Unsteady Laminar Flow Research Articles

Unsteady three-dimensional stagnation point magnetohydrodynamic flow of bionanofluid with variable properties

Unsteady three-dimensional laminar stagnation point forced convective boundary layer magnetohydrodynamic flow of a bionanofluid with variable transport properties is studied theoretically and numerically. Thermal convective and zero mass flux boundary conditions are incorporated in this study. The transport properties are assumed to be a function of nanoparticle volume fraction to get physically realistic results. The dimensional boundary layer equations along with the coupled boundary conditions are transformed via similarity transformations into a system of ordinary differential equations. The transformed equations are solved numerically using the Runge–Kutta–Fehlberg fourth-, fifth-order numerical method. The effect of selected governing parameters, namely, viscosity, thermal conductive, mass diffusivity, microorganism diffusivity, magnetic field and bioconvection Schmidt number, on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism, skin friction coefficient, heat transfer rate, mass transfer rate and microorganism transfer rate, is illustrated graphically and interpreted in detail. Comparisons with previous works are carried out for some limiting cases and found to be in good agreement.

Mixed convection heat transfer from a triangular cylinder subjected to upward cross flow

Unsteady laminar mixed (forced and free) convection heat transfer and fluid flow over long horizontal equilateral triangular cylinder subjected to upward cross flow are investigated numerically. The computation model is a two-dimensional unconfined rectangular domain with an aspect ratio of 1.4. A second order upwind scheme was used for differencing of the convection terms, and SIMPLE algorithm was adopted. The working fluids are air (Pr = 0.7) and water (Pr = 7). The equilateral isothermal triangular cylinder is placed in a uniform stream. The effect of buoyancy is incorporated into the Navier-Stokes (NS) equations using the Boussinesq approximation. This study is a case of “assisting flow” where the buoyancy-induced flow and fluid motions have the same upward direction. The basic dimensionless simulation variables, Reynolds and Richardson numbers, are varied in the range 10 ≤ Re ≤ 200 and 0 ≤ Ri ≤ 10. The flow characteristics such as the mean drag, mean rms lift coefficients and the Strouhal number are computed for each simulation. The flow patterns and isotherms are generated to interpret and understand the underlying physical mechanism. The cylinder surface mean Nusselt number was computed for mixed as well as for forced and free convection conditions. The computational data were used to develop the several Nusselt number correlations for forced, free and mixed convection flow.

Numerical Study of Unsteady MHD Flow and Entropy Generation in a Rotating Permeable Channel with Slip and Hall Effects**Support of the National Natural Science Foundation of China under Grant Nos. 51709191 and 51706149, and Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education under Grant No. ARES-2018-10

This article investigates an unbiased analysis for the unsteady two-dimensional laminar flow of an incompressible, electrically and thermally conducting fluid across the space separated by two infinite rotating permeable walls. The influence of entropy generation, Hall and slip effects are considered within the flow analysis. The problem is modeled based on valid physical arguments and the unsteady system of dimensionless PDEs (partial differential equations) are solved with the help of Finite Difference Scheme. In the presence of pertinent parameters, the precise movement of the flow in terms of velocity, temperature, entropy generation rate, and Bejan numbers are presented graphically, which are parabolic in nature. Streamline profiles are also presented, which exemplify the accurate movement of the flow. The current study is one of the infrequent contributions to the existing literature as previous studies have not attempted to solve the system of high order non-linear PDEs for the unsteady flow with entropy generation and Hall effects in a permeable rotating channel. It is expected that the current analysis would provide a platform for solving the system of nonlinear PDEs of the other unexplored models that are associated to the two-dimensional unsteady flow in a rotating channel.

On the transient behaviour of a laminar rotor–stator cavity

The unsteady laminar flow between two large rotating disks when one of them is impulsively started is described using the von Kármán similarity analysis to reduce the solution of the Navier–Stokes equations to a set of ordinary differential equations. It is found that the transient phenomenon consists of three distinct phases. Firstly, the development of the Ekman boundary layer, where a quasi-steady Stewartson-type of flow is created. Secondly, angular momentum is initially diffused in the axial direction until the inward radial convection of angular momentum becomes dominating. Thirdly, a Batchelor flow is created once the Bödewadt boundary layer is developed and the entrainment of disk and stator boundary layers are balanced. The dependences of the characteristic dimensionless times on the Reynolds number based on the cavity gap for the second and third stages have been identified numerically and analytically. It is found that the diffusive part of the transient is bypassed if the flow, initially at rest, is perturbed with a small circumferential velocity. The flow and heat transfer transient during a ramp of finite duration has been computed numerically. The integral angular momentum and energy balances of the cavity have been performed in order to understand the energy and momentum budget of the cavity. It is concluded that the spin-up and the spin-down process of a rotor–stator cavity using a quasi-stationary approximation of the fluid, where the time derivatives are neglected, is questionable for realistic gas turbine applications. Finally, the self-similar solution is compared against two-dimensional axisymmetric, steady and unsteady, laminar simulations to assess the limitations and validity of the self-similar analysis. It has been identified that in a closed squared cavity the outer shroud modifies the physics of the transient, but the general conclusions drawn from the one-dimensional model are still valid.

Fluid-structure interaction analysis of buoyancy-driven fluid and heat transfer through an enclosure with a flexible thin partition

PurposeA numerical model of an unsteady laminar free convection flow and heat transfer is studied in a cavity that comprises a vertical flexible thin partition.Design/methodology/approachThe left and right vertical boundaries are isothermal, while the horizontal boundaries are insulated. Moreover, the thin partition, placed in the geometric centerline of the enclosure, is considered to be hyper elastic and diathermal. Galerkin finite-element methods, the system of partial differential equations along with the appropriate boundary conditions are transformed to a weak form through the fluid-structure interaction and solved numerically.FindingsThe heat transfer characteristics of the enclosure with rigid and flexible partitions are compared. The effect of Rayleigh number and Young’s modulus on the maximum nondimensional stress and final deformed shape of the membrane is addressed.Originality/valueIncorporation of vertical thin flexible membrane in middle of a cavity has numerous industrial applications, and it could noticeably affect the heat and mass transfer in the enclosure.

Insights From Unsteady Flow Analysis of Underdamped Slug Tests in Fractured Rock

AbstractSlug tests generating oscillating (underdamped) responses are common in high‐transmissivity (T) zones, and the nature of the response depends on the plumbing of the test equipment and the formation properties. The standard approach for obtaining T is to measure pressure shallow in the riser pipe to obtain an accurate estimate of flow and then predict the formation response from this shallow measurement by accounting for friction and acceleration assuming steady flow conditions (parabolic radial velocity profile). In this study a mathematical solution is developed for unsteady oscillatory laminar flow that shows non‐parabolic radial velocity profiles resulting in larger frictional losses, which are out of phase with the average flow velocity, indicating that errors are introduced when using the standard approach for underdamped slug test analysis. The unsteady flow model produces correction factors that can be used to improve the standard approach for predicting the formation pressure; however, not all errors are eliminated. Consequently, a new procedure is presented and applied to underdamped slug tests observed in fractured rock that avoids errors associated with quantifying inertial and frictional effects along the test equipment. This is achieved through the use of two transducers, where one is placed shallow in the water column to infer flow, and one is placed inside the test interval to represent the formation pressure. Comparison of T estimated by the new procedure to T derived from constant head step tests show better agreement than T obtained when predicting the formation pressure from a shallow pressure measurement.

Numerical simulation of lid-driven cavity flow of micropolar fluid

Incompressible unsteady laminar flow of a micropolar fluid in a lid driven square cavity has been examined numerically with finite difference scheme. In this paper, we verify the code validation of Newtonian incompressible fluid (K = 0) with standard bench mark problem in the literature and then proceed the present computation. The vorticity-stream function formulation of Navier-Stokes equations and angular momentum equation is solved by the Euler’s explicit method. The effect of various values of Reynolds number (Re) and vortex viscosity parameter (K) of the flow characteristics is studied and discussed through several graphs.

Two-dimensional simulation of fluid flow and forced convection heat transfer from a circular cylinder with control rods

PurposeThis paper aims to study the fluid flow and forced convection heat transfer from an isothermal circular cylinder with control rods in the laminar unsteady flow regime.Design/methodology/approachThe overset grid method was used for accurate simulation of the unsteady flows around different arrangements of the cylinders. Grid generation for overset grids was performed using a general orthogonal boundary fitted coordinate system. The method of solution was based on a finite volume discretization of the Navier-Stokes equations. Simulations were carried out for the Prandtl numbers of 0.7 and 7.0 with the Reynolds numbers ranging from 60 to 300.FindingsThe results indicate that the performance of multiple control rods depends strongly on the spacing ratio. Furthermore, in a manner similar to the flow patterns, four different thermal regimes were recognized based on the variations of mean Nusselt number versus G/D, as the thermal regimes follow the categories of flow regimes at different diameter ratios. However, for different Prandtl numbers, no single trend of heat transfer variation versus the spacing ratio exists for same regime.Originality/valueFew studies have been conducted to investigate the heat transfer characteristics from control rods. The results of this study provide a comprehensive knowledge on the dynamical and thermal behavior of the flow around multiple cylinders.

Radiative Effects on a Free Convective MHD Flow past a Vertically Inclined Plate with with Heat Source and Sink

The impact of thermal radiation on unsteady laminar free convective MHD flow of a incompressible viscous fluid passes through a vertically inclined plate under the persuade of heat source and sink is presented here.Plate surface is considered to have variable wall temperature. The fluid regarded as gray absorbing / emitting, but non dispersing medium. The periphery layer dimensionless equations that administer the flow are evaluated by a finite difference implicit method called Crank Nicolson method. Numerical solutions are carried out for velocity, temperature, local shear stress, heat transfer rate for various values of the parameters (Pr, λ, Δ M, Rd ) are presented.

THERMAL AND MASS DIFFUSIVE STUDIES ON A MOVING CYLINDER ENTRENCHED IN A POROUS MEDIUM

A numerical investigation is accomplished for an unsteady laminar free convective flow of a viscous incompressible fluid over an impulsively started semi-infinite vertical cylinder embedded in a porous medium. The level of temperature and concentration at the surface area of the cylinder are assumed to vary as functions of power law type, in the axial coordinate. The problem is governed by a system of coupled nonlinear boundary layer equations with appropriate variable surface boundary conditions and the numerical results are obtained using an implicit finite difference scheme of Crank-Nicholson type. The effects of physical parameters on velocity, temperature and concentration profiles and also on local and mean skin-friction coefficient, Nusselt number and Sherwood number are interpreted graphically. It is observed that the variable temperature and concentration exists in the boundary of cylinder relegates the rate of heat and mass transfer.

On the fluid dynamics of unsteady separated stagnation-point flow of a power-law fluid on the surface of a moving flat plate

The transformation group theoretic approach is applied to perform an analysis of the unsteady separated stagnation-point (USSP) flow over a moving flat plate immersed in a non-Newtonian power-law fluid. This unsteady two-dimensional laminar boundary layer flow of a power-law fluid is governed by the classical Ostwald–de Waele power-law model. The system of governing partial differential equations reduces to an autonomous third order nonlinear ordinary differential equation via two-parameter group theoretic method. By using an efficient shooting method, we have established the existence of two different kinds of solutions, namely: (i) attached flow solution (AFS) and (ii) reverse flow solution (RFS) of this USSP flow problem under a definite negative value of the unsteadiness parameter β with a given value of the acceleration parameter a and for all values of the power-law index n considered in the present study. We have also found a unique AFS solution that is irrespective of n when β≥0. Dual solutions of the governing boundary layer equation are found for all kinds of fluids with the fixed values of a=1 and β=−1. The role of the rheological index n on the displacement thickness, skin-friction coefficient and velocity boundary layer are explored numerically. The results of this analysis reveal that the wall shear stress is always positive for AFS flow and negative for RFS flow for the above values of a and β with any given value of n. A novel result that emerges from this analysis is that the magnitude of the wall shear stress decreases and finally it approaches asymptotically to a constant value with the increase in the non-Newtonian behavior (n>1) of the fluids for both the cases of AFS and RFS.

The wake structure and transition process of a flow past a sphere affected by a streamwise magnetic field

The wake structure and transition process of an incompressible viscous fluid flow past a sphere affected by an imposed streamwise magnetic field are investigated numerically over flow regimes that include steady and unsteady laminar flows at Reynolds numbers up to 300. For cases without a magnetic field, a subregion with the existence of a limit cycle is found in the range $210<Re<270$. The point of division is between $Re=220$ and $Re=230$. For cases with a streamwise magnetic field, five wake patterns are the steady axisymmetric wake with an attached separation bubble, the steady plane symmetric wake with a small spiral dismissed, the steady plane symmetric wake with a limit cycle, the steady plane symmetric wake with a small spiral fed by the upstream fluid and the unsteady plane symmetric wake with a wave-like oscillation or vortex shedding. Under the influence of an imposed streamwise magnetic field, the wake will be transitioned to various patterns. An interesting ‘reversion phenomenon’, which describes the topological structure behind a sphere with a higher Reynolds number and a certain interaction parameter which corresponds to a lower Reynolds number case with a certain interaction parameter or a much lower Reynolds number case without a magnetic field, is also found. The principal results of the present work are summarized in a map of regimes in the $\{N,Re\}$ plane.

A Numerical Algorithm for Solving Higher‐Order Nonlinear BVPs with an Application on Fluid Flow over a Shrinking Permeable Infinite Long Cylinder

We present an efficient iterative power series method for nonlinear boundary‐value problems that treats the typical divergence problem and increases arbitrarily the radius of convergence. This method is based on expanding the solution around an iterative initial point. We employ this method to study the unsteady, viscous, and incompressible laminar flow and heat transfer over a shrinking permeable cylinder. More precisely, we solve the unsteady nonlinear Navier–Stokes and energy equations after reducing them to a system of nonlinear boundary‐value problems of ordinary differential equations. The present method successfully captures dual solutions for both the flow and heat transfer fields and a unique solution at a specific critical unsteadiness parameter. Comparisons with previous numerical methods and an exact solution verify the validity, accuracy, and efficiency of the present method.

On the Voitkunskii Amfilokhiev Pavlovskii Model of Motion of Aqueous Polymer Solutions

We study the mathematical properties of the model of motion of aqueous polymer solutions (Voitkunskii, Amfilokhiev, Pavlovskii, 1970) and its modifications in the limiting case of small relaxation times (Pavlovskii, 1971). In both cases, we examine plane unsteady laminar flows. In the first case, the properties of the flows are similar to those of the flow of an ordinary viscous fluid. In the second case, there may exist weak discontinuities that are preserved during the motion. We also address the steady flow problem for a dilute aqueous polymer solution moving in a cylindrical tube under a longitudinal pressure gradient. In this case, a flow with rectilinear trajectories (an analog of the classical Poiseuille flow) is possible. However, in contrast to the latter, the pressure in this flow depends on all three spatial variables.

Real-time implementation of Kalman filter for unsteady flow measurement in a pipe

A Kalman filter which estimates unsteady laminar flow in a pipe is implemented on a real-time computing system. The plant model is the optimised finite element model of pipeline dynamics considering unsteady laminar friction. A steady-state Kalman filter is built based on the model of pipeline dynamics. Pressure signals at both ends of a target section of a pipe are input to the model of pipeline dynamics, and as an output of the model an estimated pressure signal at a mid-point of the pipe is obtained. Difference between measured and estimated pressure signals at the mid-point is fed back to the model of pipeline dynamics to modify state variables of the model. According to the Kalman filter principle, the state variables of the model are adjusted so that they converge to real values. It is demonstrated that real-time implementation of the Kalman filter is possible with the sampling time of 0.1 ms.

Real-time implementation of Kalman filter for unsteady flow measurement in a pipe

A Kalman filter which estimates unsteady laminar flow in a pipe is implemented on a real-time computing system. The plant model is the optimised finite element model of pipeline dynamics considering unsteady laminar friction. A steady-state Kalman filter is built based on the model of pipeline dynamics. Pressure signals at both ends of a target section of a pipe are input to the model of pipeline dynamics, and as an output of the model an estimated pressure signal at a mid-point of the pipe is obtained. Difference between measured and estimated pressure signals at the mid-point is fed back to the model of pipeline dynamics to modify state variables of the model. According to the Kalman filter principle, the state variables of the model are adjusted so that they converge to real values. It is demonstrated that real-time implementation of the Kalman filter is possible with the sampling time of 0.1 ms.

Numerical simulation of two-dimensional laminar unsteady flow past a right trapezoidal cylinder at low Reynolds number: study of sharpening angle, time step, grid independence and domain size

Numerical simulation of two-dimensional laminar unsteady flow past a right trapezoidal cylinder at low Reynolds number (Re = 100), zero of the flow approaching angle and sharpening angle of the right trapezoidal of 22.5° with a side ratio B/A = 1 are carried out to provide moreapplicable data for engineering design of barred tee in aspect of structural integrity. A finite volume method, non-uniform meshing with second-order implicit time discretization into eight-node quadratic quadrilateral finite elements is employed. An incompressible flow SIMPLEC code with constant fluid properties is used. The convective terms using a third-order QUICK scheme. The numerical simulation result is compared against the published results of flow past a square cylinder. The effect of sharpening angle on the response of the right trapezoidal cylinder is investigated. A special study of the effects of flow on significant factor for time step, grid independence, blockage ratio, domain size, upstream and downstream extents, size domain next to cylinder and size domain extent are performed systematically. The Strouhal number and RMS lift coefficients of fully saturated flow are calculated. The result shown that increasing of sharpening angle, the Strouhal number is negligible changed whilst the RMS lift coefficients significantly increased.

Mixed Convection Heat Transfer in a Channel in Presence of Baffles

Mixed convection heat transfer enhancement of laminar unsteady flow in a baffled and asymmetrically heated vertical channel is numerically studied. The baffles are installed on both walls in an offset manner. The governing equations are solved by the finite volume method using OpenFOAM code. Air (Pr = 0.71) is used as the working fluid. The effects of Reynolds number (100–1400) and Grashof number (2.5 × 104 to 2 × 105) in addition to the baffle height (0.1–0.5) on heat transfer and friction factor are evaluated. The results obtained indicated that the flow passes to the self-sustained oscillatory flow at moderate Reynolds number (below 600 for a blockage ratio of 0.25). Unsteady self- sustained flow leads to heat transfer enhancement up to 2.8 times for baffle height hb = 0.25 and up to 3.7 times for baffle height hb = 0.5 as compared to the smooth channel.

Thermohydraulic transport characteristics in wavy microchannel under pulsating inlet flow condition

The numerical investigation on developing unsteady laminar fluid flow and heat transfer inside a 2D wavy microchannel, due to sinusoidal varying velocity component at inlet is done. The thermohydraulic flow was developing while the microchannel walls were kept at constant uniform temperature. The transient solution of 2DNavier-Stokes equation was attained using the SIMPLE algorithm with the momentum interpolation technique. The deionized water is used as working fluid and Reynolds number ranging from 0.1 to 100. The simulation results reports, mainly the heat transfer and pressure drop for wavy microchannel are compared with straight microchannelby keeping the cross sectional area same. By comparing with steady flow in wavy channel it was seen that imposed sinusoidal velocity at inlet can improved performance in terms of heat transfer at different amplitude (0.2, 0.5, 0.8) and frequency (1, 5, 10) while keeping the friction factor within tolerable limits.

Unsteady Flow of a Nanofluid Past a Permeable Shrinking Cylinder using Buongiorno's Model

The unsteady laminar boundary layer flow of a nanofluid and heat transfer over a permeable shrinking cylinder using the Buongiorno’s nanofluid model is investigated. Using a similarity transformation, the governing partial differential equations are transformed into a system of ordinary differential equations and then solved numerically using a shooting method. The numerical results are obtained for velocity, temperature and concentration profiles as well as the skin friction coefficient, the local Nusselt number and the local Sherwood number. Dual solutions are found to exist in a certain range of the suction and unsteadiness parameters. It is observed that suction parameter increase both the skin friction coefficient and the heat transfer rate at the surface, whereas the opposite trend is obtained for the Sherwood number. It is also observed that suction widens the range of the unsteadiness parameter for which the solution exists.