Variable Fluid Properties Research Articles

Soret and Dufour effects on MHD mixed convective unsteady flow over stretching sheet with variable fluid properties and convective boundary condition

In several industrial and engineering applications, variable fluid properties play a major role in flow and heat transport processes. The goal of this communication is to analyse the Soret and Dufour effects for an unsteady MHD flow past a stretching sheet under the influence of temperature-dependent viscosity and thermal conductivity along with the convective boundary condition. The governing partial differential equations are transformed into nonlinear coupled ordinary differential equations with the help of similarity transformations, and a numerical analysis is done by using bvp4c, MATLAB’s built-in solver. The flow properties and heat transfer characteristics have been depicted graphically and numerically. Results show that the wall temperature gradient improves by about 8.5%, while the temperature of the fluid near the stretching sheet significantly improves upon increasing the Biot number. Employing fluids with higher viscosity and thermal conductivity consequently leads to a reduction of the wall temperature gradient by about 0.3% and 10.7%, respectively. Also, as the unsteadiness parameter increases, the wall-skin friction, heat and mass transfer rates significantly rise by about 10.4%, 4.4%, and 9.8%, respectively. Further, to verify the accuracy of the generated results, the computed results have been compared with published literature.

Natural convection and variable fluid properties of tangent hyperbolic nanofluid flow with Cattaneo-Christov theories and heat generation

The main aim behind this work is that we have to determine the enhancement that happens in thermal conductivity by using the Buongiorno model of nanofluid when the nanofluid particles are added to the tangent hyperbolic base fluid moving above the stretched surface. The viscosity of tangent hyperbolic nanofluid is assumed to be temperature-dependent. The modified form of the Fourier law of heat conduction motivated us; therefore, the Cattaneo-Christov heat and mass flux model is considered to observe its significance for heat and mass transport. The chemical reaction and heat generation are also considered to determine their influence on temperature and concentration gradients. This study is crucial because of its application in industrial manufacturing processes such as the coating of wire, the thinning of copper, the production of paper, photographic films, hot rolling, and the purification of crude oil. In electronic cooling systems, the efficient dissipation of heat in smartphones, computers, and data centers is critical to preventing overheating. Nanofluids, with their enhanced thermal properties, can significantly improve heat transfer rates, ensuring better performance, stability, and energy savings. The partial governing equations arising from fluid flow, mass, and heat transfer are transformed into ordinary differential equations via appropriate similarity variables. The obtained ordinary differential equations are solved numerically by using the Runge-Kutta Fehlberg method in the MATLAB software. The effects of the emerging parameters are represented through graphs. According to the results, the velocity profile upsurges due to the natural convection parameters and curvature parameter, while the power law index declines the velocity profile. As the Brownian motion coefficient rises, the concentration profile diminishes while the temperature profile increases. Both the concentration and temperature profiles increase for larger values of the thermophoresis parameter. The concentration profile declines for larger values of chemical reaction parameters, and enhancement happens in the temperature region.

Tangent hyperbolic MHD nanoliquids on non-isothermal stretched sheets: Analyzing the impact of transport parameters, variable fluid properties and convective boundary conditions

The key focus of this research is to look at how tangent hyperbolic magnetohydrodynamic (MHD) nano-liquids move in a non-isothermal coagulated stretched sheet. In this study, we intend to explore how fluid behavior responds to alternations in transport physical parameters. The coagulated sheet is subjected to two distinct boundary conditions to inspect the heat and mass transport rate of the nano liquid. The convective heat boundary condition (CBC) and mass-convective boundary condition (MCBC) are employed to specify the physical conditions at the boundaries of the problem domain. The boundary conditions, responsible for regulating heat flow and mass transfer rates, play a crucial role in shaping the liquid’s behavior. Using a similarity solution, the partial differential equation describing the flow of mass and heat within the system transforms into an interconnected network of non-linear ordinary differential equations. These mathematical equations are subsequently figured out using a numerical finite difference method. This study additionally examines the correlation between thermophoresis and Brownian motion, two fundamental concepts in the dynamics of colloidal suspensions. The study’s findings indicate that the temperature profile increases in all scenarios when the variable thermal conductivity and variable viscosity parameters are increased. In contrast, for the same parameters, the velocity profile is decreased. Further, increasing wall thickness reduces heat dissipation; consequently, the temperature profile similarly affects the velocity power index. The Biot number improves the rates of temperature transfer. These results underscore the significant influence of these parameters in predicting the behavior of MHD tangent hyperbolic nanofluids. This study elucidates the intricate interaction among different physical parameters in the dynamics of nano liquids, which holds significant implications for various industrial applications.

Flow and heat transfer insights into a chemically reactive micropolar Williamson ternary hybrid nanofluid with cross-diffusion theory

Abstract The need for efficient nanotechnology has led to unexpected developments. Conserving continuous thermal propagation is essential in many industrial and thermal systems because it improves the efficiency of thermal engineering engines and machinery. Therefore, a promising platform to increase thermal power energy is the hybridization of magnetic nanoparticles in a heat-supporting, non-Newtonian fluid. In light of the above applications, a mathematical model is established to analyze the variable fluid features of the thermally radiative and chemically reactive flow of a micropolar Williamson ternary hybrid nanofluid with electromagnetohydrodynamic and electroosmosis forces on a porous stretching surface. Stratification boundary conditions and variable fluid properties were used to analyze the thermal and solutal behavior of the fluid flow. Furthermore, to measure the disorder of the flow system, entropy generation was considered by the impact of Joule heating and viscous dissipation. To develop the numerical scheme BVP4C in MATLAB, we first converted the mathematical flow model into two ordinary differential equations using a suitable transformation. The graphical and numerical results were determined against several parameters of a ternary hybrid nanofluid ( MWCNT , A l 2 O 3 , SiC ) ({\rm{MWCNT}},\hspace{0.25em}{\rm{A}}{{\rm{l}}}_{2}{{\rm{O}}}_{3},\hspace{0.25em}{\rm{SiC}}) and unary nanofluid ( A l 2 O 3 ) ({\rm{A}}{{\rm{l}}}_{2}{{\rm{O}}}_{3}) . The results indicate that the heat transfer rate is more prominent in the ternary hybrid nanofluid than in the unary nanofluid because the addition of nanofluids to the base fluid is used to improve the heat transport rate. It can be seen from the figures that a greater estimation of the magnetic and electric field parameters improves the fluid velocity because, for low values of M ≤ 1 M\le 1 , the aiding force is dominant compared to the retarding force, which results in an improvement in the velocity profile. Furthermore, the entropy generation rate increases for higher values of the Brinkman number and temperature ratio parameter because more heat is produced due to the greater values of Br {\rm{Br}} .

Numerical investigation of the effects of variable fluid properties on cilia-driven flow of tangent hyperbolic fluid in a channel with heat and mass transfer: A new approach to microfluidic pumps

Heat, mass transfer, and non-Newtonian fluid flow processes have gained significant interest in various industrial applications due to their substantial significance in the fields of technology, engineering, and science. The aforementioned processes hold significance in the context of polymer solutions, porous industrial materials, ceramic processing, oil recovery, and fluid beds. This study aims to investigate the impact of temperature-dependent viscosity and thermal conductivity on the cilia-driven flow of tangent hyperbolic fluid with mass and heat transfer. The objectives include analyzing how these variable properties affect the velocity, temperature, and concentration profiles within the fluid flow, thereby providing insights into potential applications in bioenergy systems and enhancing the understanding of non-Newtonian fluid dynamics. Viscous dissipation has been taken into consideration. Firstly, governing nonlinear coupled equations are solved in a fixed frame, and then the results are tracked in the wave frame. MATHEMATICA's NDSolve command is utilized to graphically discuss the findings for several different flow parameters. Analytically stated, solving a problem with such a coupled and nonlinear system is tough. The effect of new parameters is discussed on velocity and temperature profile and graphically shown. It has been observed that the thermal conductivity is improved at moderately low temperatures, whereas the opposite pattern is seen at comparatively high temperatures. On the other hand, the temperature distribution demonstrates a behaviour consistent with lowering as the number of heat Bolus increases. The findings that were provided offer beneficial insight into bioenergy systems and serve as a helpful benchmark for both experimental and extra-progressive computational Multiphysics models.

Variable coefficient-informed neural network for PDE inverse problem in fluid dynamics

Variable-coefficient equations are crucial in the field of fluid dynamics as they accurately capture the spatial and temporal variations of fluid properties. In many cases, there exist some constraints among multiple coefficients and embedding these constraints into neural networks poses a challenge. In this paper, we design a variable coefficient-informed neural network (VCINN) to address the inverse problem of variable-coefficients partial differential equation in fluid dynamics. The VCINN framework integrates the physics-informed neural network (PINN) with the constraints among multiple coefficients, encoding both constraints and physics information into the neural networks. Compared to classical PINN, VCINN enjoys such several advantages as parallelization capacity, embedding constraint information and efficient hyperparameter adjustment. Through series of examples, the capability of the approach to recover coefficients from observations has been demonstrated. Numerical results indicate that the present method achieves higher accuracy and lower training error compared to classical PINN.

Study on fluid phase behavior characteristics of low permeability reservoir under different CO2 injection amounts

M reservoir is a low peremeability reservoir located in northwest China. Currently, it faces the problem of difficult water injection, low single well production, and rapid production decline. CO2 flooding technology is considered to be implemented to solve these problems by effectively supplementing formation energy. Considering that the phase behavior of reservoir fluid during CO2 injection and its influence on the development effect are complex, the PVT test experiment of reservoir fluid is carried out to analyze the variation of reservoir fluid properties under different CO2 injection volumes. The experimental results show that the saturation pressure, solution gas-oil ratio, volume coefficient and expansion coefficient of crude oil increase with the increase of CO2 injection, while the viscosity and density of oil continue to decrease. When the CO2 injection amount reaches 32 %, the dissolved gas-oil ratio increases from the original 36.2 m³/m³to 150.2 m³/m³, the viscosity of the formation oil is reduced by about 76 % than before CO2 injection; and the volume of crude oil has expanded to 1.28 times of that without CO2 injection. Moreover, the P-T phase diagram is drawn and the influence of CO2 injection on the distribution of phase regions in the phase diagram and the critical parameters of oil is analyzed. The high pressure physical properties of reservoir fluids at different CO2 injection volumes are obtained, which can provide a good foundation for the study of enhancing oil recovery by CO2 injection in M reservoir.

Multi-scale nonlinear reservoir flow simulation based on digital core reconstruction

During the exploitation of oil and gas reservoirs, changes in reservoir physical or fluid properties will lead to alterations in formation seepage capacity, subsequently impacting the productivity of oil and gas wells. Therefore, it is crucial to evaluate the variations in reservoir physical and fluid properties as well as their influence on oil and gas well productivity during reservoir exploitation.It employs a descriptive approach to investigate cross-scale (i.e., micro-scale → small-scale → large-scale) fluid seepage phenomena in water flooding. By leveraging digital core reconstruction technology and focusing on micro-pore network simulation, it establishes an analytical framework for studying cross-scale seepage fields, facilitating the exploration of the micro-seepage mechanism that governs non-homogeneous water flooding's impact on liquid production capacity within a reservoir. Integrating constraints from micro-pore network simulation and small-scale core displacement test data, while considering macro-heterogeneity near wellbore areas as flow unit divisions and superposition bases within large-scale reservoirs, it reveals the nonlinear flow characteristics of changes in liquid production capacity in water-flooding oil reservoirs based on microscopic digital core analysis. This approach aligns with findings from small-scale core testing and sweep coefficient correction while also addressing the non-uniform distribution characteristics of physical parameters within large-scale reservoirs.By integrating permeability field characteristics at three levels, this approach optimizes its technical advantages in describing dynamic permeability fields at each level, thereby facilitating precise prediction of water drive oil development effects.

Nonlinear convective transport of nanofluid over an inclined plate situated in a Darcy–Forchheimer porous medium with viscous dissipation and varying thermo-physical features

This article presents a theoretical analysis of the effects of varying thermo-physical properties, chemical reactions, and activation energy on the quadratic convective transport of nanofluids. The flow is created through an inclined plate in a Darcy–Forchheimer porous medium. The nanofluid model includes thermophoresis and Brownian motion to account for nanoparticle movement. The original flow equations are transformed using similarity transformations, and the resulting dimensionless equations are solved with a multi-domain spectral collocation approach. The effects of physical parameters on flow variables, heat and mass transfer coefficients are discussed. Comparisons between vertical and inclined plates reveal that inclination improves thermal performance but decreases velocity and engineering-related quantities. Fluctuating viscosity and nonlinear convection speed up fluid flow, whereas temperature rises with variable thermal conductivity and Biot number. Variable fluid properties, nonlinear convection, and convective heat conditions enhance heat transport coefficients. Activation energy boosts nanoparticle volume fraction profiles but decreases mass transport rates.

CFD elucidation of high-pressure subcooled boiling flow towards effects of variable refrigerant properties using OpenFOAM empirical closures

Boiling flow presents a significant concern, especially when a liquid surpasses its boiling point, potentially leading to catastrophic consequences. This research utilizes a two-phase code in the OpenFOAM software to investigate bubble formation during flow boiling. The well-established empirical models for calculating wall heat components were selected based on the operating conditions. The study incorporates experimental data from high-pressure boiling flow (10–30 bars) with variable properties of refrigerant R-12. The predictions reveal underpredictions in void fraction and liquid temperature compared to experimental observations. Significantly, the impact of the subcooling degree on void fraction behaviour is emphasized, and a potential underprediction of the evaporation portion is highlighted, particularly near the wall. Challenges in modelling bubble size distribution are evident through discrepancies in bubble diameter and velocity data, indicating the necessity for further advancements in the code. In summary, this numerical study provides valuable insights into the intricate dynamics of high-pressure subcooled boiling flow, especially when considering variable working fluid properties. Future efforts will focus on refining models for nucleation site density, bubble departure size, and lift-off frequency to enhance prediction accuracy.

Physics-Informed Machine Learning Applied to Complex Compositional Model in a Giant Field

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 23730,“Physics-Informed Machine-Learning Application to Complex Compositional Model in a Giant Field,” by Guido Bascialla, SPE, ADNOC, and Coriolan Rat and Soham Sheth, SLB, et al. The paper has not been peer reviewed. Copyright 2024 International Petroleum Technology Conference. _ Compositional reservoir simulation is a time-intensive activity demanding complex physics. In the complete paper, the authors review the advantages of machine learning (ML) in complex compositional reservoir simulations to determine fluid properties such as critical temperature and saturation pressure. An ML approach to predict critical temperatures during simulation based on the Heidemann-Khalil method is implemented, resulting in more-accurate results with lower computational cost, outperforming the standard method and improving performance on a giant field model with compositional gradient and miscible gas injection. Field Description The case study refers to a giant offshore carbonate field composed of multiple reservoirs. Production is currently in a rampup phase; crestal miscible hydrocarbon gas injection was implemented soon after startup. The availability of high-potential gas producers as a source of makeup gas and the placement of peripheral water injectors maintains the reservoir pressure above minimum miscibility pressure. All reservoirs show complex variable slope compositional gradients along thick oil columns of hundreds of feet (Fig. 1). To match the fluid behavior and the variation of fluid properties with depth, the equation of state needs at least nine components. The rock quality mainly is controlled by diagenesis. Thirteen rock types were modeled. The permeability can change up to four log cycles for the same porosity. Most of the reservoirs are highly heterogeneous, with features such as high-permeability streaks and baffle zones. A wide range of capillary pressure curves is present; these mainly depend on permeability and lithology. Most development wells were completed with inflow control devices (ICDs) to control gas and water breakthroughs and optimize oil production. The combination of numerous ICDs and long slanted production intervals (i.e., thousands of feet) make wellbore-reservoir coupling critical for proper history matching and forecasting. The model grid size in the horizontal direction is 328 ft, which is considered optimal according to simulated sensitivities. The vertical layering is very fine in order to capture the reservoir heterogeneity; the cell thickness ranges from 1 to 1.5 ft. This results in a model with 3.5 million active cells, which makes the simulation performance and run time very challenging when coupled with compositional gradient and ICDs. Phase Labeling In this section of the complete paper, the authors review why accurate phase labeling is important in compositional simulation and how it can lead to convergence problems, particularly for cases with gas injection. A traditional method is compared with an ML method on a simple model using a complex dummy fluid model to highlight issues that may arise in more-complex simulation models.

Investigating radiative heat transfer, varied wall thickness, and slip effects on Casson nanofluid flow over a stretched sheet with heat source

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

Similar Solutions for Changing Characteristics of Natural Convection Laminar Flow around a Vertical Rectangular Inclined Plane Surface

The study investigates laminar natural convection flow around a vertical rectangular inclined plane surface, specifically focusing on the effects of viscous and pressure stress work. Previous research primarily addressed these effects in two-dimensional natural convection flow scenarios, while this study extends the analysis to encompass three exterior situations, accounting for variations in fluid properties outside compressible boundary layers. Employing numerical methods, the study aims to predict essential flow parameters including Prandtl’s number (Pr), controlling parameter (C), and additional parameters (A, B, D, E, ∅). The investigation yields velocity profiles (F'(0), S'(0)), temperature profiles , skin frictions (F''(0), S''(0)), and heat transfer coefficients θ'(0). Numerical results are presented to illustrate the impact of different parameters on these flow characteristics. Additionally, tabulated data in Tables-2 and Tables-3 offer further insights into the predicted flow parameters and their variations under varying conditions.

A Comparative study of flow and C[sbnd]C heat flux over a magnetic field under the influence of nanomaterial and carbon nanotubes

The aim of this study is to investigate convective heat transfer on a flat surface in the presence of magneto-hydro-dynamic (MHD) flow. The analysis considers the Darcy-Forchheimer porosity medium in the flow. The study focuses on analyzing the heat transfer rate, incorporating joule heating and convective-conductive heat flux effects. The influence of varying fluid properties on the flow behavior is examined. The governing flow equations are initially expressed as partial differential equations (PDEs) and then transformed into ordinary differential equations (ODEs) using appropriate similarity transformations. The numerical method RKF-45 is employed to solve these ODEs. The results highlight the impact of different parameters in the model. It is observed that a higher Darcy parameter leads to a decrease in fluid velocity. Additionally, the performance of carbon nanotubes is superior compared to MoS2 nanoparticles in this study.

Exploring double-diffusive nanofluid flow in divergent/convergent nondarcy porous space: A machine learning numerical approach with zero mass flux

In this study, authors address the problem of analyzing the Jeffrey–Hamel nanofluid flow within a nonparallel channel under the influence of a thermally balanced non-Darcy permeable medium. Our objective is to explore the behavior of the nanofluid, employing the Buongiorno nanofluid model, and considering factors such as zero mass flux conditions, variable rheological fluid properties, and the presence of temperature jump phenomena through ANN-PSO-NNA. To tackle this intricate issue, propose a novel approach using Artificial Neural Networks (ANN) integrated with particle swarm optimization (PSO) hybrid with neural network algorithm (NNA). This combined technique is referred to as ANN-PSO-NNA. The governing flow equations based on the Jeffrey–Hamel analysis are first transformed into dimensionless forms. To establish the efficacy of our approach compare it with the widely used NDSolve method. Furthermore, the study presents the absolute error analysis for four distinct cases offering a quantitative assessment of the accuracy of ANN-PSO-NNA. The absolute error between the NDsolve and the proposed ANN-PSO-NNA is given for four different cases, ranging from 1.95E-06 to 1.18E-08. The biases and weights obtained through proposed method range from −10 to 10. This enables us to gauge the performance of the ANN-PSO-NNA minimum values of the fitness function 2.37E-08, 2.30E-08, 3.92E-08, and 1.22E-08 from multiple independent runs, which are showcased to be convergent, underscoring the robustness of the ANN-PSO-NNA approach. Employing graphical representations, explores the influence of various parameters on the velocity and temperature profiles. Our integrated approach offers a comprehensive understanding of the underlying dynamics, paving the way for optimized designs and enhanced efficiency across these diverse engineering applications.

Development of a high-order solver for large eddy simulation of turbulent heat transfer at supercritical pressure based on Nek5000

Turbulent heat transfer at supercritical pressure is a complex flow phenomenon due to drastic variations in fluid properties near the pseudocritical point. Numerical simulation is an important method to reveal the underlying physics. Currently, low-order numerical methods together with Reynolds-averaged Navier–Stokes equations are the mainstream in which empirical parameters are required, preventing high-fidelity simulations. Through inventing iterative properties updating and density-weighted explicit filtering, this work develops a high-order spectral element solver based on the open-source code Nek5000. By simulating a classical problem of supercritical CO2 flowing in a heated pipe and comparing it with benchmark data, the capability of the solver in direct numerical simulation is validated. Further results suggest lowering the mesh resolution leads to inaccurate predictions of bulk parameters and turbulent statistics. Therefore, filtering-based large eddy simulation (LES) is explored with different filter weights under a coarse mesh. Results show such a method can significantly improve most of the bulk parameters, including the bulk Nusselt number. The optimal filter weight can be determined from a simple optimization problem minimizing the deviation of overall energy conservation. Being high-order and capable of LES without empirical parameter, the current solver is a powerful tool for high-fidelity simulation of turbulent heat transfer at supercritical pressure.

Theoretical analysis of blood based ternary hybrid nanofluid under the influence of magnetic dipole with variable fluid properties

Theoretical analysis of blood based ternary hybrid nanofluid under the influence of magnetic dipole with variable fluid properties

Soret and Dufour effects on an unsteady MHD flow about a permeable rotating vertical cone with variable fluid properties

The objective of the present work is to examine the characteristics of unsteady incompressible magnetohydrodynamic fluid flow around a permeable rotating vertical cone. The effects of thermal radiation, viscous dissipation, and the Soret and Dufour effects are investigated in the analysis of heat and mass transfer. The viscosity of the fluid is considered inversely proportional to the temperature, and the thermal conductivity of the fluid is considered directly proportional to the temper-ature. The governing equations are converted into ordinary differential equations using suitable similarity transformations, which are then solved numerically using bvp4c from MATLAB. Results obtained in this study are in excellent correlation with previously conducted studies. The results demonstrate that the Dufour and Soret effects subsequently reduce the heat transit rate (by –3.3%) and mass transit rate (by –1.2%) of the system. It is also detected that fluids with higher viscosity tend to increase tangential skin friction (+8.9%) and azimuthal skin friction (+8.3%). The heat transit rate of the system is found to be more efficient for fluids with higher viscosity and lower thermal conductivity and Eckert numbers. Further-more, the thickness of the momentum, thermal, and concentration boundary layers significantly reduces while the heat and mass transit rates (+17.8% and +18.3%, respectively) of the system become more efficient for greater values of the un-steadiness parameter.

A multi-modal nonlinear dynamic model to investigate time-domain responses of a micro-cantilever in fluids

In this current work, a new nonlinear dynamic model based on the forced Van der Pol oscillator is introduced to demonstrate the time-domain sensitivities of the micro-cantilever to the varying properties of the surrounding fluids. Effects of diverse multi-frequency excitations on the hydrodynamically forced displacements are investigated for the Glycerol-water solutions with different concentrations. Driving forces at the eigenmode frequencies are applied simultaneously to actuate the micro-cantilever in multi-modal operations. The hydrodynamic force induces notable variations in the observables of high-frequency steady-state vibrations. To illustrate, the frequency of the displacements decreases with increasing dynamic viscosity and density of the fluids (among 55% and 85% Glycerol-water solutions) in bimodal- and trimodal-frequency excitations. Essentially, the observable responses are often used to distinguish the surrounding fluids in which the micro-cantilever operates. In addition, steady-state observables are achieved at only particular eigenmodes in single- and multi-frequency operations. It is highlighted that the periodic oscillations are obtained for the first and second eigenmodes with the highest value of forced Van der Pol parameter (μ = 1030). Clearly, higher eigenmodes require different values of the nonlinearity parameter to acquire periodic vibrations in multi-modal operations. In general, achieving steady-state observables is substantially critical in quantifying sensitivity to varying fluid properties. For instance, the vibration frequency of around 7.33 MHz and amplitude of around 0.03 pm are obtained at the first eigenmode for 75% Glycerol-water solution in tetra-modal operations. Note that femtometer amplitudes of deflections can be measured using quantum-enhanced AFM techniques. The frequency responses obtained in this work are compared with the measured ones in the literature and the results show satisfactory agreements. Therefore, a novel multi-modal nonlinear dynamic model enables to quantify observable sensitivity to micro-rheological properties at higher eigenmodes of the micro-cantilever.

Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle

Abstract The thermo-diffusion applications of nanofluid subject to variable thermal sources have been presented. The significance of Darcy–Forchheimer effects is attributed. The flow comprises the mixed convection and viscous dissipation effects. Furthermore, the variable influence of viscosity, thermal conductivity, and mass diffusivity is treated to analyze the flow. The analysis of problem is referred to convective mass and thermal constraints. The analytical simulations are proceeded with homotopy analysis method. The convergence region is highlighted. Novel physical contribution of parameters is visualized and treated graphically. It is noted that larger Brinkman number leads to improvement in heat transfer. The concentration pattern boosted due to Soret number. The wall shear force enhances with Hartmann number and variable thermal conductivity coefficient.