Unsteady Flow Of Incompressible Fluid Research Articles

Heat and mass transfer with viscous dissipation in horizontal channel partially occupied by porous medium in the presence of oscillatory suction

This paper deals with unsteady oscillatory flow of viscous incompressible fluid with heat & mass transfer in a horizontal channel partially occupied by porous medium following the Darcy-Brinkman model. The interior territory of the channel consists of two regions; one of them is filled with porous material and second is clear fluid. At the porous medium fluid interface, interfacial coupling conditions for the fluid velocity, temperature and concentration were used to derive the analytical solution. The effects of pertinent physical fluid parameter like porosity, viscosity ratio, density ratio etc. on velocity, temperature and concentration distribution are considered and demonstrated through graphs. Also, the non-dimensional Skin-friction coefficient, Nusselt number and Sherwood number have been calculated and reported in tabular form.

Cumulative jet generation in a plane parallel potential flow of the perfect incompressible fluid

This manuscript deals with the plane parallel unsteady potential flow of the perfect incompressible fluid limited by a free boundary. As the result of the free boundary deformation, cumulative jets may form. A cumulative jet generation in a problem of cylindrical cavity deformation is considered in this manuscript. A numerical algorithm for this problem is proposed. Based on the boundary elements method with no saturation, the algorithm has a high order of approximation and reasonable computation time. The distribution of points along the length of the cavity boundary is required to be constant at computation time. This requirement provides the numerical stability of the algorithm. To verify the correctness of the proposed algorithm, conservation laws are used.

Numerical solution of inverse problems in hydrodynamics

The paper is devoted to inverse problems for the unsteady viscous incompressible fluid flow. In the problems under consideration we estimate the velocity vector on a part of the boundary using velocity measurements in a certain observation subdomain. Optimal control approach reduces this problem to the constrained minimization. For unsteady flow and the discrete measurement data we use discrete optimization methods to solve this problem. New numerical algorithm based on the finite dimensional minimization is proposed and numerical results are discussed.

Existence and approximation for Navier–Stokes system with Tresca’s friction at the boundary and heat transfer governed by Cattaneo’s law

We consider an unsteady non-isothermal incompressible fluid flow. We model heat conduction with Cattaneo’s law instead of the commonly used Fourier’s law, in order to overcome the physical paradox of infinite propagation speed. We assume that the fluid viscosity depends on the temperature, while the thermal capacity depends on the velocity field. The problem is thus described by a Navier–Stokes system coupled with the hyperbolic heat equation. Furthermore, we consider non-standard boundary conditions with Tresca’s friction law on a part of the boundary. By using a time-splitting technique, we construct a sequence of decoupled approximate problems and we prove the convergence of the corresponding approximate solutions, leading to an existence theorem for the coupled fluid flow/heat transfer problem. Finally, we present some numerical results.

NUMERICAL SOLUTION OF UNSTEADY FLOW BETWEEN PARALLEL PLATES USING HAAR WAVELET-QUASILINEARIZATION METHOD

The present study is concerned with the analysis of unsteady flow of viscous incompressible fluid between parallel rectangular and circular plates. The Navier-Stokes equations modelling the flow are transformed into a fourth order non-linear ordinary differential equation using a similarity transformation. The resulting equation is solved by a new efficient numerical scheme based on Haar wavelet-quasilinearization method. The solution representing pressure gradient is obtained for large values of Reynolds number. A comparison with numerical results generated by MATLAB routine bvp4c demonstrates that the proposed method is more efficient and promising technique for solving highly nonlinear two-point boundary value problems. The absolute error and rate of convergence of numerical results are computed to test the applicability and accuracy of the method

Enhanced coupling of solid body motion and fluid flow in finite volume framework

An enhanced coupling strategy for the resolution of 6–degrees–of–freedom rigid body motion and unsteady incompressible fluid flow in Finite Volume collocated arrangement using PIMPLE algorithm and rigid mesh motion is presented in this paper. The improved coupling is achieved by calculating the 6–degrees–of–freedom motion equations after each pressure correction step in the pressure–velocity PISO (Pressure Implicit With Splitting of Operators) algorithm. Solving the 6–degrees–of–freedom equations after each solution of the pressure equation of the PISO loop accelerates the convergence, leading to smaller number of nonlinear pressure–velocity iterations needed per time–step. The novel approach is verified and validated on a heaving decay case, while the achieved acceleration in terms of the number of PISO loops is demonstrated on seakeeping simulations of a container ship.

Transient Free Convective MHD Flow Past an Exponentially Accelerated Vertical Porous Plate with Variable Temperature through a Porous Medium

This paper is concerned with analytical solution of one-dimensional unsteady laminar boundary layer MHD flow of a viscous incompressible fluid past an exponentially accelerated infinite vertical plate in presence of transverse magnetic field. The vertical plate and the medium of flow are considered to be porous. The fluid is assumed to be optically thin and the magnetic Reynolds number is considered small enough to neglect the induced hydromagnetic effects. The governing boundary layer equations are first converted to dimensionless form and then solved by Laplace transform technique. Numerical values of transient velocity, temperature, skin friction, and Nusselt number are illustrated and are presented in graphs for various sets of physical parametric values, namely, Grashof number, accelerating parameter, suction parameter, permeability parameter, radiation parameter, magnetic parameter, and time. It is found that the velocity decreases with increases of the suction parameter for both cases of cooling and heating of the porous plate whereas skin friction increases with increase of suction parameter.

Influence of thermal and concentration gradients on unsteady flow over a stretchable surface

Abstract The aim of this letter is to investigate the unsteady flow of incompressible fluid in the presence of thermal and concentration gradients over a bi-directional stretchable flat sheet that placed in nonporous media. The nondimensional form of the model is successfully obtained after utilizing the set of similarity transformations and necessary mathematical calculations. Then, resulting two-point boundary value problem is sort out numerically with the help of Runge-Kutta scheme after reducing the flow model into a set of initial value problem. Influence of the various flow parameters on the velocity, thermal and concentration fields discussed comprehensively by means of graphs. Furthermore, quantities of practical and physical interest such as skin friction coefficient, local rate of heat and mass transfer studied with the help of graphical aid. Finally, major outcomes of the study highlighted in the last section of the manuscript.

Applications of non-integer Caputo time fractional derivatives to natural convection flow subject to arbitrary velocity and Newtonian heating

Unsteady time fractional natural convection flow of incompressible viscous fluid due to arbitrary velocity with radiation and Newtonian heating is investigated. By introducing dimensionless variables and functions, the resulting equations are solved by the Laplace transform technique. Exact solutions for temperature and velocity fields are obtained by Caputo time fractional derivatives in dimensionless form, and they are expressed in terms of Robotnov–Hartley function and Wright’s function. The rate of heat transfer on plate is obtained in terms of Nusselt number. Some known solutions from the existing literature are obtained as limiting case when \(\alpha = 1\). At the end, we have seen the significant influence of fractional parameter \(\alpha\) on the temperature and velocity graphically and observed that it has shown an opposite behavior on temperature and velocity for small and large values of time t, respectively. This shows that how fractional parameter \(\alpha\) affects the fluid flow.

Transient Heat and Mass Transfer of Micropolar Fluid between Porous Vertical Channel with Boundary Conditions of Third Kind

Abstract An investigation of heat and mass transfer characteristics of unsteady free convective flow of viscous incompressible micropolar fluid between the vertical porous plates in the presence of thermal radiation is carried out in the present work. The fluid is considered to be grey, absorbing–emitting but non scattering medium and the Cogley–Vincent–Gilles formulation is adopted to simulate the radiation component of heat transfer. The resulting system of equations is solved numerically with Crank–Nicolson implicit finite difference method. The effects of various physical parameters such as transient, micropolar parameter, radiation parameter, Reynolds number, Schmidt number, heat and mass transfer Biot numbers on the velocity, temperature and concentration field are discussed graphically.

Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

AbstractThis paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress are also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.

Unsteady self-similar viscous flow near a stagnation point

The problem of unsteady viscous incompressible fluid flow near a stagnation point is considered. Self-similar solutions describing plane and axisymmetric flows are constructed.

Unsteady flow of shear-thinning non-Newtonian incompressible fluid through a twin-screw extruder

The unsteady flow of viscous incompressible shear-thinning non-Newtonian fluid with mixed boundary is investigated. The boundary condition on the outflow is the modified natural boundary condition, it contains the additional nonlinear term, which enables us to control the kinetic energy of the backward flow. The global existence of weak solution is proved. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.

Similarity Solutions of Unsteady Mixed Convective Boundary Layer Flow of Viscous Incompressible Fluid along Isothermal Horizontal Plate

Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.

Analytical and numerical investigation of unsteady flow near a critical point

The problem of unsteady flow of a viscous incompressible fluid near a critical point on a plane boundary is investigated. A theorem on the existence and uniqueness of its solution in Hölder classes of functions on an arbitrary time interval with natural restrictions imposed on the initial function is proved. Qualitative properties of the solution are investigated. Results of a numerical analysis demonstrating the possibility of disappearance after a finite time of a counterflow zone existing at the initial time in the case of a negative pressure gradient at the rigid plane are presented. In the case when the pressure gradient is a periodic function, a periodic mode of motion as well as breakdown of the solution after a finite time is possible.

Unsteady MHD Non-Newtonian Casson Fluid Flow due to a Porous Rotating Disk with Uniform Electric Field

The unsteady MHD Non-Newtonain incompressible casson fluid flow due to a porous rotating disk with a uniform angular velocity in the presence of an axial uniform magnetic field and a uniform electric field is examined. The Hall current is not considered in this paper. The governing equations of the problem are then reduced to non-linear ordinary differential equations by introducing suitable similarity parameters. The similarity equations are derived in such a way that one can see the effects of the angular velocity explicitly unlike the usual similarity transformation of rotating disk problems. Numerical solutions to the reduced non-linear similarity equations are then obtained by adopting shooting method using the Nachtsheim-Swigert iteration technique.

Temperature Dependent Variable Properties on Mixed Convective Unsteady MHD laminar Incompressible fluid Flow with Heat Transfer and Viscous Dissipation

In the present paper we investigated that the numerical solution of mixed convective laminar boundary layer flow with uniform transverse magnetic field for a vertical porous plate. The fluid properties are considered the nonlinear functions of temperature as μ = μ∞(T / T∞)A and κ = κ∞(T / T∞)C For flue gases the values of the exponents A and C are taken as A=0.7, and C=0.83. Also time dependent suction velocity is considered. The governing equations are reduced into ordinary differential equations by introducing the suitable similarity variables and then solved numerically by using sixth ordered Runge-Kutta method and Nachtsheim Swigert iteration technique. The numerical results of our physical interest are shown graphically and tabular form.

Topology optimization of unsteady flow problems using the lattice Boltzmann method

This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems. The optimization problem is solved with a gradient based method, and the design sensitivities are computed by solving the discrete adjoint problem. For moderate Reynolds number flows, it is demonstrated that topology optimization can successfully account for unsteady effects such as vortex shedding and time-varying boundary conditions. Such effects are relevant in several engineering applications, i.e. fluid pumps and control valves.

Functional and generalized separable solutions to unsteady Navier–Stokes equations

The paper studies unsteady Navier–Stokes equations with two space variables. It shows that the non-linear fourth-order equation for the stream function with three independent variables admits functional separable solutions described by a system of three partial differential equations with two independent variables. The system is found to have a number of exact solutions, which generate new classes of exact solutions to the Navier–Stokes equations. All these solutions involve two or more arbitrary functions of a single argument as well as a few free parameters. Many of the solutions are expressed in terms of elementary functions, provided that the arbitrary functions are also elementary; such solutions, having relatively simple form and presenting significant arbitrariness, can be especially useful for solving certain model problems and testing numerical and approximate analytical hydrodynamic methods. The paper uses the obtained results to describe some model unsteady flows of viscous incompressible fluids, including flows through a strip with permeable walls, flows through a strip with extrusion at the boundaries, flows onto a shrinking plane, and others. Some blow-up modes, which correspond to singular solutions, are discussed.

Flow behavior of unsteady incompressible Newtonian fluid flow between two parallel plates via homotopy analysis method

An analysis has been performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates where the upper plate is impermeable and can move up or down and the lower one is fixed and has a porous surface. The governing equations for this problem are reduced to an ordinary form and is solved using Homotopy Analysis Method (HAM) and numerically by fourth order Runge-Kutta technique. Also, Velocity fields have been computed and shown graphically for various values of physical parameters. As an important outcome, HAM is able to solve a large class of nonlinear problems effectively, more easily and accurately; and thus it has been widely applicable in engineering and physics.