Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate

In this Letter, the problem of forced convection over a horizontal flat plate is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.     

Experimental and numerical study of the effect of conjugate heat transfer on film cooling

Combined convection heat transfer and thermal conduction for film cooling of a flat plate with 45° ribs on one wall was investigated experimentally and numerically. The flat plate surface temperature was measured using thermochromic liquid crystals. The results show that the film cooling is the main mechanism for the local cooling with a very low thermal conductivity while the convection heat transfer of the coolant in the coolant channel is the dominant heat transfer mechanism for the high thermal conductivity plate, with both film cooling and convection heat transfer by the coolant being important with medium thermal conductivity walls.     

凝华结霜霜层导热系数理论分析

研究水蒸汽凝华结霜过程在冷壁上形成的霜层的导热系数,依据随机管子多孔介质霜层模型,假设霜层是由孔隙空间与冰晶骨架构成的多孔介质,其中孔隙空间由随机毛细管及连接管子的接头形成,湿空气中的水蒸汽在霜层的孔隙空间中扩散输运并凝华结霜,根据传热传质学理论,导出霜层导热系数关系式。     

NATURAL CONVECTION FROM A VERTICAL RECTANGULAR FIN

An experimental investigation of steady-state natural convection from vertical rectangular mild steel and aluminum fins was conducted using laser holographic interferometry. Infinite-fringe interferograms demonstrate the effect of fin base heating. Depending on the fin material and base temperature, the local heat transfer coefficients vary along the fin with maximum values at positions about 22-48% of the fin height measured from the base. Temperature measurements along the fin show good agreement with the classical one-dimensional corwective and adiabalic tip solutions. Hence, in the thermal design of vertical aluminum fins of low Biot numbers, the classical one-dimensional fin solutions may be used together with an average heat transfer coefficient obtained from established correlations for natural convection from an isothermal flat plate.     

Phenomenological models of microwave heating of a flat coal mass with release of absorbed heat by the convection law

Phenomenological models of electrodynamics and heat transfer in application to microwave heating are constructed. Analytically rigorous solutions to problems of heating a flat coal mass under microwave radiation are obtained. The boundary conditions correspond to convection mechanism of absorbed heat release to the ambient medium. Mathematical models of dielectric heating for homogeneous boundary conditions are solved by a method of dual integral Laplace and Fourier transform. In the presence of inhomogeneities in the boundary conditions, a quite universal method of Green functions is used. The obtained formulas have a constraint associated with constancy of electro- and thermophysical characteristics of coal fuel, or when their piecewise constant approximation is admissible. The obtained dependences form the basis for scientific support of the microwave heating technology.     

Asymptotic analysis of solution to the nonlinear problem of non-stationary heat conductivity of layered anisotropic non-uniform shells at low Biot numbers on the front surfaces

The nonlinear problem of non-stationary heat conductivity of the layered anisotropic heat-sensitive shells was formulated taking into account the linear dependence of thermal-physical characteristics of the materials of phase compositions on the temperature. The initial-boundary-value problem is formulated in the dimensionless form, and four small parameters are identified: thermal-physical, characterizing the degree of heat sensitivity of the layer material; geometric, characterizing the relative thickness of the thin-walled structure, and two small Biot numbers on the front surfaces of shells. A sequential recursion of dimensionless equations is carried out, at first, using the thermalphysical small parameter, then, small Biot numbers and, finally, geometrical small parameter. The first type of recursion allowed us to linearize the problem of heat conductivity, and on the basis of two latter types of recursion, the outer asymptotic expansion of solution to the problem of non-stationary heat conductivity of the layered anisotropic non-uniform shells and plates under boundary conditions of the II and III kind and small Biot numbers on the facial surfaces was built, taking into account heat sensitivity of the layer materials. The resulting two-dimensional boundary problems were analyzed, and asymptotic properties of solutions to the heat conductivity problem were studied. The physical explanation was given to some aspects of asymptotic temperature decomposition.     

Numerical simulation of natural convection in a sessile liquid droplet

Heat transfer in a sessile liquid droplet was studied with numerical methods. A computer code was developed for solving the problem of convection in an axisymmetric hemispherical droplet and in a spherical layer as well. The problem of establishing an equilibrium state in a droplet was solved using several variables: temperature, stream function, and vorticity. Simulation was performed for droplets of water, ethyl alcohol, and model liquids. Variable parameters: intensity of heat transfer from droplet surface, Rayleigh and Marangoni dimensionless criteria, and the characteristic temperature difference. It was revealed that the curve of convective flow intensity versus heat transfer intensity at droplet surface has a maximum. A dual-vortex structure was obtained in a stationary hemispherical profile of liquid droplet for the case of close values for thermocapillary and thermogravitational forces. Either thermocapillary or thermogravitational vortex might be dominating phenomena in the flow structure.     

燃烧室出口辐射对气膜冷却传热影响研究

燃气轮机高温透平中包含对流/导热/辐射等复杂传热现象。本文依托高温流热固耦合实验台,提出燃烧室与透平联合计算的方法,采用数值模拟和实验对比的方式分析了平板气膜冷却的对流/导热/辐射传热特性。同时研究了不同燃气吸收系数以及不同进口辐射条件对于平板气膜冷却的表面温度分布的影响。结果表明:辐射传热是燃气轮机首级高温叶片传热特性的重要影响因素,辐射传热使得实验平板温度抬升50～70 K,燃烧室/透平联合计算方法有效地分析了燃烧室出口辐射强度对高温平板气膜冷却辐射传热的影响;高温燃气辐射特性对于平板温度分布具有明显影响。     

非牛顿流体沿竖直平板自然对流传热的计算研究

非牛顿幂次流体沿竖直平板层流自然对流为非线性两点边值问题,其速度场与温度场需耦合求解。采用几种数值方法对该问题进行了计算,研究了各种普朗特数(Pr)及不同幂次流体对沿壁面平均努赛尔数(Nu)的影响变化,并与有关文献的结果进行了对比分析。     

水平板自然对流换热的非线性特性

采用SIMPLE算法,QUICK差分方案,对封闭方腔内水平板自然对流换热进行了数值模拟.数值结果显示,低Ra数时流动和换热处于稳态,当Rayleigh数超过某一临界值时,流动和换热就会发生非稳态振荡,此时流动和换热表现出非对称性.对不同Rayleigh数,流动和换热通过单周期分岔从稳态过渡到非稳态,并通过倍周期分岔过渡到混沌.在混沌区,仍然会出现周期性窗口,并且数值结果与初始条件有关.     

方形通道内非牛顿流体的强化传热

对非牛顿流体在小尺寸方形通道内的低雷诺数受迫对流传热进行了实验研究。实验用介质为１５００ｗｐｐｍＣａｒｂｏｐｏｌ－９３４中性水溶液。通道顶壁受到等热流加热。结果表明，流体粘弹性与传热的相互作用取决于雷诺数的大小。当表观雷诺数Ｒｅ＞１１．５时，非牛顿流体开始强化对流传热。Ｒｅ数越高，传热强化的程度越大。流体的阻力系数则几乎不受粘弹性的影响。     

Modeling the onset of thermosolutal convective instability in a non-Newtonian nanofluid-saturated porous medium layer

The onset of double-diffusive (thermosolutal) convection in horizontal porous layer saturated with an incompressible couple stress nanofluid saturated is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. To represent the momentum equation for porous media, a modified Darcy-Maxwell nanofluid model incorporating the effects of Brownian motion and thermophoresis has been used. The thermal energy equation includes regular diffusion and cross diffusion (Soret thermo-diffusion and Dufour diffuso-thermal) terms. A linear stability analysis depends on the normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the representation of the Fourier series method is applied to capture the behavior of heat and mass transfer. It is found that the couple stress parameter enhances the stability of the system in both the stationary and oscillatory convection modes. The viscosity ratio and conductivity ratio both enhance heat and mass transfer. Transient Nusselt number is found to be oscillatory when time is small. However, when time becomes very large, all the three transient Nusselt number values approach to their steady state values.     

Natural and forced convective heat transfer on slender cylinders

This paper presents an experimental study of free and forced convective heat transfer along vertical slender cylinders. The local heat transfer coefficient is determined from the measurement of the surface temperature distribution performed by quantitative infrared thermography. It is found that the convective heat transfer is strongly dependent on the cylinder curvature and misalignment with the flow. The effect of proximity of two cylinders is emphasized in the case of forced convection. Correlations are proposed for the two types of convection. It is worth noting that circumstances exist where the turbulent heat transfer in free convection can be of the same order of magnitude as for laminar forced convection. The outcome of the study demonstrates the suitability of quantitative infrared thermography to solve complex problems and to provide a deeper understanding of the heat transfer on slender cylinders.     

Mathematical modeling of convective-conductive heat transfer in a rectangular domain in a conjugate statement

The results of mathematical modeling of convection of a viscous incompressible liquid in a rectangular domain with sources of mass input and output are presented. A conjugate statement within the framework of the Boussinesq approximation is used. The regimes of forced and mixed convection in a domain have been investigated. The domain has two vertical walls and one horizontal wall of finite thickness, two zones of liquid input and output, and a free surface. A plane nonstationary problem within the framework of the Navier-Stokes model for the liquid phase and the heat conduction equation for the solid phase are considered. The distributions of the hydrodynamic parameters and temperatures characterizing the main regularities of the processes under investigation have been obtained. Circulation flows have been identified. The vortex formation mechanism and the temperature distribution in the solution domain under the regimes of forced and mixed convection and different locations of mass input and output zones have been analyzed. It has been found that natural convection should be taken into account when modeling convective heat transfer with Gr number values from 10⁵ and higher.     

Frequency dependence of microwave-assisted electron-transfer chemical reactions

In this paper, the electron transfer reactions in the microwave field are studied. A classical theory is developed for a mix of reagents and polar frequency-dispersive and lossy solvent filling vessels excited by microwaves. These reactors are described by a system of non-linear partial self-consistent differential equations for non-stationary microwave field, heat and liquid dynamics, and chemical molecular kinetics. A particular solution of this system is considered for the isothermic electron-transfer reactions in the microwave field varying its frequency with the calculation of the normalised Marcus rate coefficient. It is found that for the small normalised reaction free energy, the chemical reactions are supported by microwaves in a wide frequency band with an increased value of the exponent in the Marcus rate coefficient. At higher values of this energy, these reactions are driven only by conventional microwave heating. The restrictions for the given theory are reviewed, and further experimental and semi-classical and quantum-mechanical studies are found essential for practical applications of these findings.     

HEAT TRANSFER AND TEMPORAL BEHAVIOR OF THE LAMINAR MIXED-CONVECTION FLOW AROUND A DUCTED FLAT-PLATE THERMAL FLOW SENSOR

We present experimental results of heat transfer processes in mixed-convective flow from a ducted vertical hot-plate thermal flow sensor for aiding (upward) and opposing (downward) flows. The results are obtained for three different Grashof numbers, Gr = 289, 411, and 456, using air, in the Reynolds number range from 0 to 120. The Nusselt number for aiding flows can be adequately described by Nu tot – Nu 0 = (Nu n forced + Nu n free ) 1/n , with Nu 0 = 0.5, as originally proposed by Churchill for a free flat plate. For n, a value of 1.5–1.7 is found. For opposing flows in the mixed-flow region (0.1 h Gr/Re 2 S 10), flow visualization shows an oscillating buoyant plume around the flat plate. In the transition from free to mixed and to essentially forced convection, distinct sequences of instabilities of this plume are observed, leading to several local minima and maxima in the heat transfer from the plate. The results are summarized in a bifurcation diagram. Here, several windows with instabilities are found, both nonperiodic, with strong indications of chaotic behavior, and (quasi-) periodic. Typical fundamental frequencies of the instabilities range from 0.15 to 1 Hz.     

Thermal conditions of the Er:YAG laser under stationary diode pumping

Experimental results and calculation data for the thermal conditions of the YAG:Er laser active element shaped as a flat plate under pumping by continuous radiation of a diode array (λ = 980 nm) with fiber output are presented. The thermal field and temperature in the plate optical excitation channel are measured using the thermal imaging technique. Their dependence on the pump power is studied. A comparison of calculated and experimental data allowed the determination of the heat transfer coefficient from the YAG:Er crystal to air under conditions of natural convection.     

二维高超声速后台阶表面传热特性实验研究

高超声速后台阶流动是大气层内高速飞行器发动机设计、表面热防护以及高超声速拦截器红外成像窗口气动光学效应校正等诸多先进高超声速技术研发过程中所涉及的一类基础流动问题. 研究高超声速后台阶流动特性对有效提升飞行器综合性能, 进一步掌握高超声速流动机理具有重大基础 意义. 本文以二维高超声速后台阶流动为研究对象, 在KD-01高超声速激波风洞中测量了二维后台阶模型表面传热系数和表面静压, 并将实测台阶下游表面传热系数分布同采用高超声速边界层理论所得估计值进行了比较. 为进一步验证实验结果, 使用NPLS技术测量了其中一种实验状态下台阶周围流动结构. 研究发现, 对于二维高超声速后台阶流动, 台阶下游表面传热分布受台阶处边界层外缘流动特性的直接影响; 在台阶下游分离区和再附区内, 气体黏性占主导作用; 在台阶下游远场区域, 边界层流动特性趋同于平板边界层; 下游边界层基本结构取决于台阶处边界层相对厚度. 对高超声速后台阶流动, 若使用数值模拟方法研究气动热问题, 应当使用湍流模型.     

平板热管相变传热特性的实验研究

平板热管具有很好的均热性,能够避免电子器件散热时热点的产生,使热沉具有更好的散热效果.为了研究平板热管的相变传热特性,制作了可视化平板热管,通过实验研究了加热功率、冷却风速、不同工质对平板热管性能的影响.同时,还研究了槽道结构对平板热管内部沸腾换热的强化作用.     

The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model

The stability of a couple stress fluid saturated horizontal porous layer heated from below and cooled from above when the fluid and solid phases are not in local thermal equilibrium is investigated. The Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the solid and fluid phases separately. The linear stability theory is employed to obtain the condition for the onset of convection. The effect of thermal non-equilibrium on the onset of convection is discussed. It is shown that the results of the thermal non-equilibrium Darcy model for the Newtonian fluid case can be recovered in the limit as couple stress parameter C→0. We also present asymptotic analysis for both small and large values of the inter phase heat transfer coefficient H. We found an excellent agreement between the exact solutions and asymptotic solutions when H is very small.