Numerical study of thermal boundary layer on a continuous moving surface in power law fluids

This paper investigates flow and heat transfer of power law fluids on a continuous moving surface.The tempera-ture distribution is obtained numerically by considering the effect of the power law viscosity on thermal diffusiv-ity and the characteristics of the flow and heat transfer are analyzed.The results show that the distribution of thethermal boundary layer depends not only on the velocity ratio parameter of the plate,but also on the power lawindex and Prandtl number of fluids.     

Suitable Heat Transfer Model for Self-Similar Laminar Boundary Layer in Power Law Fluids

The classical power law non-Newtonian fluids energy boundary layer equation is proved improper to describe the self-similar heat transfer. A theoretical analysis for momentum and energy boundary layer transfer behavior is made and the full similarity heat boundary layer equation is developed, which may be characterized by a power law relationship between shear stress and velocity gradient with the Falkner-Skan equation as a special case. Both analytical and numerical solutions are presented for momentum and energy boundary layer equations by using the similarity transformation and shooting technique and the associated transfer characteristics are discussed.     

Experimental investigation of dimensionless velocity and shearing stress in boundary layer flow on continuous moving surface in power law fluids

An analysis is carried out to study the steady flow characteristics from a continuous flat surface moving in a parallel free stream of non-Newtonian power law fluid. The constitutive equations of the fluid are transformed into dimensionless ones. The velocity field is measured by Particle Image Velocimetry. Experimental results are obtained for the distribution of velocity. The influence of wall velocity ratio parameter on boundary layer flow field is observed in the experiment. Dimensionless velocity distribution and shearing stress distribution are obtained by post-processing experimental results. The effects of various physical parameters like velocity ratio parameter and similarity variable on various momentum transfer characteristics are discussed in detail and shown graphically. It is indicated that dimensionless velocity increases with velocity ratio parameter and similarity variable, and that dimensionless shearing stress decreases with velocity ratio parameter and similarity variable.     

Boundary layer flow of an Oldroyd‐B fluid with convective boundary conditions

This study is presented for the flow of an Oldroyd‐B fluid subject to convective boundary conditions. The two‐dimensional equations are simplified by using boundary layer approximations. The analytic solutions in the whole spatial domain (0 ≤ η < ∞) are derived by a homotopy analysis method (HAM). Interpretation of various emerging parameters is assigned through graphs for velocity and temperature distributions and tables for surface heat transfer. The present results are compared with the previous studies in limiting cases and results are found in very good agreement. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20381     

幂律流体连续运动平板边界层的数值研究

利用数值模拟方法研究了幂律流体在连续运动平板上的层流边界层问题。利用相似变换理论推导出无量纲剪切力的计算公式,数值求解了不同幂律指数n的流体在不同运动参数ξ的连续运动平板上的层流边界层流场,分析了各个参数对边界层速度分布和剪切力大小的影响。结果表明,边界层偏微分方程组的数值解与经过相似变换求得的非线性常微分方程的数值解吻合得很好,这既说明对幂律流体连续运动平板上的层流边界层问题的研究是有效且可靠的,同时也证明了连续运动平板问题存在相似解。     

Investigation on expanded boundary layer equation

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Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet

The article examines the hydromagnetic laminar boundary layer flow and heat transfer in a power law fluid over a stretching surface. The flow is influenced by linear stretching of the sheet. Also the energy equation with temperature-dependent thermal conductivity, thermal radiation, work done by stress, viscous dissipation and internal heat generation is considered. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the equations are solved by Keller–Box method. The effects of various physical parameters on the flow and heat transfer characteristics are presented graphically and discussed.     

层流脉动流中平行圆柱体的温度边界层

采用数值模拟方法研究了一个平行圆柱体在层流脉动流中的温度边界层特性。数值模拟结果与实验数据一致。研究发现脉动流中平行圆柱体形成了形状不规则但相对稳定的温度边界层,并在流动方向上周期性脉动。脉动流中平行圆柱体的温度边界层平均厚度小于稳定流动下的温度边界层平均厚度,并以脉动流的频率进行脉动。此外, 脉动流中平行圆柱体的壁面温度小于稳定流动下的壁面温度,表明脉动流下圆柱体的对流传热得到了强化。在一个脉动周期内,圆柱体在后半周期的温度边界层厚度和热阻均小于前半周期的温度边界层厚度和热阻。     

Pressure of Newtonian fluid flow through curved pipes and elbows

Under conditions of high temperature and high pressure, the non-uniformity of pressure loads has intensified the stress concentration which impacts the safety of curved pipes and elbows. This paper focuses on the pressure distribution and flow characteristic in a curved 90 o bend pipe with circular cross-sections, which are widely used in industrial applications. These flow and pressure characteristics in curved bend pipes have been researched by employing numerical simulation and theoretical analysis. Based on the dimensionless analysis method a formula for the pressure of Newtonian fluid flow through the elbow pipes is deduced. Also the pressure distributions of several elbows with different curvature ratio R/D are obtained by numerical methods. The influence of these non-dimensional parameters such as non-dimensional curvature ratio, Reynolds number and non-dimensional axial angle α and circumferential angle β on the pressure distribution in elbow pipes is discussed in detail. A number of important results have been achieved. This paper provides theoretical and numerical methods to understand the mechanical property of fluid flow in elbow pipes, to analyze the stress and to design the wall thickness of elbow pipes.     

An experimental investigation of the dissipation mechanisms in the suction side boundary layer of a turbine blade

The present work is part of an extensive experimental activity carried out by the authors in recent years aimed at investigating the boundary layer transition phenomenon in turbine blades. The large scale of the cascade and the use of advanced LDV instrumentation and precision probe traversing mechanism resulted in high degree of spatial resolution and high accuracy of measurements. The main dissipation mechanism determining the profile losses in turbomachinery blades is the work of deformation of the mean motion within the boundary layer operated by both viscous and turbulent shear stresses. In the present paper, the local viscous and turbulent deformation works have been directly evaluated from the detailed measurements of boundary layer mean velocity and Reynolds shear stress. The results show the distributions and the relative importance of the viscous and turbulent contributions to the loss production, in relation with the boundary layer states occurring along the turbine profile.     

Skin friction and heat transfer in power-law fluid laminar boundary layer along a moving surface

Analytical and numerical solutions are presented for momentum and energy laminar boundary layer along a moving plate in power-law fluids utilizing a similarity transformation and shooting technique. The results indicate that for a given power-law exponent n(0<n?1) or velocity ratio parameter ξ, the skin friction σ decreases with the increasing in ξ or n. The shear force decreases with the increasing in dimensionless tangential velocity t. When Prandtl number N_Pr=1, the dimensionless temperature w(t) is a linear function of t, and the viscous boundary layer is similar to that of thermal boundary layer. In particular, w(t)=t if ξ=0, i.e., the velocity distribution in viscous boundary layer has the same pattern as the temperature distribution in the thermal boundary and δ=δ_T. For N_Pr?1, the increase of viscous diffusion is larger than that of thermal diffusion with the increasing in N_Pr, and δ_T(t)<δ(t). The thermal diffusion ratio increases with the increasing in n(0<n?1) and ξ.     

Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet

Viscoelastic boundary layer flow and heat transfer over an exponential stretching continuous sheet have been examined in this paper. Approximate analytical similarity solution of the highly non-linear momentum equation and confluent hypergeometric similarity solution of the heat transfer equation are obtained. Accuracy of the analytical solution for stream function is verified by numerical solutions obtained by employing Runge-Kutta fourth order method with shooting. These solutions involve an exponential dependent of stretching velocity, prescribed boundary temperature and prescribed boundary heat flux on the flow directional coordinate. The effects of various physical parameters like viscoelastic parameter, Prandtl number, Reynolds number, Nusselt number and Eckert number on various momentum and heat transfer characteristics are discussed in detail in this work.     

Second‐law analysis and optimization of microchannel flows subjected to different thermal boundary conditions

Entropy generation and transfer in microchannel flows were calculated and analyzed for different thermal boundary conditions. Due to the small flow cross‐sectional area, fluid temperature variation in the lateral direction was neglected and a laterally lumped model was developed and used in the first‐ and second‐law analyses. Since the Peclet numbers of microchannel flows are typically low, heat conduction in the flow direction was taken into consideration. Computed fluid temperature and entropy generation rate were cast into dimensionless forms, thus can be applied to different fluids and channels of different sizes and configurations. Local entropy generation rate was found to be only dependent upon the temperature gradient in the flow direction. The optimization results of microchannel flows exchanging heat with their surroundings indicate the optimal fluid temperature distribution is a linear one. Copyright © 2004 John Wiley & Sons, Ltd.     

Thermodynamic analysis of thermal efficiency and power of Minto engine

Minto engine is a kind of liquid piston heat engine that operates on a small temperature gradient. But there is no power formula for it yet. And its thermal efficiency is low and formula sometimes is misused. In this paper, deriving the power formula and simplifying the thermal efficiency formula of Minto engine based on energy distribution analysis will be discussed. To improve the original Minto engine, a new design of improved Minto engine is proposed and thermal efficiency formula and power formula are also given. A computer program was developed to analyze thermal efficiency and power of original and improved Minto engines operating between low and high-temperature heat sources. The simulation results show that thermal efficiency of improved Minto engine can reach over 7% between 293.15 K and 353.15 K which is much higher than that of original one; the temperature difference between upper and lower containers is lower than half of that between low and high temperature of heat sources when the original Minto engines output the maximum power; on the contrary, it is higher in the improved Minto engines.     

Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet

The effect of radiation on the boundary layer flow and heat transfer of a viscous fluid over an exponentially stretching sheet is studied. The homotopy analysis method (HAM) is employed to determine the convergent series expressions of velocity and temperature. The physical interpretation to these expressions is assigned through graphs. It is found that the effects of Prandtl and radiation numbers on the temperature are opposite.     

Calculation of turbulent boundary layers using the dissipation integral method

INTRODUCTIONCalculation and prediction of turbulent boundarylayers (TBL) are among the most challenging tasksof present fluid mechanics. A strong demand existsfor robust, easy-to-handle and in terms of computingeffort cheap algorithms which can be used for technical applications. Most of the difficulties occur withthe comprehensive modelling of turbulence and, despite growing computer capabilities, with the limitedcomputing capacity. If the approaches to turbulenceare analysed, a sketch …     

Effect of thermal modulation on the onset of convection in a rotating fluid layer

The stability of a rotating horizontal fluid layer heated from below is examined when, the walls of the layer are subjected to time-periodic temperature modulation. The linear stability analysis is used to study the effect of infinitesimal disturbances. A regular perturbation method based on small amplitude of applied temperature field is used to compute the critical values of Rayleigh number and wavenumber. The shift in critical Rayleigh number is calculated as a function of frequency of modulation, Taylor number and Prandtl number. It is established that the instability can be enhanced by the rotation at low frequency symmetric modulation and with moderate to high frequency lower wall temperature modulation, whereas the stability can be enhanced by the rotation in case of asymmetric modulation. The effect of Taylor number and Prandtl number on the stability of the system is also discussed. We found that by proper tuning of modulation frequency, Taylor number and Prandtl number it is possible to advance or delay the onset of convection.     

The research of laminar-turbulent transition in hypersonic three-dimensional boundary layer

The results of experimental investigation of laminar-turbulent transition in three-dimensional flow under the high continuous pressure gradient including the flow with local boundary layer separation are presented. The experimental studies were performed within the Mach number range from 4 to 6 and Reynolds number 10-60×106 1/m, the angles of attack were 0°and 5°. The experiments were carried out on the three-dimensional convergent inlet model with and without sidewalls. The influence of artificial tubulator of boundary layer on transition and flow structure was studied. The conducted researches have shown that adverse pressure gradient increase hastens transition and leads to decrease of transition area length. If pressure gradient rises velocity profile fullness increases and profile transformation from laminar to turbulent occurs. As a result of it the decrease of separation area length occurs. The same effect was reached with Reynolds number increase. These results are compared with the data on two-dimensional model with longitudinal curvature.     

Unsteadiness of Shock Wave／Boundary Layer Interaction in Supersonic Cascade

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透平端壁湍流分离_再附边界层计算

本文根据Veldman的边界层与势流相互作用模型,提出了一种带有湍流分离气泡的端壁边界层的计算方法。本文给出的计算方法适用于由凸台、凹槽、后台阶、壁面扩张角较大及根部反动度为负等因素引起的带有湍流分离气泡的边界层的计算,并且具有计算时间短,节省计算机内存等特点。