Similarity solutions to a laminar boundary layer problem in power law fluids

A suitable similarity transformatiopn is introduced to reduce the laminar boundary layer equations of power law fluids to a class of singular nonlinear two-point boundary value problems.The skin friction and shear stress distributions for boundary layer flow over a moving flat plate are investigated by utilizing the shooting technique.Results indicate that for each fixed value of the power law exponent n or the velocity ratio parameter ξ,the skin friction and shear stress decrease with the increasing of n or ξ respectively.     

Explicit analytical wave solutions of unsteady 1D ideal gas flow with friction and heat transfer

Several families of algebraically explicit analytical wave solutions are derived for the unsteady 1D ideal gas flow with friction and heat-transfer, which include one family of travelling wave solutions, three families of standing wave solutions and one standing wave solution. Among them, the former four solution families contain arbitrary functions, so actually there are infinite analytical wave solutions having been derived. Besides their very important theoretical meaning, such analytical wave solutions can guide the development of some new equipment, and can be the benchmark solutions to promote the development of computational fluid dynamics. For example, we can use them to check the accuracy, convergence and effectiveness of various numerical computational methods and to improve the numerical computation skills such as differential schemes, grid generation ways and so on.     

An efficient analytical decomposition and numerical procedure for boundary layer flow on a continuous stretching surface

1. Introduction The drag force because of “skin friction” is a fluid dynamic resistive force, which is a consequence of the fluid and the pressure distribution on the surface. Re- cently, following the pioneering work of Sakiadis [1-2], considerable att…     

Similarity solutions for the mixed convection flow over a vertical plate with thermal radiation

The steady laminar boundary layer flow adjacent to a vertical plate with prescribed surface temperature immersed in an incompressible viscous fluid,where the effect of thermal radiation was taken into consideration,was investigated.The governing partial differential equations were transformed into a system of ordinary differential equations using similarity transformation,before being solved numerically by the shooting method.Both assisting and opposing buoyant flows were considered.It is found that dual...     

Analytic decomposition and numerical procedure for solving the singular boundary value problem arising in viscous flows

1. Introduction The drag force due to “skin friction” is a fluid dy- namic resistive force, which is a consequence of the fluid viscous and the pressure distribution on the sur- face of the object [1]. In view of the theoretical analy- sis of the bounda…     

管排类元件自然对流换热研究进展

离散体自然对流速度场，温度场远比孤立体复杂，管排－一种典型的离散体在工程中有较多应用。文中论述了目前国际上管排的研究状况和存在的问题，并提出了自己的观点。为深入研究该类元件的换热机理，计算方法及优化设计指出了方向和途径。     

一个非定常自由边界问题解的存在唯一性

考虑单晶拉制非定常模型中提出来的一个自由边界问题,给出了它的存在唯一性。     

On energy boundary layer equations in power law non-Newtonian fluids

The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.     

螺旋管壁热传导问题的摄动解

本文根据张量分析理论，建立了非正交曲线柱坐标的热传导方程，采用正则摄动法求解了螺旋管壁热传导问题，获得了管壁温度分布的零阶，一阶和二阶分析解表达式，计算了热阻，结果与圆筒壁近似进行了对比，并讨论了曲率，挠率以及正则摄动对该问题的影响。     

具耗散项拟线性双曲型方程组典型自由边值问题整体经典解

考虑具耗散项一阶拟线性双曲型方程组的典型自由边值问题,证明了其经典解的整体存在性．     

Heat transfer study on solid and porous convective fins with temperature-dependent heat generation using efficient analytical method

A simple and highly accurate semi-analytical method, called the differential transformation method（DTM）, was used for solving the nonlinear temperature distribution equation in solid and porous longitudinal fin with temperature dependent internal heat generation. The problem was solved for two main cases. In the first case, heat generation was assumed variable by fin temperature for a solid fin and in second heat generation varied with temperature for a porous fin. Results are presented for the temperature distribution for a range of values of parameters appearing in the mathematical formulation（e.g. N, εG, and G）. Results reveal that DTM is very effective and convenient. Also, it is found that this method can achieve more suitable results in comparison to numerical methods.     

变化的表面传热系数对磨削温度场的影响

详细分析了磨削弧内磨削液流的状态 ,引用温度边界层的概念 ,论证了磨削弧内的磨削液膜的状态 ,并由此得出磨削弧内的表面传热系数是随变化的壁温和位置而变化的 ,在求解温度场的分布时 ,变化的表面传热系数更符合实际的情况     

三阶微分方程周期边值问题多个正解的存在性

讨论{um＋ρ3u=f（t,u）,t∈I=（0,2π）,u（i）（0）=u（i）（2π）,i=0,1,2ρ∈（0,1/3）是常数三阶微分方程的周期边值问题的多个正解存在性问题。通过与一个线性算子相关的第一特征值的讨论,运用锥拉伸与压缩不动点定理,得到上述边值问题多个正解存在的结果。     

平面非规则域内非线性边值问题稳态温度场分析

采用边界离散方法对具有辐射换热边界的平面非规则域内稳态温度场进行了分析,得到了级数形式的解。进一步指出,边界离散方法示中以解决某些可分离变量的非正交问题,而且可以解决某些非生边值问题。     

Similarity solution to a heat equation with convection in an infinite medium

A second order heat equation with convection in an infinite medium is studied. Suitable similarity transformations are used to reduce the parabolic heat equation to a class of singular nonlinear boundary value problems. Numerical solutions are presented for different representations of heat conduction, heat convection, heat flux, and power law parameters by utilizing the shooting technique. The results reveal the heat transfer characteristic and the effect of parameters on the solutions.     

热传导问题的两种边界元—有限元耦合法解

本文将边界元法(BEM)和有限元法(FEM)相结合,用于求解热传导问题,按各类边界条件的一般情况导出了相应的两种耦合算法公式。这些耦合方法取BEM 和 FEM 两者之长而避其短,可提高计算精度,减少数据准备和计算工作量,并可用于某些用单一方法较难求解的问题。文中给出了算例,并将耦合法解与解析解、有限元解、边界元解、有限差分解作了比较。     

Analytical solution and experimental verification for pulsed laser heating process with convective boundary condition

Duetothecomplexityandthetransientfeatureoflaserprocessingprocess,realtimequalitycontrolviaexactmodellingandmulti-fieldcouplinganalysisbecomeaNomenclatured,absorptioncoefficient1/m;a,thermaldiffusivitym2/s;Cp,specificheatJ/kgK;r,densitykg/m3;k,thermalconductivityW/mK;I0,laserpeakpowerdensityW/m2;rf,reflectioncoefficient;h,convectivecoefficientW/m2K;Bi,Biotnumber,namelyhkd;s,Laplacevariable;T1,ambienttemperatureK;T0,initialmaterialtemperatureK;Te,materialtemperatureattimetK;m,dynamicviscos…     

自由表面二维平面射流冲击传热的理论分析

对二维平面射流冲击平板时的层流流动（和传热）给出了速度和温度边界层的综合解析,用积分方法得到了平面射流冲击传热的驻点区和部分壁面射流区的换热关系式,并将等热流壁面的分析结果与实验数据进行比较,结果基本吻合,     

Mixed convective heat and mass transfer analysis for peristaltic transport in an asymmetric channel with Soret and Dufour effects

The present investigation addresses the simultaneous effects of heat and mass transfer in the mixed convection peristaltic flow of viscous fluid in an asymmetric channel. The channel walls exhibit the convective boundary conditions. In addition, the effects due to Soret and Dufour are taken into consideration. Resulting problems are solved for the series solutions. Numerical values of heat and mass transfer rates are displayed and studied. Results indicate that the concentration and temperature of the fluid increase whereas the mass transfer rate at the wall decreases with increase of the mass transfer Biot number. Furthermore, it is observed that the temperature decreases with the increase of the heat transfer Biot number.     

一维多孔介质热湿耦合传递问题的解析解

为准确确定建筑物的能耗,保证建筑物的使用功能,需对土壤和围护结构中的热湿迁移现象进行研究.本文基于Luikov热湿耦合传递方程,提出了一种计算一维多孔介质瞬态热湿传递的理论分析方法.通过引入无量纲温度、湿度对Luikov方程进行拉普拉斯变换,采用传递函数方法(TFM)得到了一维瞬态热湿传递方程的解析解,该解析解揭示了多...