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In this innovative study, a unique approach was engaged to simulate the flow characteristics of nanofluid inside a tank featuring a surface subjected to uniform flux. The testing fluid for this investigation was fabricated by incorporating alumina powders with varying shapes into water. The derivation of the final equations involved the application of Darcy’s law and the formulation of the stream function. The container experienced the combined efficacy of both the Lorentz force and gravity forces. The incorporation of additives resulted in a significant enhancement of the Nusselt number (Nu), demonstrating an increase of 19.8% and 40.28%, contingent on the magnitude of the Hartmann number (Ha). Moreover, an elevation in the shape factor led to a notable rise in Nu by 14%. Remarkably, as the Ha increased, there was a substantial reduction in the cooling rate by 51.33%. Furthermore, in the absence of the Ha, an escalation in the Rayleigh number (Ra) caused Nu to surge by 65.8%. This study holds paramount importance as it introduces a novel technique for simulating nanofluid flow with a sinusoidal surface, providing valuable insights into the complex interplay of forces within the container. The utilization of varying shapes of alumina powders adds a layer of sophistication to the experimentation, making this investigation a noteworthy contribution to the existing body of knowledge. The findings not only enhance our understanding of heat transfer dynamics but also offer practical implications for applications involving nanofluids in containers with nonuniform surfaces subjected to heat flux.

This paper presents a numerical solution to the problem of time-dependent blood flow via a w-shaped stenotic conduit, driven by pulsatile pressure gradient. The problem is formulated in cylindrical coordinates by employing the theoretical model of tangent hyperbolic fluid. The electro-osmotic effects are also taken into consideration. To simplify the non-dimensional governing equations of the flow problem, a mild stenosis assumption is utilized and the impact of the blood vessel wall is mitigated by employing a radial coordinate transformation. An explicit finite difference method is used to solve the resulting nonlinear system of differential equations, considering the auxiliary conditions specified at the boundary of the blood channel. After obtaining the numerical solution to the problem, an examination is carried out for various flow variables, such as axial velocity, temperature field, mass concentration, skin friction, Nusselt number, and Sherwood number. These results are presented graphically, and a concise explanation is provided using physical facts. An increase in flow rate and blood velocity leads to a rise in response, while an increase in stenosis height, Weissenberg number, and power-law exponent leads to a reverse response. Furthermore, the temperature field is significantly affected by the Brinkman number and the Prandtl number.

Transport properties of hydrocarbon liquid-based nanofluids in non-Darcy media have key significance in chemical, thermal and mechanical engineering. Therefore, the key focus of this research is to investigate the transport mechanism in nanofluid using Koo–Kleinstreuer–Li (KKL) thermal conductivity model in non-Darcy media under squeezing and permeable effects. The functional fluid is a homogenous mixture of Cu and kerosene. The problem formation is carried out via nanofluid-enhanced properties and similarity rules. Then numerical scheme was endorsed for the results analysis under increasing physical ranges. It is observed that the velocity $F(\eta )$ increased when the values of ${\alpha }_1$ vary from 1.0 to 4.0. However, quick particles movement is noticed for ${\gamma }_1$ for 1.0–4.0 and $-$1.0 to $-$4.0. Further, the thermal process in Cu/kerosene depreciates for ${\alpha }_1=0.5$, 1.0, 1.5, 2.0, ${\gamma }_1=2$, 4, 6, 8 and ${\gamma }_1=-2.0$, $-$4.0, $-$6.0, $-$8.0, respectively. The stronger permeability of the lower plate highly reduced the fluid movement and depreciation in the movement can be optimized when the fluid sucks from the channel through the lower plate.

This paper focuses on applying the Corcione model to the microchannel. The Corcione model is highly relevant because it provides accurate empirical relationships for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. These qualities are crucial for building and improving different thermal systems. The model presents and discusses two simple empirical correlating equations for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. Hence the aim of this work is to use Corcione’s model to demonstrate the fully developed laminar flow of an electrically conducting nanoliquid through an inclined microchannel. The energy equation takes into account the physical impacts of the heat source/sink, temperature jamp, and viscous dissipation. TiO₂ nanoparticles in water are taken into consideration in this work for enhanced cooling. Using the numerical program Maple, Runge–Kutta–Fehlberg 4th–5th-order method is utilized to solve the present research. Making use of graphs, all of the flow parameters are shown, and the physical consequences on the flow and temperature profiles are thoroughly examined. It is noted that a higher inclined angle enhances the velocity profile whereas a larger temperature jump declines the temperature profile. Furthermore, Corcione’s model often has greater velocities, temperatures, and reduced surface drag forces than the Tiwari–Das model.

In this research, a novel design stochastic numerical technique is presented to investigate the unsteady form magnetohydrodynamic (MHD) slip flow along the boundary layer to analyze the transportation and heat transfer in a solar collector through nano liquids which is a revolution in the field of neurocomputing. Thermal conductivity in variable form is dependent on temperature and wall slips are assumed over the boundary. For mathematical modeling, the solar collector is assumed in the form of a nonlinear stretching sheet and a quite new artificial neural networks (ANNs) based approach is used to solve the current problem in which inverse multiquadric radial basis (IMRB) kernel is sandwiched between a global search solver named genetic algorithms (GAs) and a highly effective local solver named sequential quadratic programming (SQP) i.e. IMRB-GASQP solver. The governing boundary value problem is altered in the form of a system of nonlinear ordinary differential equations (ODEs) through the utilization of similarity transformation and then the obtained system of ODEs is solved using IMRB-GASQP solver by altering the values of distinguished parameters involved in it to observe the fluctuation in the velocity and temperature profiles of nanofluid. The obtained results are effectively compared with the reference solutions using the Adams numerical technique in graphical and tabulated form. An exhaustive error analysis using performance operators is presented while the efficacy of the designed solver using various statistical operators is also part of this research.

The diffusion process of the nanofibers in a nanofluid displays a combination of diffusion and wave characteristics. The wave-like behavior is attributed to the large aspect ratio of the nanofiber, which can be modeled as a bead-spring chain system, exhibiting wave-like properties. In order to describe this mixed diffusion-wave phenomenon, a fractional diffusion-wave equation is proposed, wherein multiple time fractional derivatives are employed. By appropriately regulating the fractional time terms, the model can be transformed into either the traditional diffusion equation or the traditional wave equation, as required. A numerical schedule is developed through the implementation of suitable time and space discretization, and a stability analysis is conducted. The numerical results substantiate the reliability of the numerical schedule and its applicability to other fractional differential equations.

The impact of nanoliquid in the evolution of various industries and electronic devices is very remarkable. Motivated by these uses, this exploration describes the second law analysis in the Maxwell two-phase nanoliquid subject to the Lorentz force due to axisymmetric heated convective rotating flow with microorganisms and slip conditions. Thermal radiation, thermal variable conductivity, and chemical reaction are examined in the heat and concentration equation. The mass equation has been accounted for through the chemical reaction. Additionally, the physical properties of the entropy rate are considered. The constitution equations have been transformed into dimensionless form through the suitable transformation. The reduced system of equations has been solved analytically by the homotopy analysis method (HAM). The physical variables on Bejan number, entropy minimization, microorganism, concentration, velocity, and temperature distributions have been presented in graphical form. Computational results of moment coefficient, heat, mass, and motile density versus other factors are examined. The Maxwell fluid and slip variable display a reduction in radial velocity. An increase in the stretching parameter. The thermal layer is enlarged against the larger values of variable thermal conductivity, thermal radiation, and Biot number. Entropy generation and Bejan number are escalated due to the augment in the temperature difference variable, Brikamann number, and magnetic field.

The AISI H11 is widely used for making tools, dies and aircraft landing gears, due to its outstanding mechanical characteristics and superior wear resistance. However, these distinctive properties make it difficult to cut material. Deprived surface characters, high tool wear and higher manufacturing costs are concomitant with the machining of AISI H11. To limit the effects of the mineral oil-based flooding technique which affects the operator’s wellbeing, a vegetable oil-based minimum quantity lubrication (MQL) is represented as an alternative. In this study, graphene nanoplatelets (GNPs)-enhanced green sesame oil-based MQL is chosen for end milling. Initially, the nanofluid characteristics such as density, thermal conductivity, viscosity and surface tension at various concentrations are studied. Later, cutting temperature, surface finish, burr development, chip morphology and crystallographic structure are thoroughly examined. The results indicate that the MQL environment with nanofluid decreases the temperature by 75% and 15% compared with dry condition machining and conventional MQL environments, respectively; whereas the surface roughness reduction is observed to be 73% and 18% as compared with aforementioned atmospheres. Burr formation reduction is seen in the optical microscope examination. The smaller grain size of the machined surface and minimal amount of fibrous and curve chips show the superiority of the proposed cooling environment.

Here the Cattaneo–Christov double diffusion model explores the mixed convective flow of third-grade nanoliquid on a stretchable surface with Riga device diverging from the traditional Fourier and Fick’s law. The model incorporates entropy optimization and Soret–Dufour effects, offering a unique perspective on heat and mass transfer phenomena. By employing relevant transformations, the complex partial differential equations are converted into more manageable ordinary differential systems. An optimal analysis method is then applied to solve the resulting nonlinear differential system, shedding light on the intricate interplay of various physical variable. Through the utilization of plots, the study delves into the impact of these physical variable, providing insights into the behavior of the system under different conditions. This comprehensive approach not only enhances our understanding of the underlying mechanisms governing the convective flow of nano-liquids, but also highlights the significance of considering nonclassical models in thermal and mass transport studies. The key finding of this study is that fluid velocity enhances for material parameters due to low viscosity. Temperature and nanoparticle concentration enhance for higher values of Dufour and Soret numbers, respectively. For higher estimations of Reynold number, entropy of the system decreases.

The main motivation of this study is to examine the effects and behavior of Casson nanofluid mainly in reference to oblique stagnation points across a stretching surface. Oblique stagnation point (OSP) motions have so many applications, like artificial fibers, sticky materials, drying paper, and freezing electrical equipment, and numerous applications for endothermic and exothermic processes exist, including in heat exchangers, cooking, and drying damp clothes. Because of these applications on various domains, the Casson nanofluid OSP motion via a stretching sheet is studied with endothermic/exothermic chemical processes and convective boundary conditions (CBC). Similarity transformations are employed to convert partial differential equations (PDEs) into a collection of ordinary differential equations (ODEs). Furthermore, some significant engineering coefficients are discussed and also evaluated the behaviors of several nondimensional factors using the Runge–Kutta–Fehlberg-45 numeric method with a shooting scheme and graphical representations. The outcomes signify that temperature and concentration both rise with a rise in the Casson parameter and activation energy (AE) respectively. A higher Biot value leads to a higher temperature profile. A temperature profile increases with an enhance in the Casson parameter. The addition of a solid fraction will enrich the mass transmission rate in combination with AE.

This paper investigates the effects of radiation, internal heat source and magnetohydrodynamics (MHD) on the mixed convective boundary layer flow of a Casson nanofluid within a porous medium that is saturated and subject to an exponentially stretching sheet. The nanofluid model incorporates Brownian motion and thermophoresis, and the Darcy model is employed for the porous medium. By applying an appropriate similarity transformation, the nonlinear governing boundary layer equations are converted into a set of nonlinear coupled ordinary differential equations. These equations are then solved numerically using the Hermite wavelet method, with simulations conducted through the MATHEMATICA programming language. The analysis covers various aspects including temperature distribution, velocity, solute concentration and several engineering parameters such as skin friction coefficients, the Nusselt number (rate of heat transfer) and the Sherwood number (rate of mass transfer), all evaluated based on dimensionless physical parameters. The results indicate that elevated radiation intensifies temperatures and leads to thicker thermal boundary layers. As the Casson parameter increases, both the velocity and the momentum boundary layer become narrower. Additionally, a more pronounced chemical reaction rate reduces the thickness of the solutal boundary layer. The accuracy and reliability of the numerical Hermite wavelet method are validated through a comparative analysis with previous studies, demonstrating excellent concordance and confirming the robustness of the computational approach.

Water-based ‘nanofluid’ flow owing to an unsteady stretched surface is inspected in this paper considering Stefan blowing and thermal radiation. ‘Similarity transformations’ are applied to reduce the governing ‘partial differential equations’ (PDEs) for momentum, energy and concentration into ‘nonlinear’ ‘ordinary differential equations’ (ODEs). By using a shooting technique, those equations are solved numerically with the help of fourth-order ‘Runge–Kutta method’. ‘Wall shear stress’ rises but ‘heat transfer’ as well as ‘mass transfer coefficients’ reduce for the augmentation in ‘Stefan blowing/suction parameter’. ‘Temperature’ and ‘concentration’ of nanoliquid are found to rise but liquid’s ‘velocity’ reduces for the growing of ‘nanoparticle’s volume fraction’. Liquid’s ‘velocity’ and ‘concentration’ are observed to decrease for enhanced ‘Lewis number’. Based on the results presented here as well as their anatomical analysis, the relevant parameters significantly affect the stream, warmth and mass transports.

The problem of a steady boundary layer MHD slip flow over a stretching sheet in a water-based nanofluid containing different type of nanoparticles: Cu, Al₂O₃ and Ag has been investigated. An external strong magnetic field is applied perpendicular to the plate and the Hall effect is taken into consideration. The surface of the stretching sheet is assumed to move with a linear velocity and subject to power-law variation of the surface temperature. The governing partial differential equations are transformed into nonlinear ordinary differential equations using a similarity transformation, before being solved numerically by a Runge–Kutta–Fehlberg method with shooting technique. Effects of the physical parameters on the primary velocity, the secondary velocity and the temperature as well as on the wall shear stress and the rate of heat transfer have been presented graphically and discussed in detail. Investigated results indicate that the nanoparticle volume fraction and the slip parameter produce opposite effects on the skin friction coefficients of the primary and secondary flow. Also, the nanoparticle volume fraction and the types of nanoparticles demonstrate a more pronounced influence on the secondary flow than that on the primary flow and temperature distribution.

The aim of this work is to conduct numerical study of fluid flow and natural convection heat transfer by utilizing the nanofluid in a two-dimensional horizontal channel consisting of a sinusoidal obstacle by lattice Boltzmann method (LBM). The fluid in the channel is a water-based nanofluid containing Cuo nanoparticles. Thermal conductivity and nanofluid’s viscosity are calculated by Patel and Brinkman models, respectively. A wide range of parameters such as the Reynolds number ($\mathrm{\text{Re}}=100$–400) and the solid volume fraction ranging ($\mathrm{\Phi }=0$–0.05) at different non-dimensional amplitude of the wavy wall of the sinusoidal obstacle ($A=0$–20) on the streamlines and temperature contours are investigated in the present study. In addition, the local and average Nusselt numbers are illustrated on lower wall of the channel. The sensitivity to the resolution and representation of the sinusoidal obstacle’s shape on flow field and heat transfer by LBM simulations are the main interest and innovation of this study. The results showed that increasing the solid volume fraction $\mathrm{\Phi }$ and Reynolds number Re leads to increase the average Nusselt numbers. The maximum average Nusselt number occurs when the Reynolds number and solid volume fraction are maximum and amplitude of the wavy wall is minimum. Also, by decreasing the $A$, the vortex shedding forms up at higher Reynolds number in the wake region downstream of the obstacle.

Recently, various ways are investigated to augment heat transfer in different applications such as porous ceramic domain. Adding nanoparticles to fluid is the best operational way to increase the conduction of fluids. In this paper, migration of nanofluid inside a porous duct under the impact of magnetic force is scrutinized. LBM is applied to present comprehensive parametric analysis for various concentrations of nanofluid, Hartmann, Reynolds, and Darcy numbers. Outputs illustrate that Nu augments with improve of Lorentz forces. Augmenting Da significantly enhances the convective flow in our model.

Magnetohydrodynamic flow of nanofluids and heat transfer between two horizontal plates in a rotating system have been examined numerically. In order to do this, the group method of data handling (GMDH)-type neural networks is used to calculate Nusselt number formulation. Results indicate that GMDH-type NN in comparison with fourth-order Runge–Kutta integration scheme provides an effective means of efficiently recognizing the patterns in data and accurately predicting a performance. Single-phase model is used in this study. Similar solution is used in order to obtain ordinary differential equation. The effects of nanoparticle volume fraction, magnetic parameter, wall injection/suction parameter and Reynolds number on Nusselt number are studied by sensitivity analyses. The results show that Nusselt number is an increasing function of Reynolds number and volume fraction of nanoparticles but it is a decreasing function of magnetic parameter. Also, it can be found that wall injection/suction parameter has no significant effect on rate of heat transfer.

Computational studies have been widely applied for the thermal evaluation of the nanomaterial thermal feature in different industrial and scientific issues. The squeezed flow and heat transfer features for Al₂O₃-water nanofluid among analogous plates are investigated using the GOHAM and its validity is verified by comparison with existing numerical results. Novel aspects of Brownian motion and thermal force were accounted in the simulation of nanomaterial flow within parallel plate. Analytical investigation has been done for diverse governing factors namely: the squeeze, chemical reaction factors and Eckert number. The obtained outcomes show that $|C_f|$ has direct relationship with absolute values of squeeze factor. Nu increases for large Eckert number and absolute values of squeeze number.

Lattice Boltzmann method (LBM) was used to simulate two-dimensional MHD Al₂O₃/water nanofluid flow and heat transfer in an enclosure with a semicircular wall and a triangular heating obstacle. The effects of nanoparticle volume fraction ($0\le \varphi \le 0.05$), Rayleigh number $(10^4\le Ra\le 10^6)$, Hartmann number $(0\le Ha\le 60)$ and heating obstacle position (Cases 1–7) on flow pattern, temperature distribution and rate of heat transfer were investigated. The results show that with the enhancing Rayleigh number, the increasing nanoparticle volume fraction and the reducing Hartmann number, an enhancement in the average Nusselt number and the heat transfer appeared. The effect of Ha on the average Nu increases by increasing the Ra. It can also be found that the action of changing the heating obstacle position on the convection heat transfer is more important than that on the conduction heat transfer. The higher obstacle position in Cases 6 and 7 leads to the small value of the average Nusselt number. Moreover, the effect of Ha on average Nu in Case 1 at $Ra=10^6$ is more significant than other cases because the flow pattern in Case 1 is changed as increasing Ha.

In this paper, the natural convection flow in a square cavity filled with nanofluid water-${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$ with a hot circular cylinder in the center of the cavity is numerically analyzed. All the walls are in lower temperatures than the circular cylinder. The Navier–Stokes and energy equations in the primitive variable form are discretized and solved by the finite element method (FEM). The effect of the volume fraction, the radius of the circular cylinder, the temperature and Rayleigh number is considered on the average Nusselt number. For the calculation of the viscosity coefficient and thermal conductivity coefficient of water-${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$ nanofluid, an experimental model is used which is the function of the volume fraction, temperature and nanoparticles diameter. This model is compared to the Brinkman model for viscosity and Maxwell model for thermal conductivity which are only the functions of volume fraction and are used by many researchers. The results show the experimental model leads to different results in comparison with the Brinkman model and Maxwell model, and indicate that the rate of the heat transfer can increase or decrease with the increase in volume fraction and temperature.

The countless applications of nanofluids in the improvements of nanotechnology, thermal and physical analogies have attracted our attention to frame an unsteady mathematical model for bi-directional flow of a Newtonian nanofluid over a stretching sheet with the potencies of nonzero and zero mass fluxes. Mathematically, this newly presented analysis is more genuine, where the action of a prescribed heat source at a stretching surface is used to control the distribution of heat. Mathematical formulation is carried out using a novel two-phase nanofluid model. Dimensionless forms of governing equations are obtained with the help of a suitable set of variables. The transformed equations are then solved by using an innovative computational technique, namely, Keller–Box approach. Moreover, the convergence of the numerical solution has been discussed via grid-independence tactic. The results for reduced Nusselt and Sherwood numbers have been arranged in the form of a table with CPU run time. Graphical illustrations have been presented for concentration and temperature distributions. It is inspected that escalating amounts of heat distribution indices reduce the mass concentration and the temperature of the nanomaterial. Rate of heat transference is noticed approximately 228.62% higher, while rate of mass transference is observed approximately 16.79% lower when analysis is shifted to zero mass flux environment from nonzero normal mass flux environment.