Effect of a moving boundary on pulsatile flow of incompressible fluid in a tube

The pulsatile flow in a pipe with a moving boundary has been studied for a viscous, incompressible fluid by solving the Navier-Stokes equations numerically. The governing equations were formulated in boundary fitted curvilinear coordinates and a finite volume discretization procedure was used to solve the problem. This analysis is based on the assumption that the flow has a simple periodic pulsation and the shape of the wall changes according to the frequency of pulsation. The presence of the moving boundary causes unsteadiness in the flow behaviour as the vibrating wall has a nonlinear interaction with the flow. A detailed analysis of the flow field is presented here for a range of frequencies (5≤α≤10) where α is the reduced frequency parameter and a Reynolds number of 100.     

Natural convection heat transfer of cold water in an eccentric horizontal cylindrical annulus — a numerical study

A numerical study of the natural convection heat transfer of cold water, having the density inversion between two isothermal eccentric horizontal cylinders is studied. A general code is developed for the body fitted coordinate system. This procedure transforms an arbitrarily shaped physical domain into a rectangular (square) domain. The governing equations in this computational domain are solved by the upwind finite difference scheme. The numerical solutions are obtained for a Rayleigh number (Ra) ranging between a Prandtl number (Pr) 12.0 and inversion parameter (γ) 0,−1 and −2. The affect of the radius ratio (R) on the flow patterns and heat transfer coefficients is studied by taking the Radius ratio as 1.5 and 2. The eccentricity affect is studied by moving the center of the inner cylinder horizontally and vertically (both positive and negative directions) with respect to the center of the outer cylinder. For the cases considered in the present study, it is again for the minimum heat transfer is observed like in the case of concentric annulus.     

Free-convective heat transfer within a differentially heated vertical plane during additional heat supply through a bottom wall

This work presents results of a numerical investigation of the structure of flow and heat exchange in a vertically closed interlayer with various relative heights A = H/L = 4–16 during variation in heat supply to its bottom. The vertical walls were isothermic; top wall, bottom wall, heat flow was supplied uniformly. The nonstationary Navier-Stokes equations were solved numerically in the two-dimensional formulation for the laminar flow. At small Rayleigh numbers (Ra ≈ 10³), when conductive heat transfer prevails within the interlayer, the effect of heat supply from below results in a change of heat transfer only in an immediate vicinity of the bottom. As the Rayleigh number and supplied heat increase, flow destabilization is observed, which results in strong heterogeneity of the density of heat flow along the wall height. At the same time, the heat flow at the hot vertical wall at defined Rayleigh numbers and heating from below may change the sign to the opposite one.     

Influence of developing flow on the heat transfer in laminar oscillating pipe flow

A theoretical analysis was performed to evaluate the influence of developing flow on the heat transfer associated with laminar oscillating pipe flow. Simplified analytical approaches are briefly discussed before an investigation based on the numerical solution of the conservation equations for mass, momentum and energy is presented, assuming constant wall temperature and an incompressible viscous fluid. Focusing on operating conditions as found in heat exchangers of regenerative thermal machines, like Stirling engines or Vuilleumier heat pumps, numerous calculations of the flow field and the heat transfer have been executed covering wide ranges of the characteristic dimensionless groups. The results are presented in tems of correlations of the mean Nusselt number averaged on the pipe length and a distribution function describing the local heat transfer. Furthermore, it is shown that the derived correlations are also applicable to compressible fluid flow, provided that the relative pressure amplitude is within the limits typical of regenerative thermal machines.     

BEM and FEM based numerical simulations for biomagnetic fluid flow

We investigate numerically the biomagnetic fluid flow between parallel plates imposed to a magnetic source placed below the lower plate. The biomagnetic fluid is assumed to be Newtonian, viscous, incompressible, electrically nonconducting, and has magnetization varying linearly with temperature and magnetic field intensity. Both steady and unsteady, laminar, two-dimensional biomagnetic fluid flow equations taking into care the heat transfer between the plates are solved using both finite element and dual reciprocity boundary element methods. Treatment of nonlinear terms by using only the fundamental solution of the Laplace equation, and discretization of only the boundary of the region are the advantages of dual reciprocity boundary element method giving small algebraic systems to be solved at a small expense. Finite element method is capable of giving very accurate results by discretizing the region affected by the magnetic source very finely, but it results in large sized algebraic systems requiring high computational cost. The results indicate that the flow is appreciably affected with the presence of magnetic source in terms of vortices at the magnetic source area. The lengths of the vortices, and temperature increase with an increase in the intensity of the magnetic field.     

Parametric study of unsteady forced convection with pressure gradient

By an extension of differential method, this paper has successfully examined the unsteady forced convection heat transfer from a flow over a flat plate. Transient state is inherent to a sudden change on the heat flux density at the surface of a plate. The general case where the pressure along the direction of flow is not constant is presented. The differential momentum and heat transfer equations are solved numerically. The results are given for different values of pressure gradient parameter m, in the cases of attached boundary layer, and for several values of Prandtl number corresponding to usual fluids (0.71 ⩽ Pr ⩽ 100). The dependences of transient behaviours with Pr number and parameter m are evidenced from the evolutions in time of temperature profile, Stanton number, and duration of unsteady process. Solutions given from the beginning of transient state to the ultimate steady state are discussed. Moreover, analytical solutions, as function of Pr and m, are deduced for Stanton number and duration of unsteady regime.     

Effects of free convection on the oscillatory flow of a polar fluid through a porous medium in the presence of variable wall heat flux

The purpose of this work is to study a laminar two-dimensional free convective oscillatory flow of an incompressible polar fluid through a saturated porous medium occupying a semi-infinite region of the space which is bounded by an infinite vertical permeable plate in the presence of oscillating suction and variable wall heat flux. The governing equations are based on the local volume averaging technique. The generalized Darcy equation accounting for polar effects is employed. Analytical expressions for the linear momentum, angular momentum, and energy fields are obtained by using the two-term perturbation technique. The numerically computed results are shown graphically and compared with the corresponding ones for a viscous (Newtonian) fluid. Distribution of the mean velocity of a polar fluid is found to increase as compared to the Newtonian fluid. The analysis reveals multiple boundary-layer structure for velocity. Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 5, pp. 868–884, September–October, 2008.     

The effect of variable properties on the helical flow and heat transfer of power law fluids

Summary Laminar flow and forced convection heat transfer of the time independent non–Newtonian fluid obeying power law stress-strain relation have been investigated numerically in the annular space between two coaxial rotating cylinders. The problem is considered when the inner cylinder rotates about the common axis with constant angular velocity and the outer cylinder is at rest. The viscosity of the fluid and thermal conductivity are assumed to vary with the temperature. The outer surface of the annulus is considered to be adiabatic, while the inner surface has a uniform temperature. The tangential and axial momentum equations and energy equation have been solved iteratively by using a finite difference method. For the steady fully developed flow, the velocity distributions, temperature profiles, the volumetric flow rate, torque and the average Nusselt number have been obtained for different values of the radius ratio and model parameters.     

Prediction of incidence effects on oscillating airfoil aerodynamics by a locally analytical method

A complete mathematical model is formulated to analyse the effects of mean flow incidence angle on the unsteady aerodynamics of an oscillating airfoil in an incompressible flow field. A velocity potential formulation is utilized. The steady flow is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating airfoil. The numerical solution technique for both the steady and unsteady flow fields is based on a locally analytical method. In this method, analytical solutions are incorporated into the numerical technique, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual local computational grid elements. This flow model and locally analytic numerical solution method are then verified through the excellent correlation obtained with the Theodorsen oscillating flat plate and Sears transverse gust classical solutions. The effects of mean flow incidence on the steady and oscillating airfoil aerodynamics are then investigated.     

An Arbitrary Lagrangian-Eulerian finite element method

This paper describes an Arbitrary Lagrangian- Eulerian (ALE) finite element method for the simulation of fluid domains with moving structures. The fluid is viscous, incompressible and unsteady and the fluid motion is solved by a fractional step discretization of the Navier-Stokes equations. The emphasis is on convection dominated flows, and a three-step method is used for the convection term. The moving structure causes the mesh of the fluid domain to move, and a new algorithm is proposed to solve the important and crucial problem of the calculation of the mesh velocities. Numerical calculations of the added mass and added damping of a vibrating two-dimensional circular cylinder in the frequency Reynolds number range Re _w =20−2000 are performed to evaluate the proposed ALE finite element method. The numerically calculated added mass and added damping are compared to both analytical and numerical results. To further demonstrate the generality of the method, a numerical simulation of flow past an oscillating schematic sports car is presented.     

Heat transfer in unsteady flow through a porous medium between two infinite parallel plates in relative motion

An approximate solution to the heat transfer in a flow of a viscous incompressible fluid through a porous medium bounded by two infinite parallel plates, the lower one stationary and the upper one oscillating in its own plane, is presented. Expressions for the mean temperature, the amplitude, and phase of the first and second harmonic of the rate of heat transfer and the mean rate of heat transfer are derived. The mean temperature is shown on graphs and the numerical values of the amplitudes and the phase are entered in a table. It is observed that the mean rate of heat transfer decreases with more ease of percolation but increases with increasing the frequency ω.     

Exact solutions of non-Newtonian fluid flows with prescribed vorticity

Summary The equations of motion of a non-Newtonian second-grade fluid flow are highly nonlinear partial differential equations. For this reason, there exists only a limited number of exact solutions. Due to the complexity of the equations, inverse methods described by Nemenyi [1] have become attractive in the study of non-Newtonian fluids. In these methods, certain physical or geometrical properties of the flow field are assumed a priori.Lin and Tobak [2] studied steady plane viscous incompressible flows for a chosen vorticity function by decomposing the nonlinear fourth-order partial differential equation in the streamfunction. This excellent approach yielded two second-order linear partial differential equations in the streamfunction. Hui [3] used this approach to study unsteady plane viscous incompressible flows.During the past decade, there has been substantial interest in flows of viscoelastic liquids due to the occurrence of these flows in industrial processes. In this paper, we study the steady and unsteady incompressible viscous non-Newtonian second-grade fluid flows in which the vorticity is proportional to the streamfunction perturbed by a uniform stream. The solutions obtained are exact solutions and represent various non-parallel flows of second-grade fluids.The plan of this paper is as follows: In Sect. 2, the equations of motion of an unsteady plane incompressible second-grade fluid are given, and the vorticity function is assumed to be ² =A(–Ux–BUy ²). In Sect. 3, solutions for the steady flow are obtained. In Sect. 4, solutions for unsteady flow are obtained.     

Unsteady flows of a binary mixture of incompressible Newtonian fluids in an annulus

This paper is concerned with applying the mixture theory of two chemically inert incompressible Newtonian fluids to some simple unsteady flows in the annular region between two infinitely long coaxial cylinders. The equations governing the motion of the binary mixture under discussion are reduced to a system of coupled partial differential equations. With the help of finite Hankel transforms, the exact solutions of these equations are obtained in series form for the following three problems: (i) unsteady axial Couette flow in an annulus, (ii) unsteady Poiseuille flow in an annulus, (iii) unsteady circular Couette flow in an annulus.     

Transferts thermiques en écoulements oscillants laminaires incompressibles

Phenomena concerning the temperature variations and the heat transfer are studied in the specific case of oscillating flow with null mean velocity circulating between two infinite walls. A 1D model is established and the interesting scale parameters are deduced from theoretical equations. The particular case of an oscillating laminar flow for incompressible fluid is detailed in order to illustrate and to discuss the effects of thermal interactions between the fluid and walls. Influence of wall length comparatively to the fluid displacement is studied. Conclusions for designing thermal heat exchangers of Stirling engines or PTR are proposed.     

Flow Boiling Heat Transfer in Two-Phase Micro Channel Heat Sink at Low Water Mass Flux

Boiling heat transfer at water flow with low mass flux in heat sink which contained rectangular microchannels was studied. The stainless steel heat sink contained ten parallel microchannels with a size of 640 × 2050 μm in cross-section with typical wall roughness of 10–15 μm. The local flow boiling heat transfer coefficients were measured at mass velocity of 17 and 51 kg/m²s, heat flux on 30 to 150 kW/m² and vapor quality of up to 0.8 at pressure in the channels closed to atmospheric one. It was observed that Kandlikar nucleate boiling correlation is in good agreement with the experimental data at mass flow velocity of 85 kg/m²s. At smaller mass flux the Kandlikar model and Zhang, Hibiki and Mishima model demonstrate incorrect trend of heat transfer coefficients variation with vapor quality.     

On the effectiveness of porosity on stagnation point flow towards a stretching surface with heat generation

An analysis is made of the steady laminar flow through a porous medium of an incompressible viscous conducting fluid impinging on a permeable stretching surface with heat generation. Numerical solution for the governing non-linear momentum and energy equations is obtained. The effect of the porosity of the medium, the surface stretching velocity, and the heat generation/absorption coefficient on both the flow and heat transfer is presented and discussed.     

Finite element simulation of combined buoyancy and thermocapillary driven convection in open cavities

Thermocapillary-induced and buoyancy-driven convective flows that commonly occur in crystal growth are numerically simulated using Galerkin finite element method. The physical domain comprises of a open cavity with aspect ratio one and differentially heated vertical walls. The top gas–melt interface is free to deform subject to 90° contact angle boundary conditions at the two vertical walls. The unsteady two-dimensional Navier–Stokes equations are discretized in time using Chorin-type splitting scheme and pressure is determined from the Poisson's equation. The free surface is taken to be resting on vertical spines and its evolution in time is determined from the kinematic free surface equation. The governing equations for heat and momentum are solved in the Arbitrary Lagrangian Eulerian frame of reference to handle the moving boundary. The influence of Grashof number, Marangoni number, Bond number, Ohnesorge number and Prandtl number on the flow field and heat transfer is investigated.     

Computational study of unsteady viscous flow around a transversely and longitudinally oscillating circular cylinder in a uniform flow at high reynolls numbers

A finite difference simulation method for the time dependent viscous incompressible flow around a transversely and longitudinally oscillating circular cylinder at Reynolds numbers of Re=4×10³ and 4×10⁴ is presented. The Navier-Stokes equations in finite difference form are solved on a moving grid system, based on a time dependent coordinate transformation. Solution of the vortex street development behind the cylinder is obtained when the cylinder remains stationary and also when it is oscillating. Time eholution of the flow configuration is studied by means of stream lines, pressure contours and vorticity contours. The computer results predict the lock-in phenomenon which occurs when the oscillation frequency is close to the vortex shedding frequency in the transverse mode or around double the vortex shedding frequency in the longitudinal mode. The time dependent lift and drag coefficients are obtained by the integration of the pressure and shear forces around the body. The drag, lift and the displacement relations are also discussed.     

Unsteady oscillatory stagnation-point flow of a viscoelastic fluid

The unsteady stagnation point flow of the Walters B^′ fluid is examined and solutions are obtained. It is assumed that the infinite plate at y=0 is oscillating and the fluid impinges obliquely on the plate.