Heat transfer in a viscoelastic boundary layer flow through a porous medium

This paper examines the viscoelastic fluid flow and heat transfer characteristics in a saturated porous medium over an impermeable stretching surface with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for two different heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing equations for the boundary layer flow problem result similar solutions. For the specified five boundary conditions, it is not possible to solve directly the resulting sixth-order nonlinear ordinary differential equation. For the present incompressible boundary layer flow problem with constant physical parameters, the momentum equation is decoupled from the energy equation. Two closed–form solutions for the momentum equation are obtained and identified the realistic solution of the physical problem. Exact solution for the velocity field and the skin-friction are obtained. Also, the solution for the temperature and the heat transfer characteristics are obtained in terms of Kummers function. Asymptotic results for the temperature function for large Prandtl numbers are presented. The work due to deformation in the energy equation, which is essential and escaped from the attention of researchers while formulating the visco-elastic boundary layer flow problems, is considered. Drastic variation in the values of heat transfer coefficient is observed when the work due to deformation is ignored.The authors would like to thank the reviewers for their valuable comments/ suggestions to improve the clarity of the paper.     

Effect of pressure gradient on MHD boundary layer over a flat plate

Summary The magnetohydrodynamic (MHD) boundary layer flow over a flat plate is examined here for two cases, viz. a uniform free-stream velocity and a uniform hydrostatic pressure. The nonlinear boundary layer equations are solved using a reliable finite-difference method. The boundary layer physical parameters such as skin-friction coefficient, displacement, momentum and energy thicknesses of the boundary layer are determined. It is found that the normal surface velocity gradient decreases with the local magnetic interaction parameter for the cases of a uniform hydrostatic pressure, whereas in the case of a uniform free-stream volocity it increases with the interaction parameter.     

Influences of fluid property variation on the boundary layers of a stretching surface

Summary. In this work, the influences of temperature-dependent fluid properties on the boundary layers over a continuously stretching surface with constant temperature are investigated. Based on the boundary layer assumptions, the coupled similarity equations are obtained for special situations, in which the fluid density and heat capacity are assumed without dependence on the temperature. Those similarity equations are solved numerically. The influences of property variation on wall stresses and heat fluxes are discussed. It is found that the property variation can influence the distributions of both fluid velocity and temperature across the boundary layers. For the thermal boundary layer, using mean properties evaluated at the average temperature of wall and ambient fluid can give good results for the temperature distribution. However, for the momentum boundary layer, the difference of velocity distributions can be large.     

Micropolar fluid jet impingement on a curved surface

This paper deals with an analysis of a normally impinging micropolar fluid jet on a curved surface. The flow near the stagnation point in the impingement region is divided into inviscid and viscous flow regions. The inviscid flow solution is governed by Euler's equations of motion expressed in curvilinear coordinate system. The viscous flow solution is governed by the zeroth and the first order boundary layer equations. These boundary layer equations are solved by assuming power series expansions for both velocity and microrotation fields which give rise to two systems of ordinary coupled differential equations. The effects of surface curvature and material parameters on boundary layer characteristics have been studied and presented graphically. The gradients of zeroth order velocity and microrotation at the wall decrease and the zeroth order displacement and momentum thicknesses increase with decrease in the value of surface curvature. The reduction in curvature results in the reduction in the gradients of first order velocity and microrotation at the wall as well as first order displacement and momentum thicknesses.     

Heat transfer in boundary layer flow of a micropolar fluid past a curved surface with suction and injection

Van Dyke's singular perturbation technique has been used to study the heat transfer in the flow of a micropolar fluid past a curved surface with suction and injection. The conditions for similar solutions of the thermal boundary layer equations have been obtained. In addition to the usual “no slip” condition for velocity, the two types of boundary conditions used for microrotation are: (i) no relative spin on the boundary; (ii) the anti-symmetric part of the stress tensor vanishes at the boundary. The effect of suction or injection on velocity, microrotation, temperature, skin friction coefficient, wall couple stress coefficient, displacement and momentum thicknesses, rate of heat transfer and adiabatic wall temperature have been studied. It is observed that with the increase of injection velocity, the thickness of the boundary layer is increased and the local drag is reduced. A comparison with the results obtained for a Newtonian fluid reveals that the microelements present in the fluid reduce the velocity and frictional drag, and cool the boundary.     

Low frequency oscillations in turbulent Rayleigh-Benard convection

A locally time-periodic flow in Rayleigh-Benard convection in the range of Rayleigh number R of 10⁷ to 10⁸, Prandtl number 7, and aspect ratio 12 is reported. This time periodicity is associated with organized clusters of tilted plumes travelling steadily across the fluid layer. A scavenging plume model is presented in which prior passage of a plume has depleted the thermal boundary layer in a history-dependent way: The boundary layer is very thin where the plume has just passed, but has had time to thicken where the plume passed some time ago. Thus at any moment there is a thermal boundary layer of varying thickness, and the pressure gradient in it drives flow towards the thicker regions. There is then a shear and a down-gradient momentum flux at the wall. This boundary layer is supposed to erupt when and where its thickness reaches some critical value. Then, assuming that the interior momentum flux is entirely by Reynolds stresses, we can, by matching interior and boundary layer heat and momentum fluxes, determine the period which is shown to be in reasonable agreement with the observations. This is a contribution #386 of the Geophysical Fluid Dynamics Institute, Florida State University.     

Free convection flow of water near 4 °C past a moving plate

In the present study the unsteady free convection flow of water near 4?^°C in the laminar boundary layer over a vertical moving porous plate is investigated. The effect of the suction/injection parameter at the plate on the velocity is considered. The momentum equation is solved numerically by a fourth-order Runge-Kutta scheme. The numerical results which are obtained for the flow are shown graphically.     

Some predictions of the attached eddy model for a high Reynolds number boundary layer

Many flows of practical interest occur at high Reynolds number, at which the flow in most of the boundary layer is turbulent, showing apparently random fluctuations in velocity across a wide range of scales. The range of scales over which these fluctuations occur increases with the Reynolds number and hence high Reynolds number flows are difficult to compute or predict. In this paper, we discuss the structure of these flows and describe a physical model, based on the attached eddy hypothesis, which makes predictions for the statistical properties of these flows and their variation with Reynolds number. The predictions are shown to compare well with the results from recent experiments in a new purpose-built high Reynolds number facility. The model is also shown to provide a clear physical explanation for the trends in the data. The limits of applicability of the model are also discussed.     

An overview of air-sea interface process studies

Recent progress in the study of air-sea interface processes for momentum, heat, moisture and mass transfer are reviewed in the present article. Except for turbulent structure, we have analysed the other physical mechanisms occurring in the wave boundary layer, such as the roles of the sea surface state, droplets and bubbles due to wave breaking, which at least partly account for the existing discrepancies between theory and observations. The experiments, both over the ocean and in the laboratory, are described briefly. In conclusion, a few perspective trends in this area are suggested for further investigation. The project is financially supported by the Chinese National Science Foundation.     

MODELING OF SALTATION AND TURBULENCE EFFECTS IN A HORIZONTAL GAS-SOLID BOUNDARY LAYER

This work is devoted to the study of the behavior of solid particles in a horizontal air boundary layer. A two-fluid model is selected to analyze the particle motion in the mixed regime where both saltation and turbulence effects are important. Boundary layer approximations are applied to the solid phase equations, using conventional space/time averaging. Resulting equations are shown to be in agreement with the phase averaged equations generally used in two-fluid models. Closure is achieved by means of a gradient law, however the particle diffusion and momentum transfer coefficients are distinguished using a variable particle Schmidt number. Turbulent particle diffusion is modeled using an available analytical model, which is modified to take the saltation effect into account in the particle r.m.s. velocity. Comparison between experimental and numerical results shows that the following analysis is acceptable within the experimental and numerical error. The model slightly underestimates the particle mean velocity in the outer region of the boundary layer, but yields satisfactory values of mass fluxes. The present simple approach adequately describes the particle behavior in a horizontal turbulent boundary layer, with the main originality being the realistic dependence of the particle Schmidt number upon the saltation phenomenon.     

Simulation of Turbulent Flow Past Bluff Bodies on Coarse Meshes Using General Galerkin Methods: Drag Crisis and Turbulent Euler Solutions

In recent years adaptive stabilized finite element methods, here referred to as General Galerkin (G2) methods, have been developed as a general methodology for the computation of mean value output in turbulent flow. In earlier work, in the setting of bluff body flow, the use of no slip boundary conditions has been shown to accurately capture the separation from a laminar boundary layer, in a number of benchmark problems. In this paper we extend the G2 method to problems with turbulent boundary layers, by including a simple wall-model in the form of a friction boundary condition, to account for the skin friction of the unresolved turbulent boundary layer. In particular, we use G2 to simulate drag crisis for a circular cylinder, by adjusting the friction parameter to match experimental results. By letting the Reynolds number go to infinity and the skin friction go to zero, we get a G2 method for the Euler equations with slip boundary conditions, which we here refer to as an EG2 method. The only parameter in the EG2 method is the discretization parameter, and we present computational results indicating that EG2 may be used to model very high Reynolds numbers flow, such as geophysical flow.     

Surface tension driven flows in shallow layers due to heat or mass transfer to the free surface

In a number of physical systems a surface tension driven flow is established in a shallow layer of liquid as a result of heat or mass transfer to the free surface. Such transfer processes often produce a thin temperature or concentration boundary layer near the free surface. We have considered the relatively simple situation when this occurs in shallow two-dimensional channel flow under steady conditions. It is shown that the properties of the boundary layer can be obtained by solving a sequence of parabolic partial differential equations and that the shape of the free surface results from the solution of an integral equation. The simple case of uniform surface transfer has been considered, but the analysis developed can be extended to more complex situations.     

Nonlinear instability of developing streamwise vortices with applications to boundary layer heat transfer intensification through an extended Reynolds analogy

The intent of the present contribution is to explain theoretically the experimentally measured surface heat transfer rates on a slightly concave surface with a thin boundary layer in an otherwise laminar flow. As the flow develops downstream, the measured heat transfer rate deviates from the local laminar value and eventually exceeds the local turbulent value in a non-trivial manner even in the absence of turbulence. While the theory for steady strong nonlinear development of streamwise vortices can bridge the heat transfer from laminar to the local turbulent value, further intensification is attributable to the transport effects of instability of the basic steady streamwise vortex system. The problem of heat transport by steady and fluctuating nonlinear secondary instability is formulated. An extended Reynolds analogy for Prandtl number unity, Pr=1, is developed, showing the similarity between streamwise velocity and the temperature. The role played by the fluctuation-induced heat flux is similar to momentum flux by the Reynolds shear stress. Inferences from the momentum problem indicate that the intensified heat flux developing well beyond the local turbulent value is attributed to the transport effects of the nonlinear secondary instability, which leads to the formation of 'coherent structures' of the flow. The basic underlying pinions of the non-linear hydrodynamic stability problem are the analyses of J. T. Stuart, which uncovered physical mechanisms of nonlinearities that are crucial to the present developing boundary layers supporting streamwise vortices and their efficient scalar transporting mechanisms.     

A conservative embedded boundary method for an inviscid compressible flow coupled with a fragmenting structure

We present an embedded boundary method for the interaction between an inviscid compressible flow and a fragmenting structure. The fluid is discretized using a finite volume method combining Lax–Friedrichs fluxes near the opening fractures, where the density and pressure can be very low, with high‐order monotonicity‐preserving fluxes elsewhere. The fragmenting structure is discretized using a discrete element method based on particles, and fragmentation results from breaking the links between particles. The fluid‐solid coupling is achieved by an embedded boundary method using a cut‐cell finite volume method that ensures exact conservation of mass, momentum, and energy in the fluid. A time explicit approach is used for the computation of the energy and momentum transfer between the solid and the fluid. The embedded boundary method ensures that the exchange of fluid and solid momentum and energy is balanced. Numerical results are presented for two‐dimensional and three‐dimensional fragmenting structures interacting with shocked flows. Copyright © 2015 John Wiley & Sons, Ltd.     

鲜食玉米冻结过程传热分析及冻结时间的研究

采用数值方法，将鲜食玉米模拟为具有同轴的双层圆柱，建立数学模型，并用改进的焓法进行求解，对鲜食玉米的冻结过程进行传热分析和冻结时间的预测。研究结果表明，该模型可以用来预测具有同轴双层圆柱特征尺寸的食品的冻结时间，最大相对误差为5．6％。冻结过程中玉米轴部分相变界面的移动速度明显小于玉米粒部分。而且鲜食玉米冻结时间随着送风速度的不同有很大的变化。     

Direct resonance analysis and modeling for a turbulent boundary layer over a corrugated surface

Summary Effects of surface corrugation on turbulent flow in a boundary layer are studied using a model based on the direct resonance theory. The induced mean flow due to weakly nonlinear waves, superimposed on the mean and fluctuating components of turbulence, is determined. The mean turbulent flow is affected by the surface corrugation throughout the boundary layer. The corrugated surface generates higher harmonics and affects the streamwise vortices generated by the waves superimposed on turbulence whose mean flow includes secondary induced mean flow components due to the corrugation.     

Studies on laminar thin film flow along a vertical wall

Summary The problem of a laminar thin-film flow along a vertical wall is examined here. Using a fourth-degree polynomial velocity profile function inside the boundary layer, the momentum integral equation is solved analytically to determine the boundary layer thickness and the corresponding film-thickness.     

Turbulence in a Roughness Layer

Consideration is given to a model of turbulent flow in a roughness layer; the model is formed by the equations for turbulent momentum and turbulence-energy density and by free boundary conditions at self-establishing boundaries of the turbulent zone in the entire layer and in roughness cells. The model describes the interactions of the flow with the elements of roughness and the processes in the cells of different scales. Certain calculated characteristics of turbulence in vegetation are given. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 4, pp. 143–151, July–August, 2005.     

A coupled BEM and arbitrary Lagrangian–Eulerian FEM model for the solution of two‐dimensional laminar flows in external flow fields

This paper describes a new computational model developed to solve two‐dimensional incompressible viscous flow problems in external flow fields. The model based on the Navier–Stokes equations in primitive variables is able to solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the pressure projection method. The external flow field is simulated using the boundary element method by solving a pressure Poisson equation that assumes the pressure as zero at the infinite boundary. The momentum equation of the flow motion is solved using the three‐step finite element method. The arbitrary Lagrangian–Eulerian method is incorporated into the model, to solve the moving boundary problems. The present model is applied to simulate various external flow problems like flow across circular cylinder, acceleration and deceleration of the circular cylinder moving in a still fluid and vibration of the circular cylinder induced by the vortex shedding. The simulation results are found to be very reasonable and satisfactory. Copyright © 2001 John Wiley & Sons, Ltd.     

Modelling frazil ice and grease ice formation in the upper layers of the ocean

A mathematical model for the formation of frazil ice and grease ice in the upper layers of the ocean is developed. The boundary layer considered is a turbulent Ekman layer, where buoyancy effects become important. The model is based on the conservation equations for mean momentum, temperature, salinity, frazil ice concentration and grease ice concentration. The turbulent exchange coefficients are calculated using a two-equation model of turbulence.The initial frazil ice formation is due to mass exchange with the atmosphere. The grease ice formation is due to flocculation of frazil ice crystals.The calculations focus attention to the time evolution and the vertical structure of the upper layers of the ocean during ice formation events. Also considered is at what frazil ice concentrations the flocculation or the grease ice formation become important.Several processes, such as cooling, supercooling, frazil ice formation, grease ice formation, and salt rejection, are treated by the model. The calculations based upon idealized meteorological input data seem to yield realistic results, and the model can therefore serve as a good guide for further studies, particularly together with field data.