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.     

Nonsimilar boundary layer flow of Cross fluid induced by a heated stretched sheet

This paper deals with the nonisothermal boundary layer flow of Cross fluid due to a stretching sheet. Unlike previous studies on boundary layer flow of Cross fluid, a nonsimilar formulation is adopted to transform the boundary layer equations into nondimensional form. The problem is characterized by three dimensionless parameters, namely, the Deborah number, the Prandtl number, and dimensionless distance along the sheet. The transformed equations are simulated by a numerical scheme with the help of MAPLE software. The velocity and temperature profiles inside the boundary layer are calculated and shown graphically. The skin friction coefficient and Nusselt number at various axial stations are also tabulated for several values of Deborah number and Prandtl number.     

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.     

Exact and analytical solutions for self-similar thermal boundary layer flows over a moving wedge

This article aims to achieve exact and analytical solutions for the classical Falkner–Skan equation with heat transfer (FSE-HT). Specifically, when the pressure gradient parameter , there already exists a closed-form solution in the literature for the Falkner–Skan flow equation. The main purpose here is to extend this case to obtain a closed-form solution to the heat transport equation with the solubility condition . An algorithm is presented and is found to be new to the literature that enriches the physical properties of FSE-HT. It is shown that for the moving wedge parameter $$, the momentum and temperature equations show multiple solutions analytically. The skin friction coefficient and the heat transfer rate are also obtained in analytical form. The thus-obtained solution is then adapted to derive an analytical solution applicable to a wide range of pressure gradient parameters $$ and Prandtl numbers $$. Furthermore, an asymptotic analysis is conducted, focusing on scenarios where the moving wedge parameter becomes significantly large ( $$). Nevertheless, in all the above-mentioned cases, the skin friction coefficient ( $$) and the heat transfer rate ( $$) are compared with the direct numerical solutions of the boundary layer equations, and it is found that the results are in good agreement. These solutions provide a benchmark and shed light on further studies on the families of FSE-HT.     

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.     

Hydromagnetic boundary layer flow with heat transfer past a rotating disc embedded in a porous medium

In this study, the effect of Coriolis force along with the Darcy parameter has been analyzed on time-dependent forced convective boundary layer flow of conducting fluids over a rotating disc embedded in a porous medium. The modeled system is solved by power series approximations in the Mathematica environment shooted values. The significant impact of the rheological properties, such as Darcy parameter $\beta$ and Prandtl number $\mathit{Pr}$, of water, hydrocarbon, and kerosene-based conducting fluids for the deviation of parameter $\xi$ (Karman) has been noted and then analyzed qualitatively and quantitatively with graphs and tables.     

Viscoelastic boundary layer analysis of constant surface temperature plate embedded in saturated porous media

Mathematical models and numerical solutions of Williamson fluid flow under influences of various boundary conditions provide important support to experimental studies in the solar energy field. Therefore, the present study is concerned with the effects of forced convection of the viscoelastic boundary layer on a horizontal plate embedded in saturated porous media subjected to constant surface temperature. The study explores the profiles of shear stress, velocity, temperature, and heat transfer coefficient. The governing equations in nondimensional forms are obtained by using a model of Darcy–Forchheimer–Brinkman and finally are solved numerically by using bvp4c with MATLAB package. The results of the numerical solution show an insignificant rise in the distribution of the velocity boundary layer and shear stress profile as the Darcy parameter is increased, while a decrease in the temperature and Nusselt numbers are found. On the other hand, as the viscoelastic parameter is increased, the Darcy parameter shows a reverse response. Finally, insignificant increases in profiles of boundary layer velocity, temperature, shear stress, and Nusselt number are observed at high values of the Forchheimer number.     

An integral boundary layer engineering model for vortex generators implemented in XFOIL

To assess and optimize vortex generators (VGs) for flow separation control, the effect of these devices should be modelled in a cost and time efficient way. Therefore, it is of interest to extend integral boundary layer models to analyse the effect of VGs on airfoil performance. In this work, the turbulent boundary layer formulation is modified using a source term approach. An additional term is added to the shear‐lag equation, to account for the increased dissipation due to streamwise vortex action in the boundary layer, forcing transition at the VG leading edge where applicable. The source term is calibrated and a semi‐empirical relation is set up and implemented in XFOIL . The modified code is capable of addressing the effect of the VG height, length, inflow angle, and chordwise position on the airfoil's aerodynamic properties. The predicted polars for airfoils with VGs show a good agreement with reference data, and the code robustness is demonstrated by assessing different airfoil families at a wide range of Reynolds numbers.     

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.     

Analysis of activation energy and thermal radiation on convective flow of a power‐law fluid under convective heating and chemical reaction

The purpose of the present article is to explore the influence of activation energy in the mixed convective flow of a power‐law fluid over a permeable inclined plate. The energy expression is incorporated with thermal radiation effect. Additionally, the suction/injection effect and convective thermal conditions are considered at the surface of the inclined plate. The convection along with a nonlinear Boussinesq approximation (i.e., quadratic or nonlinear convection) and usual boundary‐layer assumptions are used in the mathematical formulation. A combined local non‐similarity and successive linearization techniques are used to evaluate the highly complicated governing equations. The effect of pertinent parameters on the fluid flow characteristics and its solutions are conferred using this study with the help of graphs. This kind of investigation is useful in the mechanism of combustion, aerosol technology, high‐temperature polymeric mixtures, and solar collectors, which operate at moderate to very high temperatures.