Governing Flow Equations Research Articles

Investigation of thermal stratification and nonlinear thermal radiation in Darcy-Forchheimer transport of hybrid nanofluid by rotating disk with Marangoni convection

In current frontier of fluid technology, hybrid nanofluid has sparked the curiosity of investigators due to its thermal characteristics and potential which gives an amended outcome compared to nanofluid in improving the heat transfer efficiency. Nanoparticles like (Ferro and Alumina ) and (Copper Cu and Titanium ) with water as base fluid are incorporated. Due to such properties, this article investigated the 3-D steady flow of hybrid nanofluid with the features of thermal stratification and nonlinear thermally radiative over a rotating disk with the Marangoni convection. The coupled transport equations (PDEs) are renovated into the nondimensional ODEs via suitable similarity variables after that cracked numerically through bvp4c solver via the computational software MATLAB. The physical and numerical outcomes of governing parameters such as thermal radiation parameter, thermal stratification parameter, local inertial parameter, Prandtl number, local Reynolds number and porosity parameter against governing flow equations are illustrated through graphs and tables. From the outcomes, it is observed that velocity has positive magnitude for porosity parameter, Reynolds number and variable permeability. The porosity parameter causes an increment in temperature distribution.

Numerical solution of chemically reactive and thermally radiative MHD Prandtl nanofluid over a curved surface with convective boundary conditions

This study intends to elaborate the heat and mass transfer analysis of Prandtl nanofluid flow over a vertically heated curved surface together with MHD, thermal radiation, and chemical reaction effects. The boundary layer approximations developed the governing flow equations such as momentum, energy, and diffusion balance equations. The nonlinear system of PDEs is changed into nonlinear ordinary differential equations via proper transformations. By taking the assistance of the bvp4c algorithm, the numerical technique is imposed explicitly for attaining the dimensionless form of the fundamental equations. The nondimensional outcomes are apprehended here which rely on numerous physical constraints. The impression of these physical parameters on momentum and thermal boundary layers along with concentration outlines are discussed and demonstrated graphically. The impact of drag force, heat transfer coefficient, and mass flow rate are computed and presented through tables.

Numerical Simulation of Magnetic Dipole Flow Over a Stretching Sheet in the Presence of Non-Uniform Heat Source/Sink

The main objective of current communication is to present a mathematical model and numerical simulation for momentum and heat transference characteristics of Maxwell nanofluid flow over a stretching sheet. Further, magnetic dipole, non-uniform heat source/sink, and chemical reaction effects are considered. By using well-known similarity transformation, formulated flow equations are modelled into OD equations. Numerical solutions of the governing flow equations are attained by utilizing the shooting method consolidated with the fourth-order Runge-Kutta with shooting system. Graphical results are deliberated and scrutinized for the consequence of different parameters on fluid characteristics. Results reveal that the temperature profile accelerates for diverse values of space dependent parameter, but it shows opposite behaviour for escalated integrity of temperature dependent parameter.

A comparative study of three dimensional flow of Casson–Williamson nanofluids past a riga plate: Spectral quasi-linearization approach

In the present investigation, the impact of variable transport properties on the magnetized three dimensional motion of Casson–Williamson nanofluids with nonlinear radiation influence past a Riga plate is discussed. For proper utilization of nanoliquids, a good account of distinct fluid transport variables in any flow geometry is essential. The governing flow equations of a stretching Riga plate of variable viscosity, mass diffusivity and thermal conductivity are obtained after imposing an appropriate similarity variables. The spectral quasi-linearization method (SQLM) was employed to get good account of all pertinent flow parameters. Apart from excellent agreement with earlier known work in literature, the method performance (numerical estimation tools) are discussed via CPU time, errors (L∞ and L1), and comparison with Galerkin weighted residual method. Also engineering dimensionless parameters were presented for the present problem. The results therein established that flow resistivity of Williamson fluid is higher when compared to the Casson fluid. In addition, Casson fluid diffuses and conduct lesser in respect to Williamson fluid. With opposing characterization of viscosity parameter, variable thermal conductivity and mass diffusivity enhances the species and thermal boundary layer, while the viscosity property appreciated the momentum(s) profiles. This study is found applicable while forecasting the right fluid rheology to use, proffer solution to noise/turbulence effect, to safeguard boundary layer isolation, and establishing a force parallel to the surface for both industrial, engineering and biomedical use.

Predicting the Non-Linear Conveying Behavior in Single-Screw Extrusion: A Comparison of Various Data-Based Modeling Approaches used with CFD Simulations

Abstract The traditional approach to modeling the polymer melt flow in single-screw extruders is based on analytical and numerical analyses. Due to increasing computational power, data-driven modeling has grown significantly in popularity in recent years. In this study, we compared and evaluated databased modeling approaches (i. e., gradient-boosted trees, artificial neural networks, and symbolic regression models based on genetic programming) in terms of their ability to predict – within a hybrid modeling framework – the three-dimensional non-linear throughput-pressure relationship of metering channels in single-screw extruders. By applying the theory of similarity to the governing flow equations, we identified the characteristic dimensionless influencing parameters, which we then varied to create a large dataset covering a wide range of possible applications. For each single design point we conducted numerical simulations and obtained the dimensionless flow rate. The large dataset was divided into three independent sets for training, interpolation, and extrapolation, the first being used to generate and the remaining two to evaluate the models. Further, we added two features derived from expert knowledge to the models and analyzed their influence on predictive power. In addition to prediction accuracy and interpolation and extrapolation capabilities, we evaluated model complexity, interpretability, and time required to learn the models. This study provides a rigorous analysis of various data-based modeling approaches applied to simulation data in extrusion.

Thermal behavior of a flat-plate direct absorption with water-nanohorn mixture

A numerical analysis on a two-dimensional steady state forced convection inside a solar collector with direct absorption due to a nanofluid composed of water and nanoparticles of carbon nanohorns is carried out. The analysis allows to provide the main fluid flow and thermal characteristics of a simple flat solar collector with a distance between the glass and the collecting plate of 1.2 mm and a length of 1.0 m. The solar collector presents heat losses from the upper wall towards the ambient by an external surface heat transfer coefficient. The governing flow equations for the nanofluid are written assuming the single-phase flow and the heat transfer due to the radiation, for the local absorption of nanoparticles, is evaluated by the non-grey discrete ordinates method. The carbon nanohorns optical and thermal properties are estimated by the data available in literature. The finite volume method is used to solve the problem and the results are carried out employing the ANSYS-FLUENT code. The results are given in terms of temperature and velocity fields and transversal profiles inside the channel for different values of mass flow rates, solar irradiance, volumetric nanoparticle concentrations and assigned values of external surface heat transfer coefficient and temperature.

A numerical and statistical approach to capture the flow characteristics of Maxwell hybrid nanofluid containing copper and graphene nanoparticles

The principal goal of the present investigation is to inspect the flow characteristics of an electrically conducting hybrid nanofluid containing copper and graphene nanoparticles past a linearly stretched sheet with velocity slip condition at the interface. Since, the non-Newtonian fluid models result in a better understanding of the flow and heat transfer attributes of the nanofluids, therefore, non-Newtonian Maxwell nanofluid has been chosen as the base fluid in our study with an unsteady magnetic field applied at a certain angle to the direction of the flow. Consideration of thermal radiation along with heat absorption under the mutual influence of viscous and Joule dissipations is one of the key features of this research investigation. With the help of similarity transformations, the governing flow equations have been converted into a system of coupled non-dimensional differential equations. After that, Shooting method along with Runge–Kutta–Fehlberg numerical technique is employed to find the solutions for velocity and temperature of the hybrid nanofluid. The obtained numerical results are well demonstrated with a number of graphs and tables. Apart from this numerical technique, a statistical method is implemented of multiple quadratic regression estimation analysis on the various graphs of skin friction coefficient and wall temperature gradient to establish the connection among physical entities and heat transfer rate. The applications of this investigation in solar energy, ventilation, heating as well as refrigeration , medical science, defence sector etc. Some noteworthy findings include that Maxwell parameter, velocity slip and porosity have a tendency to reduce the hybrid nanofluid velocity whereas graphene Maxwell hybrid nanofluid’s temperature is getting enhanced for rising the values of magnetic field’s inclination angle, radiation, unsteadiness parameters, Biot number and viscous dissipation whereas a reverse trend is visible for heat absorption parameter. Furthermore, the permeability of the porous medium has a more significant impact on changing the nanofluid velocity than that of magnetic parameter whereas the rate of heat transfer is high sensitive for thermal radiation than that of viscous dissipation. As per authors’ knowledge there is no such attempt where the mutual effects of hybrid Maxwell nanofluid (graphene and copper), porous media and viscous dissipation have been considered.

Numerical simulation of electroosmotic force on micropolar pulsatile bloodstream through aneurysm and stenosis of carotid

Smoking and hypertension are significant risk factors for atherosclerotic carotid artery disease, but also for intracranial aneurysms. The medical results suggest incidental intracranial aneurysms in patients with internal carotid artery (ICA) stenosis arteries. Which led to a study of the comparison between stenosis and aneurysm segments through the artery. A mathematical and numerical model for blood solidification and its rupture in a diseased artery is described in this paper. The interaction between the blood flow and a diseased arterial wall was formulated. The blood flow is formulated as a micropolar incompressible fluid with heat and mass transfer under the control of electro-osmotic and electromagnetic forces through an artery that contains stenosis and aneurysms. The approximation of mild stenosis is used to derive the governing flow equation, which is then solved using a method of finite difference. Particular attention is paid to the impact on axial velocity, flow rate, resistance impedance, and wall shear stress of geometrical parameters of the arterial wall and rheological blood parameters. In the instantaneous pattern of streamlines, the global behavior of blood is also investigated. Finally, the effect of all parameters on the blood flow through artery whose stenosis and aneurysm are investigated as a comparison of both segments.

Electro-osmotically driven generalized Newtonian blood flow in a divergent micro-channel

A theoretical analysis of electro-osmosis peristaltic flow of generalized Newtonian fluid bounded in a complex wavy divergent channel is performed. There are many complex rheological generalized Newtonian fluids, out of which Ellis fluid model is considered to approximate the fluid present within the channel. The flow equations are modelled using balances of mass and momentum while the body force term is introduced using well known Poisson equation. An analytical solution to the governing flow equations is presented and the closed form expressions for longitudinal velocity, flow rate and stream function are developed. The numerical solution of pressure rise is obtained via NIntegrate build in command of Mathematica 12.3. Influence of diverse rheological and electrical parameters on flow characteristics are analysed via plots.

Multiple slips and heat source effects on MHD stagnation point flow of casson fluid over a stretching sheet in the presence of chemical reaction

The numerical analysis of the steady MHD stagnation point flow of a Casson fluid flow over a stretching sheet in the presence of a heat source and the first-order chemical reaction with multiple slip boundary conditions taking into account viscous dissolution, Joule warming, and the first-order chemical response with multiple slip boundary conditions is performed. The governing flow equations are interpreted with the assistance of identity transmutations, and the condensed nonlinear coupled ordinary differential equalisations are determined applying the shooting approach. With the use of graphs, the impacts of several factors on the dimensionless velocity, temperature, and concentration profiles are demonstrated. In addition, graphical representations of the variation in skin friction coefficient for different values of the Casson fluid parameter against the Eckert number, the variation in the rate of heat transfer coefficients for various values of the Radiation specification against the Schmidt number, and the variation in the rate of mass transfer for different values of the chemical reaction specification against the Schmidt number are provided. Our findings indicate that when there is an increase in Heat source and Chemical reaction parameter always leads to degeneration in temperature profile and Chemical reaction. The Chemical reaction parameter was found to enhance the Sherwood number.

Bioconvection in Magneto Hydrodynamics Casson Nanoliquid (Fe3O4-Sodium Alginate) With Gyrotactic Microorganisms Over an Exponential Stretching Sheet

The present investigation focuses on the influence of motile gyrotactic microorganisms and thermal heat flux on three-dimensional convective flow of a Casson nanoliquid over an elongated surface. The flow equations are modelled by using Tiwari-Das nanofluid model. Sodium alginate (SA) is considered as the base fluid together with Ferromagnetic oxide (Fe3O4) nanoparticles. The governing flow equations are changed into a system of ODEs with the aid of similarity variables and are then addressed computationally. Influence of various pertinent parameters on different physical quantities is examined graphically. The outcomes of present investigation is validated through comparison study and is found to be in good arrangement. It is noticed that the coefficient of heat transfer rises with growing radiation and Biot numbers. Also the mass transfer coefficient surges for higher values of Schmidt number and generative chemical reaction parameter.

New approach of inverse design of transonic compressor rotor blade via prescribed isentropic Mach distributions without modification of governing equations

Shock loss is the primary source of total pressure loss of transonic axial compressors. Reducing the shock by redesigning the geometry of rotor is of great interest for turbomachinery designers. However, the complex flow field involving shock waves, shock-boundary interaction, intense secondary flows, etc., in the compressor makes the design of rotor difficult. The conventional method of design and optimization is computationally intensive and time-costly. This study introduces an inverse design method to design rotor blades corresponding to prescribed isentropic Mach number distributions with no modification of flow-governing equations. An artificial neural network is trained to predict the isentropic Mach number distributions of any deformed blades. Then, with the pattern search optimization, the blade corresponding to the prescribed isentropic Mach number distributions can be achieved. When the aerodynamic parameter database is calculated and the neural network is obtained, this method can design large numbers of blades of changed isentropic Mach number distributions immediately, without modifying the computational fluid dynamics (CFD) flow solver. The design process is fully automatic and efficient. In this study, NASA Rotor 37 is redesigned and optimized as test cases. Some analysis on the influence of blade shape on aerodynamic characteristics of the rotor is represented in this study.

Effectiveness of Magnetized Flow on Nanofluid Containing Gyrotactic Micro-Organisms over an Inclined Stretching Sheet with Viscous Dissipation and Constant Heat Flux

The bioconvection phenomenon, through the utilization of nanomaterials, has recently encountered significant technical and manufacturing applications. Bioconvection has various applications in bio-micro-systems due to the improvement it brings in mixing and mass transformation, which are crucial problems in several micro-systems. The present investigation aims to explore the bioconvection phenomenon in magneto-nanofluid flow via free convection along an inclined stretching sheet with useful characteristics of viscous dissipation, constant heat flux, solutal, and motile micro-organisms boundary conditions. The flow analysis is addressed based on the Buongiorno model with the integration of Brownian motion and thermophoresis diffusion effects. The governing flow equations are changed into ordinary differential equations by means of appropriate transformation; they were solved numerically using the Runge–Kutta–Fehlberg integration scheme shooting technique. The influence of all the sundry parameters is discussed for local skin friction coefficient, local Nusselt number, local Sherwood number, and local density of the motile micro-organisms number.

Influence of Hall and Joule heating on a magnetic nanofluid (Fe3O4) flow on a rotating disk with generalized slip condition

AbstractThis study analyzes Hall current and Joule heating effects on the ferro‐nanofluid flow by the rotation of the disk incorporated with generalized slip condition. By using the well‐known Von Karman transformation, formulated flow equations are modeled into ordinary differential equations. Numerical solutions of the governing flow equations are attained by utilizing the shooting method consolidated with the fourth‐order Runge–Kutta scheme. The impacts of different parameters on skin friction coefficient, velocity, temperature, and Nusselt number are given in graphs and tables and investigated in detail. Furthermore, an association with formerly published articles is given and met in remarkable correspondence.

An Improved Hybrid Cartesian/Immersed Boundary Method for Flow Simulation with Moving Boundaries

To simulate flow problems with moving fluid-solid interfaces, a boundary treatment technique based on a hybrid Cartesian/immersed boundary method is presented. In the vicinity of the immersed boundary, a forcing term is added into the governing flow equations to modify the discretization scheme for the viscous term during its spatial discretization. Addition of such a term enforces desired boundary condition on the immersed boundary. A one-dimensional linear interpolation scheme is used to obtained required information for the modified discretization scheme when dealing with a moving boundary. The present method is essentially second-order accurate and can obtain results that are in good agreement with benchmark references when simulating the flow induced by the in-line oscillation of a circular cylinder.

Numerical study on trajectory of released store with manipulation of grid connections

PurposeThis study aims to present a moving grid method based on the manipulation of connections.Design/methodology/approachIn this study, the grid’s connections were manipulated to simulate a released store’s displacement. The selected model in this research is the EGLIN test case. In the introduced method, connections are modified in specific nodes of the grid. Governing flow equations were solved with the finite volume method. The major characteristic of this technique is using the averaging method for calculating the flux of cells.FindingsThis method maintains the grid’s quality even in large displacements of the released store. The three-dimensional simulation was carried out in transonic and supersonic regimes. Comparison of the results with experimental data were highly satisfactory.Research limitations/implicationsUsing this moving grid method is recommended for simulating other models.Practical implicationsPrediction of store trajectory released from air vehicles is one of the most critical issues under study especially in the design of new stores.Originality/valueThe most prominent advantage of this method is maintaining the grid quality simultaneous with large displacements of the released store.

Numerical treatment with Lobatto-IIIa scheme magneto-thermo-natural convection flow of casson nanofluid ([formula omitted]) configured by a stretching cylinder in porous medium with multiple slips

In biological instruments, medicines and agriculture, the agglomeration of nanofluids and biotechnological mechanisms can offer significant advantages. The nanofibers, nanowires, droplets are more useful in the field of nanotechnology. There is a significant demand for nanotechnology and one can expect that the future of these materials is very bright. Due to the different shapes and sizes of the nanomaterials, it is exemplified into various types. In one of them are carbon nanotubes (CNTs). These nanotubes are carbon allotropes. Carbon nanotubes are more practiced in the field of energy storage, optics, thermal stability, nanotubes transistors, and electromagnetic interference and in many areas. Keeping in such practical applications of nanotubes and nanofluid, we have scrutinized the magneto Casson nanofluid flow past a cylinder with carbon nanotubes (MWCNT and SWCNT). Here the sodium alginate is utilized as a regular fluid and nanoparticles MoS2 and Cu are dispersed in it. The impacts of multi slip behavior are considered in the presence of nonlinear thermal radiation. Multi degree governing flow equations are remodeled by similarity transformation and then tackled via shooting algorithm with Lobatto-IIIa formula. The physical flow behaviors of interesting parameters against velocity and temperature field are elaborated in Figures using Matlab software. Results indicate that flow of fluid is decline with fluid parameter. Further, volume fraction of nanoparticles reduces the temperature. The study is relevant to efficient thermal transportation in heat exchangers and electronic appliances.

Embedded training of neural-network subgrid-scale turbulence models

The weights of a deep neural network model are optimized in conjunction with the governing flow equations to provide a model for sub-grid-scale stresses in a temporally developing plane turbulent jet at Reynolds number $Re_0=6\,000$. The objective function for training is first based on the instantaneous filtered velocity fields from a corresponding direct numerical simulation, and the training is by a stochastic gradient descent method, which uses the adjoint Navier--Stokes equations to provide the end-to-end sensitivities of the model weights to the velocity fields. In-sample and out-of-sample testing on multiple dual-jet configurations show that its required mesh density in each coordinate direction for prediction of mean flow, Reynolds stresses, and spectra is half that needed by the dynamic Smagorinsky model for comparable accuracy. The same neural-network model trained directly to match filtered sub-grid-scale stresses -- without the constraint of being embedded within the flow equations during the training -- fails to provide a qualitatively correct prediction. The coupled formulation is generalized to train based only on mean-flow and Reynolds stresses, which are more readily available in experiments. The mean-flow training provides a robust model, which is important, though a somewhat less accurate prediction for the same coarse meshes, as might be anticipated due to the reduced information available for training in this case. The anticipated advantage of the formulation is that the inclusion of resolved physics in the training increases its capacity to extrapolate. This is assessed for the case of passive scalar transport, for which it outperforms established models due to improved mixing predictions.

Investigation of rock properties distribution effect on pressure transient analysis of naturally fractured reservoirs

Naturally fractured reservoirs (NFRs) are considered as one of the main resources of oil and gas around the world. The nature of fractures in this kind of reservoirs splits these reservoir rocks into two parts; matrix and fracture. In these two media, geometrical properties like matrix block size and also petrophysical properties such as porosity and permeability cannot considered to be constant and they usually contain heterogeneity in extent of the reservoir. In this study, a statistical distribution concept is used to be able to model variance of properties including matrix block size, matrix and fracture permeability, and matrix and fracture porosity as independent statistical variables. For the purpose of investigating effect of the five aforementioned properties distribution on pressure transient analysis (PTA) plots, five distinct cases of property distributions are considered with their corresponding precise statistical modeling applied on governing flow equation of a dual-porosity base case reservoir model. Abovementioned distributed parameters are included in semi-analytically derived dual porosity reservoir models and results are compared to their corresponding constant-value response. In each case the constant parameter is the median of corresponding statistical distribution. The statistical approach is validated using numerical modeling and field data applications are also presented. Different unimodal and bimodal matrix properties (block size, permeability, and porosity) distribution have slight to intense effects on PTA plots of an NFR. In matrix block size and porosity distribution cases, lower values, and in matrix permeability distribution case, higher values of the range dominate the pressure behavior of the fractured system. On the other hand, although fracture permeability and porosity distribution can shift PTA plots of the model but the effect is not significant and both fracture permeability and porosity distribution can be represented by constant representative values instead of a statistical model. It is worth mentioning that all matrix properties bimodal distribution has a common signature on PTA plots which is similar to the triple porosity reservoir response (i.e. the presence of double-bump descent on pressure derivative plot).

Numerical simulation of mixed convection flow and heat transfer in the lid-driven triangular cavity with different obstacle configurations

There are several industrial applications, particularly lid-driven walls, for mixed convection heat transfer characteristics across various cavities. In order to increase the effectiveness of cooling, electrical, electronic and nuclear devices and to monitor the fluid flow and heat exchange of solar thermal installations and thermal storage, such a problem requires further investigation. The main goal of this profound study is to examine the convective heat transfer nature of thermal convection on Newtonian MHD fluid in a lid-driven triangular cavity subjected to heating by a thick triangular wall, including the effects of varying Richardson number, Reynolds number, Hartmann number, and cold circular obstacle. Graphical illustration shows that the upper wall having temperature Th is moving from left to right, whereas inclined sidewalls are adiabatic. Further, a cold circular obstacle containing temperature T∗∗ is placed near the left and right wall of the triangular cavity with T∗∗ < Th. The governing flow equations are tackled by the Galerkin Finite Element Method (GFEM) to prepare the desired results. Velocity contours, isotherms and heat transfer rates demonstrate flow kinematics and heat transport processes. The high estimate of the Reynolds number has been found to provide a decent rate of convective heat transfer to a good liquid progression. For a higher number of Grashof, which achieves the maximum convection intensity, it is checked that natural convection dominates within the convection system. The Richardson number is a rising function of the Nusselt number, while the opposite trend is observed due to the rise in the Hartmann number.