Improvement of surface flux calculation:A study based on measurements over alpine meadow in the eastern Tibet Plateau in summer

An improved flux-gradient relationship between momentum φm（ζ） and sensible heat φh（ζ） is obtained by the use of the observational data over an alpine meadow in the eastern Tibet Plateau, in Maqu of China during the period June to August, 2010. The empirical coefficients of Businger-Dyer type function for the cases of unstable and stable stratification are modified. Non-dimensional vertical gradients of wind and potential temperature are calculated by three fitting func- tions; that is, the log-linear, log-square, and log--cubic functions, respectively. It is found that the von Karman constant approaches 0.4025 and the Prandtl number is about 1.10 based on the measurements in near-neutral conditions, which are within reasonable range proposed in previous studies. The revised flux-gradient profile functions of -1/5 power law for momentum and - 1/3 power law for sensible heat are best fitted in unstable stratification conditions. Meanwhile, 2/5 power law, instead of linear functions, is more appropriate in stable stratification cases for momentum and sensible heat. Com- pared with results from previous studies in which traditional functions are used, the momentum and sensible heat fluxes estimated by the revised profile functions in the current study are much closer to the observations for the unstable and stable stratification conditions.     

Power law decay of stored pattern stability in sparse Hopfield neural networks

Hopfield neural networks on scale-free networks display the power law relation between the stability of patterns and the number of patterns.The stability is measured by the overlap between the output state and the stored pattern which is presented to a neural network.In simulations the overlap declines to a constant by a power law decay.Here we provide the explanation for the power law behavior through the signal-to-noise ratio analysis.We show that on sparse networks storing a plenty of patterns the stability of stored patterns can be approached by a power law function with the exponent-0.5.There is a difference between analytic and simulation results that the analytic results of overlap decay to 0.The difference exists because the signal and noise term of nodes diverge from the mean-field approach in the sparse finite size networks.     

Optimization of fin geometry in heat convection with entransy theory

The entransy theory developed in recent years is used to optimize the aspect ratio of a plate fin in heat convection.Based on a two-dimensional model,the theoretical analysis shows that the minimum thermal resistance defined with the concept of entransy dissipation corresponds to the maximum heat transfer rate when the temperature of the heating surface is fixed.On the other hand,when the heat flux of the heating surface is fixed,the minimum thermal resistance corresponds to the minimum average temperature of the heating surface.The entropy optimization is also given for the heat transfer processes.It is observed that the minimum entropy generation,the minimum entropy generation number,and the minimum revised entropy generation number do not always correspond to the best heat transfer performance.In addition,the influence factors on the optimized aspect ratio of the plate fin are also discussed.The optimized ratio decreases with the enhancement of heat convection,while it increases with fin thermal conductivity increasing.     

Effects of Slip on Unsteady Mixed Convective Flow and Heat Transfer Past a Stretching Surface

Unsteady mixed convective boundary layer flow and heat transfer over a stretching vertical surface in the presence of slip axe investigated. It is noted that fluid velocity decreases due to the increasing velocity slip parameter resulting in an increase in the temperature field. The rate of heat transfer decreases with the velocity slip parameter while it increases with unsteadiness parameter. The same feature is also noticed for thermal slip parameter.     

Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid

In this article, the unsteady magnetohydrodynamic （MHD） stagnation point flow and heat transfer of a nanofluid over a stretching/shrinking sheet is investigated numerically. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the fourth-order Runge-Kutta method with shooting technique. The ambient fluid velocity, stretching/shrinking velocity of sheet, and the wall temperature are assumed to vary linearly with the distance from the stagnation point. To investigate the influence of various pertinent parameters, graphical results for the local Nusselt number, the skin friction coefficient, velocity profile, and temperature profile are presented for different values of the governing parameters for three types of nanoparticles, namely copper, alumina, and titania in the water-based fluid. It is found that the dual solution exists for the decelerating flow. Numerical results show that the extent of the dual solution domain increases with the increases of velocity ratio, magnetic parameter, and permeability parameter whereas it remains constant as the value of solid volume fraction of nanoparticles changes. Also, it is found that permeability parameter has a greater effect on the flow and heat transfer of a nanofluid than the magnetic parameter.     

Physiological Flow of Jeffrey Six Constant Fluid Model due to Ciliary Motion

The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ciliated tips in the presence of heat and mass transfer. The effects of viscous dissipation are also considered. The flow equations of non-Newtonian fluid for the two-dimensional tube in cylindrical coordinates are simplified using the low Reynolds number and long wave-length approximations. The main equations for Jeffrey six constant fluid are considered in cylindrical coordinates system. The resulting nonlinear problem is solved using the regular perturbation technique in terms of a variant of small dimensionless parameter α. The results of the solutions for velocity, temperature and concentration field are presented graphically. B_k is Brinkman number, ST is soret number, and SH is the Schmidth number. Outcome for the longitudinal velocity, pressure rise, pressure gradient and stream lines are represented through graphs. In the history, the viscous-dissipation effect is usually represented by the Brinkman number.     

Heat transfer for boundary layers with cross flow

An analysis is presented to study the dual nature of solutions for the forced convective boundary layer flow and heat transfer in a cross flow with viscous dissipation terms in the energy equation. The governing equations are transformed into a set of three self-similar ordinary differential equations by similarity transformations. These equations are solved numerically using the very efficient shooting method. This study reveals that the dual solutions of the transformed similarity equations for velocity and temperature distributions exist for certain values of the moving parameter, Prandtl number, and Eckert numbers. The reverse heat flux is observed for larger Eckert numbers; that is, heat absorption at the wall occurs.     

Strong coupling between height of gaps and thickness of thermal boundary layer in partitioned convection system

A direct numerical simulation(DNS) method is used to calculate the partitioned convection system with Ra number ranging from 10~7 to 2×10~9.Using the boundary layer thickness to normalize the height of gaps d, we find a strong consistency between the variation of the TD number(the average value of the temperature in each heat transfer channel is averaged after taking the absolute values) with the change of the height of gaps and the variation of the TD number with the change of Ra number in partitioned convection.For a given thickness of partition, heights of gaps are approximately equal to 0.5 or 1 time of the thermal boundary layer thickness λ_θ at different Ra numbers.TD number representing temperature characteristics is almost the constant value, which means that TD number is a function of d/λ_θ only.Analysis of local temperature field of area in gaps shows that the temperature distribution in the gaps are basically the same when d/λ_θ is certain.The heat transfer Nu number of the system at d/λ_θ≈ 0.5 is larger than that of d/λ_θ≈ 1, both of them have the same scaling law with Ra number and N_u～Ra~(0.25).     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

Melting phenomenon in magneto hydro-dynamics steady flow and heat transfer over a moving surfacein the presence of thermal radiation

The Lie group method is applied to present an analysis of the magneto hydro-dynamics(MHD) steady laminar flow and the heat transfer from a warm laminar liquid flow to a melting moving surface in the presence of thermal radiation.By using the Lie group method,we have presented the transformation groups for the problem apart from the scaling group.The application of this method reduces the partial differential equations(PDEs) with their boundary conditions governing the flow and heat transfer to a system of nonlinear ordinary differential equations(ODEs) with appropriate boundary conditions.The resulting nonlinear system of ODEs is solved numerically using the implicit finite difference method(FDM).The local skin-friction coefficients and the local Nusselt numbers for different physical parameters are presented in a table.     

A numerical study of laminar natural convective heat transfer inside a closed cavity with different aspect ratio

Two-dimensional steady-state laminar natural convection was studied numerically for differentially heated air-filled closed cavity with adiabatic top and bottom walls. The temperature of the left heated wall and cooled right wall was assumed to be constant. The governing equations were iteratively solved using the control volume approach. In this paper, the effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively.Variations of the maximum stream function and the average heat transfer coefficient were also shown. The average Nusselt number and was correlated to the Rayleigh number based on curve fitting for each aspect ratio. The investigation covered the range 10⁴ ≤ RA ≤ 10⁷ and is done at Prandtl number equal to 0.693. The result shows the average Nusselt number is the increasing function of Rayleigh number. As the aspect ratio increases, Nusselt number decreases along the hot wall of the cavity. As Rayleigh number increases, Nusselt number increases. Result indicates that at constant aspect ratio, with increase in Rayleigh number the heat transfer rate increases.     

Influence of conduction heat loss on enhancing the heat transfer performance of a square flat plate with constant heat flux by an impinging jet in cross-flows

An experimental setup was built to study the influence of conduction heat loss on the convective heat transfer performance enhanced by an impinging jet in cross-flows. Results revealed that the conduction heat loss ratio (E_c/E) is between 12.0% and 40.1%, and it decreases nonlinearly with the ratio of jet-to-cross-flow velocity. The relative Nusselt number increases with the ratio of jet-to-cross-flow velocity. The maximum peak value and the average are 8.1 and 6.4, respectively. The distribution of the relative Nusselt number seems to be flattened by assuming a constant conduction heat loss ratio.     

微针肋槽道内去离子水换热特性

设计了槽肋比为1:2和2:1的矩形大长宽比微针肋散热器,并实验研究了去离子水在其内的流动换热性能。结果表明:当进口温度为40 ℃、微针肋槽道在雷诺数小于650、最高壁面温度低于77 ℃时,单位面积散热量可达21.32 W/cm2。当雷诺数一定时,同一个槽道壁面温度沿着流动方向不断增加、同一个位置壁面温度随着加热功率的增加而增大,局部努谢尔数沿着流动方向先减小后逐渐增加并趋于定值。当针肋流动换热长度较长时,其入口效应可以忽略,槽道平均努谢尔数随着雷诺数的增大而增大,与加热功率无关;为了更好地表达微针肋槽道内的换热特性,考虑了槽肋比、流动雷诺数等影响,拟合了去离子水在微针肋槽道内的对流换热关系式。     

微方肋冷却系统的换热特性

采用去离子水为冷却介质,对自行设计的不同结构微方肋散热器内的换热特性进行实验研究,结果表明:在进口温度为20 ℃、进口流量为57.225 L/h、底面平均温度为73.4 ℃时,散热器散热量可达2.83106 W/cm2,可以满足当前高热流密度散热需求;当散热面温度一定时,散热量随着散热器进口流量的增加而增加,但增速随散热器底面温度的增加变缓;努谢尔特数随雷诺数的增加而成幂次方增加,常规针肋结构和微针肋结构换热关系式不满足微方肋散热器特性。为了更好地表达微方肋散热器内的换热特性,拟合了微方肋散热器内对流换热关系式。     

Heat transfer behaviour of nanofluids in a uniformly heated circular tube fitted with helical inserts in laminar flow

The CFD simulation of heat transfer characteristics of a nanofluid in a circular tube fitted with helical twist inserts under constant heat flux has been explained using Fluent version 6.3.26 in laminar flow. Al₂O₃ nanoparticles in water of 0.5%, 1.0% and 1.5% concentrations and helical twist inserts of twist ratios 2.93, 3.91 and 4.89 has been used for the simulation. All thermophysical properties of nanofluids are temperature dependent. The heat transfer enhancement increases with Reynolds number and decreases with twist ratio with maximum for the twist ratio 2.93. By comparing the heat transfer rates of water and nanofluids, the increase in Nusselt number is 5%–31% for different helical inserts and different volume concentrations. The maximum heat transfer enhancement is 31.29% for helical insert of twist ratio 2.93 and for the volume concentration of 1.5% corresponding to the Reynolds number of 2039. The data obtained by simulation match with the literature value of water with the discrepancy of less than ±10% for plain tube and tube fitted with helical tape inserts for Nusselt number.     

Laminar Heat Transfer Augmentation through A Square Duct and Circular Tube Fitted with Twisted Tapes

Experimental studies on friction factor and heat transfer characteristics for the laminar flow of ethylene glycol in a square duct fitted with twisted tapes of different twist ratios under nearly uniform wall temperature conditions are reported in this article. The Nusselt numbers were found to be 5.44–7.49 and 2.46–4.87 times that of plain square duct forced convection values based on constant flow rate and constant pumping power criteria, respectively, for y = 2.66. The augmented friction factor and Nusselt number for a square duct is about 1.9 and 2.10 times higher than that for an augmented circular tube.     

Experimental Investigation of Heat Transfer for a Jet Impinging Obliquely on a Flat Surface

An experimental study investigated the effects of the inclination of an impinging circular jet on heat transfer from a horizontal flat plate. Local Nusselt number distribution was determine depending on inclination angle, jet-to-plate distance, and Reynolds number. The results show that the maximum heat transfer point moves toward the uphill side of the plate and that the maximum heat transfer decreases as the inclination angle decreases. The correlations were conducted to predict maximum and local Nusselt number as a function of Re, θ, L/D, and x/D for three specific regions.     

微通道-微槽群中间换热器特性实验研究

 对用于固体激光介质冷却的组合式中间换热器的流动与传热特性进行了实验研究。实验研究结果表明：努塞尔数随雷诺数的增加而增加，总热阻随微通道侧蒸馏水流量的增加而减小，总换热量随微通道侧蒸馏水流量的增加而增加，且换热器的传热系数可以达到1.5×104 W/(m²·K)，总热阻小于0.3 K/W，能较好地解决当前固体激光介质冷却系统中间换热器所存在的问题。     

高温吸热管内超临界CO2传热特性的数值模拟

研究超临界CO2在高温吸热管内的传热特性是将其应用于聚光太阳能热发电技术中的基础.本文对此进行了数值模拟研究,分析了流体温度、流动方向、系统压力、质量流率和热流密度对对流传热系数和Nu数的影响.结果表明:高温区(800—1050 K)的对流传热系数和Nu数受流动方向和系统压力的影响均很小,但都随着质量流率的增大以及热流密度的减小而明显增大;而随着流体温度的升高,对流传热系数近似线性增大,Nu数则近似线性减小.另外,本文研究发现在高温区可忽略浮升力对传热的影响,而由高热流密度引起的流动加速效应会明显恶化传热.最后,选取了八种管内超临界流体传热关联式与模拟结果进行对比,发现使用基于热物性修正的关联式对高温区传热数据预测的结果优于使用基于无量纲数修正的关联式得到的结果,且其中预测效果最优的关联式得到的计算结果与模拟结果之间的平均绝对相对偏差为8.1%.     

AN EMPIRICAL CORRELATION FOR NATURAL CONVECTION FROM CONFINED ELLIPTIC TUBE

An experimental study was conducted to obtain a correlation for free convection heat transfer from isothermal elliptic tubes of minor to major axis ratios of ∈ = 0.53, 0.67, 0.8, and 1 confined between two adiabatic walls. Local and average Nusselt numbers were determined for several different tube axis ratios, Rayleigh numbers, and wall spacings by means of the Mach-Zehnder Interferometery (MZI) technique. For each tube axis ratio, the Rayleigh number varied from 1,000–2,750 and the wall spacing to tube minor axis ratio from 1.25–∞. For all the tube axis ratios, the periphery and length of the tubes were kept constant. Experimental data are presented with a correlation which gives the average Nusselt number as a function of the tube axis ratio, Rayleigh number, and wall spacing to tube minor axis ratio. As the tube axis ratio decreases the average heat transfer coefficient increases. Also, for a constant Rayleigh number and tube axis ratio there is an optimum wall spacing which maximizes the heat transferred from the tube.