Unsteady Fluid Flow Research Articles

Numerical appraisal of the unsteady Casson fluid flow through Finite Element Method (FEM)

Numerical appraisal of the unsteady Casson fluid flow through Finite Element Method (FEM)

Numerical investigation of unsteady flow and heat transfer of a free convective second-grade fluid passing through exponentially accelerated vertical porous plate

Numerical investigation of unsteady flow and heat transfer of a free convective second-grade fluid passing through exponentially accelerated vertical porous plate

Analytic similarity solutions for fully resolved unsteady laminar boundary layer flow and heat transfer in the presence of radiation

In this paper, we have compared a new type of similarity transformation derived systematically by using Lie point symmetries with the existing similarity transformations for unsteady fluid flow and heat transfer in the boundary layer in the presence of radiation. It is observed that the existing transformations map the steady and marginally accelerating flows only, while the Lie similarity transformations provide solutions for all types of accelerating flows and are independent of unsteadiness in the fluid. The previous transformations are valid for a specific time interval which depends on a range of unsteadiness parameter, however the Lie similarity transformations provide valid solutions at any given time. This implies that the Lie similarity transformations yield solutions for previously unexplored ranges of unsteadiness in the fluid. Boundary layer flow physics for both types of transformations is discussed by employing the Homotopy analysis method. We show that for accelerating fluids, in the developing region, the boundary layer thickness first increases and than starts to decrease with increase in unsteadiness for fully developed flow. Detailed comparison of velocity and temperature profiles in the boundary layer is made using the tables and graphs which show that with Lie similarity transformations the region of study of the considered flow extends significantly for the unsteadiness parameter. The effect of the Prandtl number and radiation parameter on temperature distribution is also compared for both types of similarity transformations. The Lie symmetry similarity transformations are shown to explain the unsteady laminar boundary layer flow and heat transfer to an extent where the existing similarity transformations do not work.

Unsteady MHD Casson fluid flow with Dufour and Soret’s effects due to a rotating cone

This study discusses the unsteady Casson fluid flow over a rotating cone. The effects of Dufour and Soret, MHD, mixed convection, thermal radiation and chemically reactive species are also considered. The modeled governing equations are solved by using the Homotopy technique. We start the analysis by comparing the current results with the existing literature work on a limited intellect. The effects of different physical parameters on concentration, velocity and temperature are analyzed and presented graphically. The effects of the skin friction, Nusselt number and Sherwood number for various parameters are presented in a tabular form. The skin friction graph in azimuthal and tangential directions is a reverse function of the unsteady parameter.

Processing to pass unsteady MHD flow of a second-grade fluid through a porous medium in the presence of radiation absorption exhibits Diffusion thermo, hall and ion slip effects

ABSTRACT ‘This research aims to look at the consequences of diffusion thermo, Hall, ion slip, and radiation absorption on the unsteady MHD turbulent rotational flow of second-grade fluid through porous materials while also regarding the outcomes of the chemical retort and heat absorption. When the ratio between the number of collisions between fluid electrons in a cyclotron and the number of collisions between electrons and atoms is large, Hall effects (the Hall parameter) become important. The regular perturbation approach investigates the outlines of velocity segments, temperature dispersion, and concentration. The statistics for shear stress, the Nusselt numeral, and the Sherwood factor are written down on the panel. Graphs show how changes in different physical parameters cause changes in a fluid’s speed, temperature, and concentration patterns. In the end, it can be said that the primary and secondary velocities speed up significantly as the Hall and ion-slip parameters get bigger. This effect was also seen in the shearing stress’s axial and transverse components. The increasing importance of the thermal diffusion parameter increases both the initial and secondary velocities’.

Theoretical Error Analysis of Hybrid Finite Difference–Asymptotic Interpolation Method for Non-Newtonian Fluid Flow

In this paper, we utilized a hybrid method for the unsteady flow of the non-Newtonian third-grade fluid that combines the finite difference with the asymptotic interpolation method. This hybrid method is used to satisfy the semiunbound domain condition of the fluid flow’s length approaching infinity. The primary issue with this research is how much of the hybrid approach’s error may be accepted to guarantee that the method is significant. This paper discussed theoretical error analysis for numerical solutions, including the range and norm of error. The perturbation method’s concept is used to assess the hybrid method’s error. It is discovered that the hybrid approach’s relative error norm is lower than that of the finite difference method. In terms of the error standard, the hybrid approach is more consistent. Error analysis is performed to check for the accuracy as well as the platform for variable mesh size finite difference method in the future research.

Bioconvective unsteady fluid flow across concentric stretching cylinders with thermal-diffusion and diffusion-thermo effects

The current study emphasizes bioconvective viscous fluid flow between two horizontal deformable cylinders. At the cylindrical walls, the Newtonian heat and mass condition with velocity slip is examined. The thermal and solutal transfer is optimized by amalgamating Soret–Dufour effects with variable heat source/sink. The equations that regulate the flow are simplified via appropriate transformations. The bvp4c algorithm is employed to obtain the numerical solution. The ramifications of the emerging parameters are portrayed graphically. Numerical values for drag force coefficient, heat flux, mass flux, and local motile density numbers are enumerated in tabulated form. Axial velocity accelerates on varying the unsteadiness parameter. The thermal field elevates by augmenting the Dufour number and thermal conjugate parameter. The drag force coefficient exhibits a decreasing behavior on enhancing the unsteadiness and velocity slip parameters. An opposite behavior is exhibited by heat and mass flux on amplifying the Soret and Dufour number. Motile density deteriorates on elevating the Lewis number and unsteadiness parameter. A substantial correlation has been noticed by graphically comparing the results of this study with the previous literature.

Hydrodynamic Permeability in Axisymmetric Flows of Viscous Fluids through an Annular Domains with Porous Layer

Mass, energy, and momentum transfer processes between fluid-saturated porous media and the adjacent free flow occur in many natural and technical systems. The flow dynamics in the porous region and the adjacent free flow is strongly controlled by the mechanisms at the common interface and conditions on the outer surface of the free-flow. The present paper considers unsteady axisymmetric flows of viscous fluids through an annular domain with a porous layer covering a cylindrical solid core. Fluid flow in the domain filled with porous material and in transparent domain is described by Brinkman model and Navier Stokes equations, respectively. Analytical solutions for the dimensionless velocity fields in the Laplace domain are determined using Bessel functions, Laplace transform, and the appropriate interface and boundary conditions. The inversion of the Laplace transforms is done with the help of a numerical algorithm. In addition, the hydrodynamic permeability is determined. The dependence of the dimensionless velocity fields and of hydrodynamic permeability on characteristic parameters of the porous layer is numerically and graphically discussed. Since the velocity on the outer surface is given by an arbitrary function of time, the results in this paper could be used to study various filtration problems.

Numerical and Experimental Study of a Large-Scale Natural Circulation Helium Loop

This paper deals with the one-dimensional unsteady fluid flow model of a natural circulation loop. The governing equations are solved according to both the Euler and Lagrange approaches on two parallel computational grids. The linearization of equations and a semi-implicit discretization scheme are used to enhance the algorithm’s effectiveness. The results of the simulations were verified by using experimental data obtained on an experimental rig that was a scale model of an emergency system for the removal of residual heat after reactor shutdown. The parameters compared were the helium temperature at two locations and the heater outlet pressure. The simulation results generally did not differ from the experimental data by more than 10%. The best agreement was obtained for scenarios in which the helium pressure was highest in combination with slow changes in the input parameters (less than 4%). Conversely, the results differed the most for the scenario with extremely fast device cooling (20%).

Model of LDL-C concentration of blood flow through a vertical porous microchannel with multiple stenoses: computational simulation

The accumulations of lipid low-density lipoprotein cholesterol (LDL-C) and other chemicals on the artery wall are known as atherosclerosis. Atherosclerosis can constrict the arteries and obstruct the blood flow. Our goal is to debate the model of unsteady pulsatile Cross fluid (blood model) flows through a vertical porous microchannel with multiple stenoses under the influence of thermal radiation and Joule heating. The equations of momentum, energy, and LDL-C concentration have been simplified with the help of mild stenosis approximation. Then they have been solved numerically by using the finite difference method. It is noticed that the blood velocity increases and reaches a steady state in the case of non-pulsating flow, while the blood velocity fluctuates in the case of pulsating flow. Moreover, the value of LDL-C concentration in the case of a chemical reaction is lower than in the absence of a chemical reaction.

Free Convection Caputo-Fabrizio Casson Blood Flow in the Cylinder with Slip Velocity

Recently, fluid with fractional-order derivative model attracted many researchers to further study compared with the classical fluid mode since it is more precise and realistic. To imitate the applications of blood flow in narrow arteries, researchers focused on the fractional Casson fluid flow in the cylinder. However, most researchers solved the problems numerically and without considering the slip effect at the boundary. Thus, obtaining solutions analytically to the unsteady fractional Casson fluid flow in the slip cylinder with free convection is the goal of this study. The Caputo-Fabrizio fractional derivative approach is utilized to model this problem. By joining the approach of the Laplace transform and finite Hankel transform, the fractional governing equations are solved, and analytical solutions to the velocity and temperature profiles are gained. The fluid velocity rises as the slip velocity and Grashof number increase and it declines with the increment of the Casson parameter and Prandtl number. Increasing the fractional parameter will result in an increase in fluid velocity and temperature for a large time interval. The slip velocity effect influenced fluid flow, especially at the cylinder’s wall. These findings are beneficial to explore the more fractional-order derivative model and for studying the problems in biomedical engineering.

Lie group method for unsteady heat flow of a third-grade fluid between two parallel heated plates

In this paper, we use the classical Lie group method, to investigate the symmetries of the heat transfer flow of a third-grade fluid. This approach allows one to reduce the coupled partial differential equations governing the problem, to a system of nonlinear ordinary differential equations. Point symmetries of such systems are used to construct some classes of solutions. By using travelling wave solutions, we studied the influence of third-grade fluid parameters on the flow.

On the Generalized Fick’s and Fourier’s Laws for an Unsteady Casson-Williamson Fluids Over a Stretching Surface: A Spectral Approach

In this comparative examination, the paradox of mass diffusion and heat conduction on the improved surface of weakly hydromagnetic and unsteady fluid flow is examined. Material relaxation time is believed to be one of the contributing factors militating against an effective heat and mass transfer. This flow process is estimated to predict accurately the fluids enhancement and condensation/evaporation properties. With a workable similarity variable, the formulated model of modified Fick’s and Fourier’s laws assumed in the Riga surface-induced flow conveying Casson-Williamson fluids with variable transport properties are transformed to the systems of ordinary differential equations. The spectral iterative technique (SLLM in particular), thus employed to analyze the flow distributions and ascertain the validity of the obtained results. However, cohesion force between the fluid particle establishes abnormalities of both Fick’s and Fourier’s laws indicating that extra time will be required for effective mass and heat convection to the immediate environment. Generalized heat flux parameter minimizes the fluid temperature and accelerated the nanoparticle concentration, relative minimization of the fluid temperature resulted to much more nanoparticle concentration. Moreover, Williamson fluid demonstrated a higher conductivity/diffusivity capacity in constract to the Casson fluid. When compared to Casson fluid, the modified Hartman number has a stronger influence on Williamson fluid.

Induced by heat source on unsteady MHD free convective flow of Casson fluid past a vertically oscillating plate through porous medium utilizing finite difference method

In this research, the unsteady MHD flow of a Casson fluid past a vertical plate that oscillates while maintaining a constant wall temperature and the heat source is the subject of this article. The fluid is electrically conductive and moves through a porous media. Partial differential equations with initial and boundary conditions are used to model this phenomenon. There are a few appropriate non-dimensional variables introduced. Using the finite difference method(FDM), the consistent dimensionless equations with circumstances are resolved. The energy and velocity equations are solved precisely. Expressions for Nusselt number and skin friction are also assessed. The outcomes of computations are analyzed for newly developing flow parameters. Additionally, skin friction and the Nusselt number effects are explained using table values. Furthermore, increasing the heat source parameter causes a rise in temperature and velocity.

Unsteady Pressure-Driven Electrokinetic Slip Flow and Heat Transfer of Power-Law Fluid through a Microannulus

To guarantee the transporting efficiency of microdevices associated with fluid transportation, mixing, or separation and to promote the heat transfer performance of heat exchangers in microelectronics, the hydrodynamic behaviors at unsteady and steady states, as well as the thermal characteristics at the steady state in a pressure-driven electrokinetic slip flow of power-law fluid in a microannulus are studied. To present a more reliable prediction, the slip phenomenon at walls and nonlinear rheology of liquid are incorporated. The modified Cauchy momentum equation applicable to all time scales and energy equations, are analytically solved in the limiting case of a Newtonian fluid and numerically solved for power-law fluids. The transient velocity profile, time evolution of flow rate, temperature profile, and heat transfer rate are computed at different flow behavior indices, electrokinetic width, slip lengths, and Brinkman numbers, thereby, the coupling effect of nonlinear rheology, slip hydrodynamics, and annular geometry on flow and thermal behaviors is explored. The unsteady flow takes a longer time to achieve the steady state for shear thinning fluids or greater slip lengths. The flow behavior index and slip length play a significant role in the flow rate and heat transfer performance. The relevant discussion can serve as a theoretical guide for the operation and thermal management of annular geometry-related flow actuation systems.

Mathematical modelling of unsteady Oldroyd-B fluid flow due to stretchable cylindrical surface with energy transport

The unsteady boundary layer flow and thermal transportation analysis of an incompressible Oldroyd-B nanofluid driven by stretching cylinder is scrutinized with analytically approach in this study. The governing unsteady boundary layer equations (PDEs) are first established, and then these PDEs are converted into highly nonlinear ordinary differential equations (ODEs) using appropriate similarity transformations. The obtained equations are then solved in the form of series solutions via homotopy analysis method (HAM) for the velocity, temperature, and concentration fields. Additionally, the convergence analysis of the analytic series solutions is discussed. The model under consideration predicts the features of both the relaxation and retardation times effects. The aspects of thermophoresis and Brownian motion characteristics due to nanoparticles are studied by employing Buongiorno's model. The findings demonstrated that when the curvature parameter increases, the velocity, temperature, and concentration distributions near the cylinder's surface enhanced. Moreover, the velocity profile, for relaxation and the retardation times parameters, showed the opposite behavior. Also, the unsteadiness parameter enhanced the fluid velocity. The comparison of some current and old results is remarkable.

Study of unsteady non-Newtonian fluid flow behavior in a two-sided lid-driven cavity at different aspect ratios

Study of unsteady non-Newtonian fluid flow behavior in a two-sided lid-driven cavity at different aspect ratios

Transient MHD flow of fractional Burger's fluid model through a parallel microchannel with heat transfer and slip boundary condition

The combined influence of magnetic field, electro-osmotic flow (EOF), and pressure gradient on the unsteady magnetohydrodynamic fluid flow through a parallel microchannel is investigated. The Burger's liquid model is used for the fractional partial differential equation, which allows us to study the behavior of viscoelastic liquid velocity profile in the parallel microchannel. The Laplace transform (LT) in concert with the Fourier cosine transform are used to obtain the analytical solution of the velocity profile. Furthermore, using the method of separation of variables, the energy equation, Joule heating, energy dissipation, and electromagnetic effects are calculated to obtain the temperature within the microchannel. The influence of some relevant parameters like heat transfer, temperature distribution, Hartmann number (Ha), and Brinkman number (Br) on fluid flow velocity are presented graphically and discussed. The results obtained show that temperature decreases with Ha and Br of the transverse electric field for slip flow. Close to the middle of the microchannel, fluid flow velocity increases with decrease in the delay time parameter value and increase in the Burger's parameter value, while the opposite trend is found for the velocity near to the middle of the microchannel. In addition, Burger's liquid is quite general, such that Oldroyd-B, Maxwell, and Newtonian liquids are readily obtained as limiting cases. The study is significant in the application fields of chemical analysis and biological analysis, drug delivery, bacteria detection, and some others.

The Effect of Concentration on the Radiative Flow of Unsteady Magneto hydro – Dynamics (MHD) in a Vertical Channel

The article discusses the effect of concentration on the radiative flow of unsteady Magneto Hydro – Dynamics (MHD) in a porous vertical channel. The approach used in this article is transversely imposed magnetic field on the combination of porosity and viscosity on unsteady incompressible fluid flow and heat transfer. The resulted sets of non – linear coupled differential equation with the governing equations are solved by perturbation technique. The following parameters: Womersely Parameter (AI), Eckert Number (EC), Reynolds Number (Re), Prandlt Number (Pr), Grashof Number (Gr), Schmidt Number (Sc), Chemical Reaction Parameter (Ki) and the Mass Grashof Number (Gc) are used in investigating the nature of the flow due to velocity, temperature and concentration profile. Graphical results are presented and discussed.

Scrutinization of unsteady MHD fluid flow and entropy generation: Hybrid nanofluid model

The goal of the present paper is to scrutinize the heat transport of an unsteady stagnation-point flow of a hybrid nanofluid over a stretching/shrinking disk in the presence of a variable magnetic field and thermal radiation. The entropy generation analysis for the system is also made. The suitable similarity transformation is utilized for the reduction of a set of governing equations which are solved numerically by using fourth order Runge–Kutta procedure with shooting technique. The impact of different physical parameters under the realistic passive control of nanoparticles on the flow, heat transfer and concentration profiles are analyzed and demonstrated graphically. The analysis of the results obtained shows that multiple solutions exist for a certain parametric domain. With the increase in magnetic parameter (M), fluid velocity is found to increase for the first solution whereas opposite behavior is observed for the second solution. Also as M increases, the temperature at a point decreases for the first solution branch. Further, the influences of Reynolds number, Brinkmann number and volumetric concentrations on entropy generation are sketched and discussed. The novel result that emerges from the analysis is that among two solution branches, the first solution branch is linearly stable and physically meaningful whereas the second solution branch is linearly unstable and cannot be realized physically.