biosensors, and functioning as micro pumps in drug‐delivery systems. Although there are some studies on cilia driven flows, however, electroosmotic flow of Williamson nanofluid in a non‐uniform ciliated channel has not been reported before. Keeping in view, the present study aims to investigate electroosmotic transport of blood through a non‐uniform wavy ciliated channel. The Williamson fluid model is employed to investigate the properties of blood. Graphene oxide nanoparticles are inserted within blood to examine the flow and thermal characteristics. Moreover, streamline patterns, average pressure rise, and temperature contours are also portrayed against sundry physical parameters to present a detailed physical analysis. The obtained results revealed that concentration profile declines with Eckert number Ec,$Ec,$ Soret number Sr$Sr$, Weissenberg number We,$We,$ and nanoparticle volume fraction ϕ$\phi $ while it enhances with Grashof number Gr$Gr$. Temperature of the fluid significantly drops by enhancing Grashof number Gr$Gr$ and volume flow rate Q,$Q,$ while it rises with Eckert number Ec,$Ec,$ Weissenberg number We,$We,$ and nanoparticle volume fraction ϕ$\phi $. The average pressure rise per unit wavelength escalates with a rise in the volume fraction of nanoparticles (ϕ) in the peristaltic pumping region. However, beyond a critical value, it diminishes in the free and augmented pumping regions. Streamline patterns indicates a shrinking in the size of trapping bolus by enhancing the volume flow rate Q.$Q.$ Temperature contours are significantly influenced by enhancing the Eckert number Ec$Ec$. [ABSTRACT FROM AUTHOR]

This article aims to investigate the hall current consequences on the transfer of clean water containing silver in addition to copper nanoparticles suspended nanofluids through vertical rotating channel. Boussinesq approximation is taken into consideration. Exact analytical solutions of governing equations subject to physical boundary conditions are obtained using the techniques of non‐dimensionalization. The impacts of Grashof number, radiation parameter, Prandlt number, frequency parameter, magnetic parameter, Hall parameter, parameter of rotation and its effects on primary as well as secondary velocity and temperature profiles are presented graphically. We analyze the Hall effects and mixed convection in magnetohydrodynamic (MHD) flow of nanofluids through a vertical rotating channel, based on extensive research and applications. An analytical approach is used to derive the exact solution to this problem. A comparative study for silver and copper nanoparticles is made. A tabular solution for impacts of said parameters on convection rate and skin friction coefficient is also presented. This study is applicable for geophysical dynamics and engineering applications. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates how thermal radiation, viscous dissipation, double-diffusive convection, and slip boundaries collectively affect the peristaltic movement of a magneto-pseudoplastic nanofluid within a uniform channel. The inclusion of slip boundary conditions at the channel walls helps to accurately represent the flow behavior of the nanofluid near these boundaries. The magneto-pseudoplastic nanofluid exhibits peculiar rheological features to flow dynamics due to pseudoplastic characteristics of nanoparticles in its composition and exposure to magnetic force. The mathematical formulation of motion equations is done through appropriate technique combining the properties of heat radiation, magnetic flux, double diffusion convection, and rheological features. The equation is further simplified by suitable method. The current study aims to evaluate the peristaltic movement under influence of slip boundaries characteristics, sort of concentration, heat radioactivity, flux properties, and temperature profile. Moreover, it will assess the flow dynamics with ratio of mass and heat exchange under the effect of critical parameters which include Prandtl number, Grashof number, slip limitations, and Hartmann number. So, the research will widen the theoretical underpinning of complex fluid transportation of magneto-pseudoplastic nanofluids under peristaltic flux and explicate the practical outcomes in terms of slip boundary settings in such systems. The results and conclusions are imperative for restructuring and devising biomedicine engineering, microfluidic equipment and gadgets, manufacturing techniques for complex fluid with peristaltic flow under the influence of slip limitations and magnetic force. [ABSTRACT FROM AUTHOR]

The study investigates the effect of using electroosmotic pumps on the cooling of electrical devices in micro scales. The mutual effects of the microchannel inclination (ranging from 0 ° to 75 °) and configuration of the electric field on the heat transfer have not been investigated. To this end, a numerical code based on the finite volume method (FVM) and Semi-Implicit Method for Pressure Linked Equations (SIMPLE) was developed in Fortran to model the two-dimensional flow dynamics and heat transfer. Two different arrangements were considered for the discrete heat sources and electroosmotic fields to examine their effects on fluid dynamics and heat transfer rate at Re = 10. In addition, the effects of electrical parameters, which directly affect the flow dynamics, were also considered. Results indicate that decreasing the heat transfer rate at higher angles is because of the velocity mitigation, whereas an increase in the Grashof number causes a reverse effect. Altering the layout of heaters and electric field from the condition in which heat sources are facing each other (Arrangement 1) to the condition in which heat sources are not facing each other (Arrangement 2), leads to the formation of swirling flow, increased flow rate, and decreased average Nusselt number. The optimum configuration for maximum cooling performance is found in Arrangement 1 with the Grashof number of 0 and inclination angle of 0 ° , in which the highest average Nusselt number of 5.815 is achieved. Despite the reduction in cooling efficiency at higher angles, Arrangement 1 outperforms Arrangement 2. [ABSTRACT FROM AUTHOR]

Theoretical analysis is performed to investigate the double-diffusive convection in Sisko fluid on peristaltic propulsion under inclined magnetic field and asymmetric channel. The mathematical modeling of Sisko fluids with double-diffusive convection and inclined magnetic field with various wave forms is given. Under the constraints of long wavelength and low Reynolds number, exact and numerical solutions are obtained. With aid of computational data achieved using Mathematica software, the impact of thermophoresis, Brownian motion, Soret and Dufour parameters, Grashof numbers (concentration, nanoparticle and thermal) on peristaltic pumping with double-diffusive convection are examined. [ABSTRACT FROM AUTHOR]

The study of flow behavior in the simultaneously developing transitional regime of mixed convection flows is rare. It has been believed that the transitional regime will give a good compromise between pressure drop and heat transfer compared to laminar and turbulent flow regime. In this experimental study, the friction factor (f) and Nusselt number (Nu) characteristics for buoyancy-assisted and opposed flows of water in concurrently developing transitional regime of mixed convection through a vertical tube are studied. Experiments were done for Reynolds numbers (Re) varying from 500 to 15,000, Grashof numbers (Gr) from 1.25 × 104 to 5 × 106, Prandtl numbers (Pr) from 3 to 7, and Richardson numbers (Ri) from 0 to 0.1 subjected to uniform heat flux boundary conditions. A flow visualization provision after the test section which confirms an early transition in buoyancy-opposing flow (Rec = 2264) compared to buoyancy-aiding flow (Rec = 2468) at a fixed Ri of 0.1. Further, with the increase in Ri from 0 to 0.1, the average f decreases, and the average Nu increases in both aiding and opposing flows. It confirms that the onset of transition gets delayed with the increase of heat flux supplied in both the flows. Based on the present outcomes, an efficient heat exchanging device can be operated either to delay or advance the transition in a vertical pipe flow for optimum heat transfer. [ABSTRACT FROM AUTHOR]

The current study investigates the effects of thermal radiation and Lorentz's force on heat and mass flow in a nanofluid with a magnetic field and free convection, as it passes over a vertical permeable sheet. The dominant PDEs are turned into linked nonlinear ODEs using an appropriate similarity transformation. Using the MATLAB ODE45 tool, dimensionless ODEs are numerically computed using the finite difference procedure. Four different water-based nanofluids are considered, including copper, titanium dioxide, aluminum oxide, and silver. The influence of emerging dimensionless numbers and other parameters, such as the magnetic force parameter, the radiation parameter, the suction parameter, the Prandtl number, the Schmidt number, the Dufour number, as well as for constant values of the modified local Grashof number and local Grashof number on the concentration, velocity, and temperature profiles is emphasized and mentioned. Moreover, the visual representation of the effects of a volume percentage of up to 4% copper nanoparticles on the distributions of concentration, temperature, and velocity is also shown. The temperature profile, concentration profile, and velocity profile all grow with an increase in the volume percent of copper nanoparticles between 0.00 and 0.04. Furthermore, numerous scenarios are investigated for the distributions of the local Sherwood number, the local Nusselt number, and the local skin friction coefficient. The local Nusselt number decreases, and the local skin friction coefficient and Sherwood number increase about by 30 %, 45 %, and 60 % respectively due to increasing the value of volume fraction from 0 % to 4 %. The local skin friction coefficient increases and the local Nusselt number decreases by about 15 % and 39 % respectively for rising values of the thermal radiation number from 0.5 to 3.5. In addition, for magnetic force parameter values between 0.5 and 4.0, the local skin friction coefficient drops by about 13 %. [ABSTRACT FROM AUTHOR]

This study examines the generation of irreversibility and the behavior of stagnation point hybrid nanofluid flow on a Riga plate. The effects of nonlinear thermally convective and solar radiation are incorporated in the modeled equations. The nanoparticles of (Cu) and (Al2O3) are mixed with Glycol (C3H8O2) to hybridized it. The leading equations have been changed to dimension-free form by using the set of appropriate variables and then have been evaluated by Artificial Neural Network (ANN) approach. It is revealed in this work that, the velocity panels are amplified with expansion in Grashof number and electromagnetic factor while declined with escalation in magnet/electrode factor and nanoparticles concentration. Upsurge, in Eckert number for both the scenarios (Ec < 0) and (Ec > 0), the radiation factor and nanoparticles concentration cause augmentation in thermal characteristics. Radiation factor has positive impacts on Bejan number and generation of Entropy. Moreover, Bejan number is retarded while entropy is augmented with growth in Brinkman number. It is also established in this work that the principle of entropy generation for hybrid nanoparticles supports the efficient delivery of drug in cancer treatment. [ABSTRACT FROM AUTHOR]

This research investigates the transient magnetohydrodynamic (MHD) flow of a non-integer Maxwell fluid over a vertical plate, taking into account the effect of diffusion-thermo and parameter of heat absorption. The fractional derivative Caputo-Fabrizio is employed to model the problem. Using the Laplace integral transform technique, we solve the dimensionless governing equations to obtain the profiles of velocity, concentration, and temperature, which are then presented in graphical form for easy comparison and interpretation. The influence of several parameters—specifically, the fractional parameter and heat absorption is thoroughly analyzed and illustrated through a series of graphical representations. Furthermore, a comparison between traditional as well as fractionalized velocity fields is provided. The results show that chemical reactions and magnetic fields reduce the velocity profile, while diffusion-thermo and mass Grashof number increase the fluid velocity. [ABSTRACT FROM AUTHOR]

The Soret effect, also known as thermal diffusion, plays a crucial role in the phenomenon of double diffusion convection in liquids. This study investigates Soret-driven convection within a vertical double-diffusive layer of Maxwell-Cattaneo (M-C) fluids, where the boundaries maintain constant temperatures and solute concentrations that are distinct from each other. The heat transfer equation for Maxwell-Cattaneo fluids is governed by a hyperbolic rule of heat conduction, rather than the typical Fourier parabolic one. The Chebyshev collocation method is employed to solve the corresponding stability eigenvalue problem. The neutral stability curve shows significant fluctuation responses due to the M-C effect. When the Cattaneo number (C) reaches 0.02, multiple local minima appear in the critical Grashof number (Gr). The instability the thermal convection is found to be amplified by the combined effects of Maxwell-Cattaneo and Soret, along with the Grashof number, while the double diffusion effect appears to suppress the instability of convective system. The influence of Soret effect on convective instability will diminish dramatically as the Gr number rises above 8200. [ABSTRACT FROM AUTHOR]

Nanofluidic peristaltic transport is an emerging field of research with potential biomechanical, industrial, and biotechnological applications. Motivated by these utilizations, the present investigation addresses the mixed convective magneto peristaltic flow of radiative Ree-Eyring nanofluid through an inclined divergent channel under the consequences of energy generation, activation energy, viscous and Ohmic dissipation effects. In order to mimic the problem, we employ Cartesian coordinates along with the lubrication approach. The computational software MATLAB is implemented to actualize the numerical shooting process. The impact of major factors on velocity, skin friction coefficient, temperature, heat transfer rate, concentration, and Sherwood number is explored extensively with graphical and tabular representations. The findings discovered that both thermal and solute Grashof numbers cause an upsurge in the distribution of velocity. The Brownian movement parameter decreases the mass transfer rate and increases the heat transfer rate at the channel walls. Temperature distribution of the Ree-Eyring liquid enhances for Eckert number and energy generation parameter. Further, it is found that the concentration field of Ree-Eyring nanofluid is an enhancing function of activation energy. [ABSTRACT FROM AUTHOR]

The MHD finite element analysis naturally convective flow across an exponentially accelerating plate with viscous dissipation is investigated numerically. In this process dimensional partial differential equations are changed to dimensional less form. The Galerkin finite element method is emerged to solve non-dimensional partial differential equations. Obtained results are effectively depicted through the utilization of graphs, allowing for a comprehensive understanding of the impact that different physical parameters on primary velocity, transverse velocity, temperature, and concentration profiles. The study effectively differentiated between the present and prior findings, ultimately demonstrating a strong consensus of excellent agreement between the results. The key findings of this study are: The primary velocity increases on growing the values of Thermal Grashof number, Solutal Grashof number, Eckert number, and Dufour number and decreases on climb up the values of Magnetic parameter, Prandtl number, Schmidt number, and Hall parameter. The secondary velocity increases on raising the values of Thermal Grashof number and Solutal Grashof number and diminishes on enhancing the value of Hall parameter. The temperature increases on increasing the values Eckert number and Dufour number and decreases on improving the value of Prandtl number. The concentration decreases on increasing the value of Schmidt number. [ABSTRACT FROM AUTHOR]

In this paper, the effect of the rotation variable and other variables on the peristaltic flow of Sutterby fluid in an Inclined asymmetric channel containing a porous medium with heat transfer is examined. In the presence of rotation, mathematical modeling is developed using constitutive equations based on the model of Sutterby fluid. In flow analysis, assumptions such as long wavelength approximation and low Reynolds number are used. The resulting nonlinear ordinary differential equation was analytically solved using the perturbation method. The effects of the Grashof number, the Hartmann number, the Reynold number, the Froude number, the Hall parameter, the Darcy number, the magnetic field, the Sutterby fluid parameter, and heat transfer analysis on the stream function, and the pressure gradient are analyzed graphically. Utilizing MATHEMATICA software, numerical results were computed. It is discovered that the size of boluses decreases as some parameters increase, whereas the pressure gradient is directly proportional to the majority of parameters. [ABSTRACT FROM AUTHOR]

This paper’s goal is to investigate the oscillatory flow of double-diffusive convection in a Voigt fluid. We re-design the basic equations of the channel flow, which initially appear dimensional, in a dimensionless manner using non-dimensional variables. The oscillation technique transforms the governing equations into coupled ordinary differential equations (CODEs). We have derived the analytical expressions for velocity, temperature, and concentration distribution by solving the CODEs using the direct analytical method. The study focuses on how physical factors, like the thermal Grashof number, the solutal Grashof number, the Prandtl number, the Lewis number, and the Voigt fluid parameter, affect different aspects of flow, such as speed, temperature, concentration, rate of heat transfer, and mass transfer. Notably, the study finds that skin friction increases on both channel plates with increasing injection on the heated plate. The significance of double-diffusive oscillatory flow lies in its ability to improve heat and mass transfer rates, as well as its impact on pattern formation and stability, which influences a wide range of applications from engineering design to environmental studies. [ABSTRACT FROM AUTHOR]

The major aim of this work is to analyze the thermophysical properties of hybrid nanoliquid inside a square lid driven enclosure under the effect of applied magnetic field and mixed convection. The Hybrid nanofluid is considered a suspension of Iron-oxide (Fe3O4) and Copper (Cu) nanoparticles into water. The cavity walls have varying properties such as top adiabatic wall is moving continuously while the lower wall is maintained at a high constant temperature, in addition, the vertical walls are kept at a low fixed temperature. The magnetic field is applied to the right vertical wall in a horizontal direction. Additionally, the effects of buoyancy forces caused by temperature gradients and shear forces caused by continuous lid motion are considered. The mathematical modelling of problem with all assumptions yields the nonlinear partial differential system. First this system is transferred into non-dimensional form and then transformed system is solved by using Galerkin finite element method (GFEM) along with Gaussian elimination method. Results for isotherms, streamlines and average Nusselt number are obtained versus Richardson number (0.1 ≤ Ri ≤ 15), Grashof number (10 ≤ Gr ≤ 10000), Hartmann number (0 ≤ Ha ≤ 100), volume fractions of solid nanoparticles (0.005 ≤ ϕ1 ≤ 0.02) and (0.005 ≤ ϕ2 ≤ 0.02). It is observed that the Richardson number and Grashof number have significant impacts on both flow velocity and temperature. In addition, concentration of hybrid nanoparticles improves the heat transfer performance. The obtained results may be crucial for thermal management in the cooling of electronics, heat exchangers, solar thermal collectors, industrial operations, medical equipment, HVAC systems, food processing, and renewable energy systems. [ABSTRACT FROM AUTHOR]

This study is intended to determine the thermal management capability of different closed-loop controllers inside a cylindrical three-dimensional cooling system with multiple O-Ring type heat sources. The motivation for this research stems from the need for efficient thermal regulation in advanced cooling systems, which is critical for applications ranging from electronics cooling to industrial processes. The uniqueness of this study lies in its comprehensive evaluation of different controllers such as proportional (P), proportional–integral (PI), and proportional–integral–derivative within a geometrically complex cooling environment using a novel trial-and-error approach for tuning controller parameters. The observational domain is a hollow cylinder, and the four discrete heat sources are placed at regular intervals along the cylinder's longitudinal axis, with all the remaining walls insulated. At the center of the system is a temperature probe that measures and provides feedback to the control module to continuously compare it to a pre-specified setpoint temperature. The flowing fluid, air, enters through the semi-circular inlet at one end, whose velocity is controlled by a controller response, and is discharged through the semi-circular outlet at the other end at atmospheric conditions. This study uses the Galerkin finite element method, using proper initial and boundary conditions to solve the governing equations, namely, the Navier–Stokes and heat energy equations. We analyze the time-dependent behaviors of the cooling system by measuring controller responses such as overshoot, rise time, oscillation, steady-state error, and settling time. Additionally, the impacts of the Reynolds number (Re), Richardson number (Ri), and Grashof number (Gr) on the overall mean Nusselt number over time are observed to understand the influence of flow regulation due to the controllers' actions. This comprehensive analysis provides insights into the controllers' inlet flow control based on the set temperature at the probe's center location. A unique trial-and-error approach for selecting Kp and Ki values, which is crucial for controller analysis, is also presented. Based on the results, it can be inferred that increasing the Kp value from 0.003 to 0.010 ms−1 K−1 reduces the steady-state error from 40.8% to 13.97%. For a Ki value of 0.006 ms−2 K−1, the PI controller achieves a zero steady-state error with faster settling at 3.29 s, along with an overshoot of approximately 80.51%. Conversely, a lower Kd value of about 0.0001 mK−1 results in a reduction in the settling time and overshoot compared to the PI controller, while a higher Kd value ensures optimum stability with a higher settling time and a stable Nusselt number of 1.93. This trial-and-error approach to parameter tuning provides valuable insights into the design of controlled environments and the effective management of thermal conditions in various thermo-fluidic applications. [ABSTRACT FROM AUTHOR]

In this study, a new control of the heat transport process utilizing phase-change materials (PCMs), as latent thermal energy storage, and nanofluid flow in a thermal system is explored numerically. The proposed model comprises PCM domain divided square enclosure, filled with two different nanofluids (TiO2 and CuO) heated and cooled, respectively, at the left and right sides of the enclosure. Horizontal walls are adiabatic. The coupled mathematical model comprises phase-change materials, nanofluids, and thermal gradients, which are solved numerically following the finite volume-based approach. The enthalpy-porosity technique is adopted to assess the melting behavior of the PCM domain. The thermo-hydraulic performance of the complex system of nanofluids and the melting process of PCM is assessed for the set of control variables such as Grashof numbers (Gr) and nanoparticle concentration (ϕ). Analysis revealed that the melting performance of the PCM domain is significantly influenced by the concentration of the nanoparticles on both sides. The results revealed that, for the early stage of the melting process, the thickness of the melted layer strongly depends on the interaction of the thermal gradient inside the cavity. Higher Gr value and ϕ lead to higher thermal convection in the heated section, which allows the faster melting process of the PCM domain and more amount of thermal energy storage inside the PCM. This transport process further enhances with the increase in the nanoparticles concentrations. A higher Gr value with higher nanoparticle concentrations is always beneficial for the higher amount of thermal energy storage and storage goes up to 35.80%. [ABSTRACT FROM AUTHOR]

The hybrid nanofluid is the modified class of nanomaterials with impressive thermal impact and preserves significant applications in extrusion systems, thermal management systems, engineering processes, cooling and heating materials and many more. The aim of this research is to communicate the thermal enhancement of water (H2O) and sodium alginate (C6H9NaO7) base fluids with interaction of hybrid nanofluids. The Casson fluid model is used to endorse the properties of such base liquids. The titanium dioxide and silver nanoparticles incorporate the thermal impact of hybrid nanofluid properties. The fractional simulations are performed by using the Caputo–Fabrizio (CF) time-fractional derivatives. The integration of problem is computed via Laplace technique. It is observed that the velocity profile enhanced the Grashof number. The increasing observations for Nusselt number and wall shear force due to fractional parameters are obtained. [ABSTRACT FROM AUTHOR]

The impact of Hall current on the multiphase thermal transfer of an incompressible electrically conductive Jeffrey flow over an infinitely vertical plate when heat absorption and chemical reaction are present has been examined. Partial differential equations have been used to describe the process, accounting for heat and mass transfer effects. This study uses extended Fourier's and Fick's laws together with the recently announced constant proportional Caputo (CPC) fractional operator. The fractional model is converted into a nondimensional form by applying some appropriate quantities. The nondimensional produced fractional model for momentum, heat, and diffusion equations based on the CPC fractional operator has been calculated semi‐analytically by applying the Laplace method. The Mathcad 15 software to sketch the graphs for several factors, like the Grashof number, mass Grashof number, Schmidt number, Prandtl number, Hall, and magnetic field parameters, is used to describe the velocity profile. Additionally, a graphical explanation is provided for the influence of the appeared parameters, particularly the effect of the fractional parameters. It is concluded that the result of the fluid model developed by the generalized constitutive relations is more accurate and generalized than the results of the artificially contracted fractional model. A fractional derivative is therefore the ideal option to achieve controlled concentration, temperature, and velocity. The current study is immediately relevant to geophysical, cosmically fluid dynamics, medical, biological, and any other processes that are significantly enhanced by a low gas density and a high magnetic field. [ABSTRACT FROM AUTHOR]

Convective energy and mass transfer in a non-Newtonian fluid layers a wide-spread physical phenomenon in natural and technical systems. Triple diffusive convection plays a crucial role in chemical engineering by enabling the understanding and optimisation of mass transfer processes involving multiple components. It is essential for designing efficient separation systems, optimising catalysts, predicting reaction kinetics, and improving environmental processes. The motivation of this paper is to explore an Oscillatory flow of a triple diffusive convection in a Voigt fluid layer. The governing partial differential equations are transformed into coupled ordinary differential equations with the help of the oscillation technique. The study emphasises the effects of known physical parameters, such as the thermal Grashof number, solutal Grashof number, Prandtl number, Lewis numbers and Voigt fluid parameters on velocity, temperature, concentrations and rate of heat and mass transfers. In particularly, the study finds that skin friction increases on both channel plates with increasing injection on the heated plate. [ABSTRACT FROM AUTHOR]

This study is devoted to an analysis of natural convection and the emergence of delamination in an incompressible fluid encapsulated in a closed region heated from the side. Weak, medium and intensive modes of stationary laminar thermal and thermo-concentration convection are considered. It is shown that nonlinear flow features can radically change the flow structure and characteristics of heat and mass transfer. Moreover, the temperature and concentration segregation in the center of the square region display a non-monotonic dependence on the Grashof number (flow intensity). The formation of a nonstationary periodic structure of thermal convection in boundary layers and in the core of a convective flow in the closed region is also examined. Details of the formation of countercurrents inside the region with the direction opposite to the main convective flow are given. Finally, the influence of vertical and horizontal vibrations on oscillatory convection is analyzed in detail. [ABSTRACT FROM AUTHOR]

The transition from steady-state flow to periodic oscillatory flow for the natural convection by Hopf bifurcation is investigated in a three-dimensional (3D) cavity. The spectral collocation method (SCM) in combination with the artificial compressibility method (ACM), which is developed by ourselves as a numerical method SCM-ACM with high accuracy, is employed to solve the governing equations directly instead of linear stability analysis method that is commonly used for the research on flow instability. The results show that the amplitude decays exponentially with time and the decay rate is linear with the Grashof number (Gr). The critical Grashof number for steady-oscillatory transition is obtained as Gr cr = 3.423 × 106. The dimensionless angular frequency ω cr = 0.24 is also determined by Fourier analysis. In this work, we also examine the heat-momentum interactions within the boundary layers, visualize the periodic oscillations of temperature and velocity amplitudes, and analyze the origin of instability from multiple angles. The results show that large oscillations of velocity and temperature are observed near the isothermal walls. The oscillation is enhanced by the increase of thermal boundary layer thickness and flow velocity at both ends of isothermal walls. The maximum velocity and temperature amplitudes appear at the lower left and upper right corners of the mid-plane (Z = 0.5), where are the origin of instability, and the spanwise walls are almost independent of oscillations. The oscillatory flow of natural convection in three-dimensional cavity originates from the continuously increasing buoyancy force, and its transition occurs by Hopf bifurcation. Moreover, the temperature amplitude exhibits a wavy distribution on the mid-plane (X = 0.5) and strongly depends on the depth Z. These results provide benchmark data for future numerical studies and engineering application. • The high-precision SCM-ACM developed by authors is employed to directly solve the governing equations. • The critical Grashof number for the steady-oscillatory transition of natural convection is predicted. • The evolution pattern of velocity, amplitude and frequency is analyzed. [ABSTRACT FROM AUTHOR]

The use of free convection in various industries grows, which is due to the increase in heat loads, and also to the closer attention to energy efficiency. Thus, for air-cooled apparatuses at certain parameters of the outside air, there is a possibility to decouple fan drives and to operate the apparatuses in an energy-saving free-convection regime. Here, a distinctive feature of the free-convection regime are high values of heat-transfer coefficients to compensate for which the heat-transfer surface on the source side of the air is increased by finning the tubes. With the aim of raising the efficiency of heat-transfer processes, it is expedient to optimize the geometric parameters and arrangement of a bundle, the number of rows, and the location of the bundle in space. The paper presents a review of experimental and numerical investigations into the heat transfer of multirow horizontal and inclined bundles of finned tubes in a free-convection regime. This paper is a continuation of [1] in which a review has been presented of experimental and numerical investigations into the free-convection heat transfer on air-cooled annular-finned tubes and single-row bundles thereof. Importantly, the character of the dependences of the heat transfer of single-row bundles on the transverse pitch of the tubes differs fundamentally from similar dependences for multirow staggered bundles because of the influence of upper rows. [ABSTRACT FROM AUTHOR]

In this research work, numerical simulations and mathematical modeling are introduced for the mixed convection hybrid nanofluid flow over a curved stretching surface. The energy equation is modeled subjected to viscous dissipation, a heat source with radiative heat flow. Convective and velocity slip conditions are assumed at the stretchable surface. The Eckert number and Grashof number contained the independent variable "s" which is not suitable for the dimensionless parameters. In this regard, the problem is solved by a nonsimilar approach. The nonsimilar approach has not been tried before on a curved stretching surface. Furthermore, alumina and copper are taken as nanoparticles, and blood is taken as a base fluid. A nonsimilarity transformation is used to transform the governing equation into dimensionless (PDEs). Converting these PDEs into ODEs by using the local nonsimilarity method. The familiar Bvp4c is used to perform numerical computations for a dimensionless nonlinear system. Significant results for velocity and temperature profiles for different parameters are comprehensively presented and discussed. Results indicated that increasing the volume fraction of the base fluid increased the fluid velocity and temperature. The volume fraction of alumina and copper nanoparticles decreases the fluid velocity and boundary layer thickness. Furthermore, the slip condition decreases the fluid velocity, and the fluid becomes static if the slip parameter value is greater than fifty. [ABSTRACT FROM AUTHOR]

Stratified Taylor–Couette flow (STCF) undergoes transient growth. Recent studies have shown that there exists transient amplification in the linear regime of counter-rotating STCF. The kinetic budget of the optimal transient perturbation is analysed numerically to simulate the interaction of the shear production (SP), buoyancy flux (BP), and other energy components that contributes to the total optimal transient kinetic energy. These contributions affect the total energy by influencing the perturbation to extract kinetic energy (KE) from the mean flow. The decay of the amplification factor resulted from the positive amplification of both BP and SP, while the growth is attributed to the negative and positive amplification of BP and SP, respectively. The optimal SP is positively amplified, implying that there is the possibility of constant linear growth. These findings agree with the linear growth rate for increasing values of Grashof number. [ABSTRACT FROM AUTHOR]

Background: The mixed convection flow of viscous fluid due to an oscillating plate is inspected. The external heating effects and chemical reaction assessment are predicted. Moreover, the flow applications of the entropy generation phenomenon are claimed. Results: The dimensionless system is expressed in partial differential forms, which are analytically treated with the Laplace scheme. The physical aspects of the flow model are graphically observed. The optimized phenomenon is focused on flow parameters. The results for the Bejan number are also presented. The dynamic of heat transfer and entropy generation phenomenon is observed with applications of Bejan number. Conclusions: It is claimed that an enhancement of entropy generation phenomenon is noticed due to heat and mass Grashof coefficients. The Bejan number declined due to mass Grashof number. Furthermore, the velocity profile boosted due to Grashof constant. [ABSTRACT FROM AUTHOR]

In this research, the Magnetohydrodynamic flow model within a porous vessel containing blood was examined. What makes this study intriguing is the inclusion of a fractional-order derivative term in the Magnetohydrodynamic flow system equations. Fractional derivatives were chosen for their ability to encompass both integer and fractional-order derivatives, leading to more realistic modeling results. The numerical solution for the partial differential equation system was obtained using the finite differences method. Solutions were derived using both central difference and backward difference approaches to enhance the reliability of the results. The Grunwald-Letnikov derivative approach was employed for the fractional derivative term, while the Crank-Nicolson method was applied for other terms. Solutions were obtained for velocity, temperature, and concentration profiles. Subsequently, a thorough analysis was conducted to investigate variations in these solutions for changing values of significant flow parameters such as Hartmann number, Grashof number, solute Grashof number, a small positive constant, radiation parameter, Prandtl number, and Schmidt number. Additionally, the study analyzed changes in the fractional derivative order. Finally, the impact of flow parameters on flow in a nonporous medium was investigated, and the results were presented graphically. The study highlighted the significant effects of various parameters on blood flow. [ABSTRACT FROM AUTHOR]

A detailed study of the erratic circulation around an unbounded inclined plate under fluctuating temperature and isothermal mass dispersion was carried out with a chemical reaction. This work concentrated on the harmonic inclination of the plate in its plane, and the accurate solution of the non-dimensional governing formulations was made possible by the Laplace transform technique. To evaluate their impact on different profiles, the investigation examined a variety of physical factors, including phase inclination, chemical response variable, Schmidt number, thermal Grashof number, mass Grashof number, and duration. Notably, the speed per second increased with decreasing phase angle. Furthermore, a decrease in either the thermal radiation variable or the chemical response variable induced an increase in velocity. [ABSTRACT FROM AUTHOR]

The problem of magnetohydrodynamics of immiscible liquid flow in a channel having inclined orientation with porous space and different types of nanoparticles has been investigated. The channel is separated into two regions. The lower region is filled with Al2O2-water, and the upper region is occupied by Cu-water. The governing equations are numerically solved using R-K 4th-order with a shooting technique to highlight the effect of the magnetic field parameter, Grashof number, inclination angle, viscous dissipation, and the ratio of permeability of two regions. As the Hartmann number increases, there are two regions where the fluid's temperature and velocity decrease. The effects of different nanoparticle combinations on flow variables have also been discussed. Tabulated numerical data for the distribution of shear stress are provided for a range of physical parameters. [ABSTRACT FROM AUTHOR]

The effect of triple diffusion on convection of viscous liquid in a vertical channel saturated with permeable material is explored subject to Robin conditions on the boundaries. Inside the duct, the salts of distinct compositions are diffused. Non‐Darcy approach is used to describe the porous material influence on transport processes. Symmetric and asymmetric heating conditions are considered for the ambient temperatures close to the vertical channel borders. Heat is exchanged between the vertical plates and the external fluid. Initially, the solutions are found without an influence of viscous dissipation and buoyancy forces. Inclusion of these two effects leads to nonlinear equations and adopting Brinkman parameter as the perturbation characteristic for the solutions is procured. Owing to the limitation on the perturbation characteristic, the conservation relations are solved numerically using the Runge–Kutta procedure combined with shooting technique. The flow patterns are depicted for the properties of the heat and mass Grashof numbers, porous parameter, inertial parameter, Brinkman number, Biot numbers, and chemical reaction characteristics. The effects of these parameters are explored on the skin frictions and Nusselt numbers. In the case of dissipations caused by viscosity and Forchheimer drag term, the perturbation results and numerical solutions are equal for low magnitudes of perturbation characteristic. [ABSTRACT FROM AUTHOR]

Adding fins is considered to be a promising method to enhance heat transfer. As for the vertical latent thermal storage tube, it can be observed that the phase change materials in the upper part have much shorter charging time than in the lower part. To further enhance the heat transfer to boost the overall energy storage efficiency and reduce the apparent inhomogeneity of melting characteristics, fins with gradient height are packed. In this study, vertical shell-and-tube thermal energy storage tubes with fins of positive and negative gradient height are analyzed. After using experiments to verify the established numerical model, the phenomenological thermal characteristics are revealed and then additional analysis is used to investigate the thermal characteristics of the charging process, including melting, temperature distributions, and flow features. Results show that the negative gradient fins perform better than the positive gradient fins compared to the uniform ones. Furthermore, the complete melting time is reduced by 32.47% with a measured gradient of −0.8. A 42.11% enhancement in the time-integral average proportion of phase change materials (PCMs) in medium-temperature and a 78.74% suppression in the ratio of overheated PCMs at the final moment are achieved by the negative finned tube of −0.8 compared to a case with uniform fins. A tube with a higher bottom fin has a higher transient maximum velocity of the liquid phase transition material during melting, which also has a time-integral Grashof number (Gr) improvement of 31.46% compared to a uniform fin. The average energy storage is improved by using the negative gradient height fins of −0.8, as much as 1.34 times that of uniform height fins. [ABSTRACT FROM AUTHOR]

Direct numerical simulations are utilised to investigate mass-transfer processes at gas-evolving electrodes that experience successive formation and detachment of bubbles. The gas-liquid interface is modelled employing an immersed boundary method. We simulate the growth phase of the bubbles followed by their departure from the electrode surface in order to study the mixing induced by these processes. We find that the growth of the bubbles switches from a diffusion-limited mode at low to moderate fractional bubble coverages of the electrode to a reaction-limited growth dynamics at high coverages. Furthermore, our results indicate that the net transport within the system is governed by the effective buoyancy driving induced by the rising bubbles and that mechanisms commonly subsumed under the term 'microconvection' do not significantly affect the mass transport. Consequently, the resulting gas transport for different bubble sizes, current densities and electrode coverages can be collapsed onto one single curve and only depends on an effective Grashof number. The same holds for the mixing of the electrolyte when additionally taking the effect of surface blockage by attached bubbles into account. For the gas transport to the bubble, we find that the relevant Sherwood numbers also collapse onto a single curve when accounting for the driving force of bubble growth, incorporated in an effective Jakob number. Finally, linking the hydrogen transfer rates at the electrode and the bubble interface, an approximate correlation for the gas-evolution efficiency has been established. Taken together, these findings enable us to deduce parametrisations for all response parameters of the systems. [ABSTRACT FROM AUTHOR]

Air-cooled heat exchangers in various industries enjoy an increasingly wider use thanks to their environmental friendliness and absence of the need for cooling water. Air-cooled heat exchangers from annular finned tubes are widely used in chemical, petrochemical, oil-refining, gas, and food industries, and also at automobile compressed natural gas filling stations (NGV gas stations), in heat power engineering, electric power engineering, refrigeration technology, and at nuclear power plants. The thermal capacity of air-cooled heat exchangers is largely determined by the characteristics of the motion of a flow of cooling air through them that can be organized with consumption of electric power by means of a ventilator or in an energy-saving regime by free convection. Unfortunately, the region of ambient air temperatures at which it is possible to use air-cooled heat exchangers under the conditions of free convection is limited. Low heat transfer intensity compared to forced convection is the main drawback of the free-convection regime which is usually compensated by an increase in a heat-emitting area, namely, by finning the heat transfer surface. By equipping air-cooled heat exchangers with additional devices making it possible to intensify free convection, the thermal performance of heat exchangers can be improved significantly. The paper provides an overview of experimental and numerical investigations of free-convection heat transfer in annular finned tube bundles with an exhaust shaft installed above them. [ABSTRACT FROM AUTHOR]

The stability of buoyant flow in an infinite vertical fluid layer bounded by imperfectly conducting rigid walls, called imperfectly conducting eigenflows, is discussed. The third kind boundary conditions describing heat transfer to the external environment are applied to perturbations in temperature. The linear stability analysis is carried out numerically by employing the Chebyshev collocation method. Instability arises when the Grashof number G exceeds its critical value, which depends on the Prandtl number P r and the Biot number B i. It is found that the onset of instability changes dramatically depending on the magnitude of Prandtl and Biot numbers particularly when the instability is through the traveling-wave mode. The numerical results show that the Biot number plays a pivotal role in determining the transition Prandtl number P r T at which the instability switches over from one mode to another mode. The novel outcomes suggest the presence of a single P r T for B i < 2.1739 while three distinct values of P r T for B i ≥ 2.1739. The departure from the conventional single value typically observed at isothermal boundaries signifies the complexity of the instability mechanism. [ABSTRACT FROM AUTHOR]

Mixed convective characteristics of the combustion of a nanoparticles-laden fuel (n-butanol nanofluid) in a vented cavity are investigated. The nanofluid and the oxidizer enter the cavity through the inlets on the left and right vertical walls, respectively. However, the resulting product produced from the oxidation process of the fuel exits the cavity through the outlet at the bottom wall. Heat generated from the oxidation process causes natural convection within the cavity. The conjugate effect of natural and forced convection finally gives rise to mixed convection phenomena. In this regard, a mathematical model for mixed convection flow in a vented cavity is formulated with no-slip and isothermal boundary conditions. Having transformed the model into a dimensionless form, the stream function-vorticity formulation is used. The resulting equations are then solved numerically using the finite difference method. Numerical results are illustrated with the streamlines, isotherms, and isolines of fuel and oxidizer concentrations. The maximum values of the stream function (ψmax) and the temperature (θmax) are found to increase with an increase in the Frank–Kamenetskii number (Λ), volume fraction of nanoparticles (φ), and stoichiometric ratio (χ). On the contrary, they decrease with the increase in the Reynolds number (Re). When the Grashof number (Gr) is increased, ψmax increases and θmax decreases. The remaining concentrations of fuel, (CF)min, and oxidizer, (CO)min, are higher for an increase in Gr, whereas the opposite is recognized for increasing Λ. With the increase in Gr and Λ, the steady-state flow in the cavity tends to be oscillating and then chaotic. [ABSTRACT FROM AUTHOR]

This investigation explores the convective MHD stagnation point flow of Casson nanofluid over a stretching sheet in a porous medium with higher-order chemical reactions and multiple slips. The examination of heat transmission is carried out in the presence of radiation, Joule heating, viscous dissipation, and heat source. The system of governing equations was simplified by using appropriate transformations. The transformed equations are tackled numerically by a Runge-Kutta-based shooting technique with the bvp5c MATLAB package. The graphical and numerical results for different parametric values are discussed and presented through figures and tables. It is observed that an increase in the magnetic field, porosity, and Casson fluid parameter reduces the velocity whereas the opposite trend is seen in the case of the thermal Grashof number and the solutal Grashof number. Increasing values of radiation and Joule heating parameters, and the Eckert number, lead to an increase in the temperature. The chemical reaction, suction, and solutal slip were found to reduce the concentration. The friction factor was reduced due to the higher values of the thermal Grashof number, solutal Grashof number, and the velocity ratio parameter. Also, an increase in the Brownian motion and thermal slip parameters decreases the heat transfer rate. The computational results of the Nusselt number have been validated with published results in the literature and found good agreement. The results obtained in this investigation have applications to biomedical, engineering, and industrial sectors such as food processing, polymer manufacturing, glass, and fiber production, improving oil recovery, and material processing. [ABSTRACT FROM AUTHOR]

In this article, the authors investigate the existence and degenerate regularity of trajectory statistical solutions for the 3D incompressible non-Newtonian micropolar fluids in bounded domain. They first prove the existence of the trajectory attractor, and construct the trajectory statistical solution via the trajectory attractor and generalized Banach limit. Then they establish that the trajectory statistical solutions possess degenerate regularity of Lusin's type when the associated Grashof number is small enough. [ABSTRACT FROM AUTHOR]

The aim of the present work is to apply the Caputo-fractional derivative to the heat transformation of unsteady incompressible magnetohydrodynamic (MHD) Casson nanofluid flow. Ethylene Glycol-Graphene oxide and Ethylene glycol-Multiwall Carbon nanotubes considered as nanofluids. The current study helps in understanding the fluid dynamics involved in water purification, energy conservation, solar energy, coolants, cancer therapies, and physiological fluid dynamics. By using appropriate non-dimensional variables, the leading PDE of the problem are non dimensionalized. The governing equations are solved by the combined integral transforms of Fourier sine and Laplace transform technique. For an extensive study of the problem, graphical illustrations and tables are developed by using the MATLAB software. The effects of the order of the Caputo derivative, thermal Grashof number, viscous dissipation, and Casson parameter oscillations on the fractional heat and momentum equations are inspected. The thermal and velocity profiles are increased for thermal Grashof number and Casson parameter. Symmetry phenomena are also observed in the case of cooling and heating plate for thermal Grashof number. Different shapes of nanoparticles are performed for ordinary fractional parameters which is increased for temperature as well as velocity. [ABSTRACT FROM AUTHOR]

This paper studies the mixed convective flow of a magnetohydrodynamic micropolar fluid over an extending sheet. The first-order velocity slip condition is taken to observe the slip flow of the fluid. The applications of solar radiation toward the micropolar fluid flow are analyzed in this paper. Furthermore, the Brownian motion, thermophoresis and Joule heating impacts are also studied. Also, the Cattaneo-Christov heat flux model, chemical reaction and activation energy are observed. The leading PDEs have been transformed to ODEs and then solved with the help of homotopy analysis technique. The impacts of different physical parameters have been evaluated theoretically. The outcomes exhibited that the material factors have augmented the microrotation and velocity profiles. Moreover, the velocity slip parameter has a reverse relation with velocity and microrotation profiles, while there is a direct relation of a velocity slip with the energy curve. The velocity profile has increased with higher thermal and mass Grashof numbers. With increasing Brownian motion parameter, the thermal profile is amplified while the concentration profile is declined. On the other hand, the thermal and mass profiles have been boosted with greater thermophoresis parameter. The velocity profile has decreased with higher magnetic parameter, whereas the temperature profile has augmented with higher magnetic parameter. The couple stress and skin friction have been augmented with material parameter, whereas the skin friction has been reduced with thermal and mass Grashof numbers. [ABSTRACT FROM AUTHOR]

This work presents a theoretical numerical study of the bioconvection flow of Prandtl–Eyring nanofluid through a stretching cylinder with gyrotactic microorganisms. The mathematical model developed also incorporated the inclined magnetic field and heat generation effects. Further, stratification conditions are considered at the boundary of the stretched cylinder. The described flow problem conducting coupled high‐order partial differential equations (PDEs) is first reduced to the nonlinear system of ordinary differential equations (ODEs) by introducing suitable mathematical transformations. The resulting highly nonlinear flow equations are treated numerically by applying the shooting method. A comparison of the adapted method with previously reported data is also made to validate the presented results. The comparisons are in excellent agreement. The individual effect of controlling flow parameters/numbers on the flow profiles and physical quantities of engineering interest are represented graphically with physical descriptions. The significant results of the present analysis revealed that a rise in bioconvection Rayleigh number, thermal Grashof number, and angle of inclination boosts the velocity profile. The study shows that thermal stratification, mass stratification, and motile density stratification parameters diminish the temperature, concentration, and microorganism profiles, respectively. The nondimensional Sherwood number is decelerated significantly by thermophoresis and mass stratification parameters. [ABSTRACT FROM AUTHOR]

We examine how stationary solutions to Galerkin approximations of the Navier–Stokes equations behave in the limit as the Grashof number $ G $ tends to $ \infty $. An appropriate scaling is used to place the Grashof number as a new coefficient of the nonlinear term, while the body force is fixed. A new type of asymptotic expansion, as $ G\to\infty $, for a family of solutions is introduced. Relations among the terms in the expansion are obtained by following a procedure that compares and totally orders positive sequences generated by the expansion. The same methodology applies to the case of perturbed body forces and similar results are obtained. We demonstrate with a class of forces and solutions that have convergent asymptotic expansions in $ G $. All the results hold in both two and three dimensions, as well as for both no-slip and periodic boundary conditions. [ABSTRACT FROM AUTHOR]

The analysis of blood flow in the stenotic artery is imperative as the existence and progression of stenosis effectively disturbs the blood flow in the artery, which may cause vascular disease. In this study, we considered the linearized Phan-Thien–Tanner (PTT) fluid model to study the non-Newtonian nature of blood flow in the stenosed artery inclined at an angle γ. The artery is considered to have multiple stenoses and a cross-section of elliptical shape. The PTT model is appropriate for this analysis as viscoelastic properties and shear-thinning characteristics characterize it. The elliptical cross-section of the artery raises the nonlinearity of the mathematical model and makes it effortful to solve the equations analytically. The mathematical equations of the model are processed to non-dimensional form under the assumptions of mild stenosis, which help us to get the exact solutions of the equations in the elliptical domain. The analytically acquired solutions are investigated in detail by their graphical interpretation. It is analyzed that progressive height of stenosis generates the more significant disorder in the narrowed part of the channel as the velocity reverses its behavior in that region. The advancing values of the Weissenberg number, Grashof number and extensional and heat source parameters cause to lessen the axial velocity and slow the fluid flow. The rising Grashof number has nearly no impact on the velocity in the center of the channel. The wall shear stress aggrandizes with the growth of stenosis height, and its behavior for other physical constraints is similar to the flow velocity. It also has a practical enhancement in the stenotic region of the conduit. It is observed that fluid velocity and wall shear stress have larger values for zero angles of inclination than the inclination angle of 9 0 ∘ . The streamlined examination indicates the generation of the vortices in the stenotic part of the artery. Moreover, the flow velocity and wall shear stress have lower values for the nonuniform shape than for the uniform form of stenosis. [ABSTRACT FROM AUTHOR]

A vertically oscillating plate with a temperature difference and mass diffusion is used to investigate the role of thermal radiation and chemical reaction in the unexpected convection flow of a viscous unstable rotating fluid. The results of the calculations indicate that the fluid is a grey medium that absorbs and emits radiation. With time, both the plate's and the surrounding environment's temperatures and concentrations rise. The Laplace transform method finds solutions to the dimensionless governing equations for a plate, which is oscillating in its own plane. In relation to one another, the phase angle, radiation parameter, Schmidt number, thermal Grashof number, mass Grashof number, and time are all investigated. [ABSTRACT FROM AUTHOR]