Measurement of Transient Fluid Temperature in a Pipeline

The aim of this paper is to develop a method of determining the heat transfer coefficients on the inner surface of the pipeline and outer surface of the thermometer used to measure the temperature of a fluid flowing under high pressure. The method is based on the solutions to the inverse heat conduction problems for the thermometer and the pipeline wall. The heat transfer coefficients are determined based on the measurement of the temperature of a cylindrical metal thermometer and the temperature of the wall of a cylindrical pipeline. The temperature sensor is located in the pipeline wall close to the inner surface. The correlations for the Nusselt numbers used to determine heat transfer coefficients on the outer surface of the thermometer and the inner surface of the pipeline contain unknown coefficients which are found using the least squares method. The unknown coefficients are selected so that the sum of the squares of differences between the fluid temperature determined based on the measurement of the temperature of the pipeline wall and the fluid temperature obtained from measurements inside the thermometer, calculated for several dozen set time points, is as small as possible.     

理想流体对流传热问题的理论解

研究理想流体受迫对流传热和自然对流传热问题的理论解。采用流体无垂直于壁面法线方向运动(即无穿透)的条件取代黏性流体在壁面无滑移条件，解决了流体在边界上有滑移时计算对流传热系数的困难，给出了理想流体与平壁受迫对流传热、理想流体与竖直壁面自然对流传热和理想流体在管内受迫对流传热的理论解。结果表明：理想流体的对流传热与黏性流体同样存在着热边界层。在外部流动的情况下，无论受迫对流传热还是自然对流传热，对流传热系数都与流体的导热系数、密度和比热三乘积的二分之一次方成正比。在管内受迫对流的情况下，当无因次长度大于0．05时，局部Nu和界面无因次温度分布都不再变化，对于恒热流边界条件，Nu等于8，截面无因次平均温度等于2；对于恒壁温边界条件，Nu等于5．782，截面无因次平均温度等于2．316。     

Numerical analysis of heat and mass transfer during absorption of hydrogen in metal hydride based hydrogen storage tanks

In this paper, hydriding in a cylindrical metal hydride hydrogen storage tank containing HWT5800 (Ti_0.98Zr_0.02V_0.43Fe_0.09Cr_0.05Mn_1.5) is numerically studied with a two-dimensional mathematical model. The heat and mass transfer of this model is computed by finite difference method. The effects of supply pressure, cooling fluid temperature, overall heat transfer coefficient and height to the radius ratio of the tank (H/R) on the hydriding in the hydrogen storage tank are studied. It is found that hydride formation initially takes place uniformly all over the bed and hydriding processes take place at a slower rate at the core region. Supply pressure, cooling fluid temperature and overall heat transfer coefficient play significant roles during the absorption of hydrogen. At the H/R = 2 both maximum bed temperature and the average bed temperature are the highest, and the hydride bed takes the longest time to saturate.     

Characteristics of heating scheme and mass transfer on the peristaltic flow for an Eyring–Powell fluid in an endoscope

In this article Eyring–Powell peristaltic fluid flow with heat and mass transfer analysis have been investigated. New fluid model have been presented in peristaltic literature. The governing equations for proposed Eyring–Powell fluid model are derived in cylindrical coordinates both in fixed and moving frame of reference. Complex system of equations have been simplified using long wavelength and low Reynolds number approximation. The momentum and heat/mass transfer balance equations are solved analytically and numerically by employing perturbation method and shooting technique. Graphical results have been discussed for pressure rise, frictional forces, temperature and concentration profile. Comparison of perturbation and numerical solutions have been presented through table and figures. Five different waves forms have been considered for analysis. Trapping phenomena have been presented for different wave forms.     

Heat transfer coefficient of wheel rim of large capacity steam turbines

A way of calculating the overall equivalent heat transfer coefficient of wheel rims of large capacity steam turbines is presented. The method and formula to calculate the mean forced convection heat-transfer coefficient of the surface of the blade and for the bottom wall of the blade passage, are introduced. The heat transmission from the blade to the rim was simplified by analogy to heat transmission in the fins. A fin heat transfer model was then used to calculate the equivalent heat transfer coefficient of the blade passage. The overall equivalent heat transfer coefficient of the wheel rim was then calculated using a cylindrical surface model. A practical calculation example was presented. The proposed method helps determine the heat transfer boundary conditions in finite element analyses of temperature and thermal stress fields of steam turbine rotors.     

An Inverse Problem Method for Overall Heat Transfer Coefficient Estimation in a Partially Filled Rotating Cylinder

The objective of this article is to study the estimation of an overall heat transfer coefficient in a partially filled rotating cylinder. Herein is an inverse analysis for estimating the overall heat transfer coefficient in an arbitrary cross-section of the aforementioned system from the temperatures measured on the shell. The material employs the finite-volume method to solve the direct problem. The hybrid effective algorithm applied here contains the local optimization algorithm to estimate the unknown parameter by minimizing the objective function. The data measured here are simulated by adding random errors to the exact solution. An investigation is made of the impact of the measurement errors on the accuracy of the inverse analysis. Two-optimization algorithms in determining the overall heat transfer coefficient are used. It is determined that the Conjugate Gradient Method is better than the Levenberg-Marquardt Method because the former produces greater accuracy for the same measurement errors. The resulting observation indicates that good agreement exists between the exact value and estimated result for both algorithms.     

Non-iterative estimation of heat transfer coefficients using artificial neural network models

The Inverse Heat Conduction Problem (IHCP) dealing with the estimation of the heat transfer coefficient for a solid /fluid assembly from the knowledge of inside temperature was accomplished using an artificial neural network (ANN). Two cases were considered: (a) a cube with constant thermophysical properties and (b) a semi-infinite plate with temperature dependent thermal conductivity resulting in linear and nonlinear problem, respectively. The Direct Heat Conduction Problems (DHCP) of transient heat conduction in a cube and in a semi-infinite plate with a convective boundary condition were solved. The dimensionless temperature-time history at a known location was then correlated with the corresponding dimensionless heat transfer coefficient/Biot number using appropriate ANN models. Two different models were developed for each case i.e. for a cube and a semi-infinite plate. In the first one, the ANN model was trained to predict Biot number from the slope of the dimensionless temperature ratio versus Fourier number. In the second, an ANN model was developed to predict the dimensionless heat transfer coefficient from non-dimensional temperature. In addition, the training data sets were transformed using a trigonometric function to improve the prediction performance of the ANN model. The developed models may offer significant advantages when dealing with repetitive estimation of heat transfer coefficient. The proposed approach was tested for transient experiments. A ‘parameter estimation’ approach was used to obtain Biot number from experimental data.     

Investigation of heat transfer characteristics in plate-fin heat sink

The present study applies the inverse method in conjunction with the experimental temperature data to investigate the accuracy of the heat transfer coefficient on the fin in the plate-fin heat sink for various fin spacings. The commercial software is applied to solve the governing differential equations with the RNG k–? model in order to obtain the heat transfer and fluid flow characteristics. Under the assumption of the non-uniform heat transfer coefficient, the entire fin is divided into several sub-fin regions before performing the inverse scheme. The average heat transfer coefficient in each sub-fin region is assumed to be unknown. Later, the present inverse scheme in conjunction with the experimental temperature data is applied to determine the heat transfer coefficient and fin efficiency. In order to determine a more reliable heat transfer coefficient, a comparison between the present inverse and numerical results and those obtained from the existing correlations will be made. The numerical fin temperatures will also be compared with the experimental data.     

Monitoring of transient 3D temperature distribution and thermal stress in pressure elements based on the wall temperature measurement

Abstract

Two methods for monitoring the thermal stresses in pressure components of thermal power plants are presented. In the first method, the transient temperature distribution in the pressure component is determined by measuring the transient wall temperature at several points located on the outer insulated surface of the component. The transient temperature distribution in the pressure component, including the temperature of the inner surface is determined from the solution of the inverse heat conduction problem (IHCP). In the first method, there is no need to know the temperature of the fluid and the heat transfer coefficient. In the second method, thermal stresses in a pressure component with a complicated shape are computed using the finite element method (FEM) based on experimentally estimated fluid temperature and known heat transfer coefficient. A new thermometer with good dynamic properties has been developed and applied in practice, providing a much more accurate measurement of the temperature of the flowing fluid in comparison with standard thermometers. The heat transfer coefficient on the inner surface of a pressure element can be determined from the empirical relationships available in the literature. A numerical-experimental method of determination of the transient heat transfer coefficient based on the solution of the 3D-inverse heat conduction problem has also been proposed. The heat transfer coefficient on the internal surface of a pressure element is determined based on an experimentally determined local transient temperature distribution on the external surface of the element or the basis of wall temperature measurement at six points located near the internal surface if fluid temperature changes are fast. Examples of determining thermal and pressure stresses in the thick-walled horizontal superheater header and the horizontal header of the steam cooler in a power boiler with the use of real measurement data are presented.     

大功率汽轮机叶轮轮缘传热系数的研究

提出了大功率汽轮机叶轮轮缘总传热系数的计算方法.介绍了汽轮机动叶片叶身平均对流换热表面传热系数和叶片流道下壁面对流换热表面传热系数的计算方法和计算公式.把汽轮机叶片对叶轮的传热简化为肋片传热,使用肋片传热模型计算汽轮机叶片流道的等效传热系数,采用圆筒壁模型计算汽轮机叶轮轮缘的总传热系数,并给出了应用实例.在汽轮机转子的温度场与热应力场有限元分析中,该计算方法为确定叶轮轮缘的传热边界条件提供了依据.     

Countercurrent Double-Pipe Heat Exchanger Subjected to Flow-Rate Step Change,Part I: New Steady-State Formulation

This article deals with a new steady-state formulation of temperatures along a double-pipe heat exchanger in counterflow configuration when the mass flow rate is submitted to step change. The steady-state method is based on estimation of the exponential factor of temperature profile. This method, compared to results obtained from correlations, gives an alternative approach to the well-known procedures for sizing and rating heat exchangers in industrial applications, such as the k -NTU and LMTD methods. It is based on the average convective heat transfer coefficients of the hot and cold sides, while the other methods are based on the overall heat transfer coefficient.     

ENHANCEMENT OF HEAT TRANSFER IN TURBULENT SEPARATED AND REATTACHING FLOW BY LOCAL FORCING

This article presents numerical solutions for solving the problem of a mixed convective micropolar fluid flow and heat transfer along a vertical wavy surface with a discontinuous temperature profile. The overall surface is equally divided into a heated section succeeded by an unheated section alternately. The problems in the present study have been formulated by using a simple transposition theorem and the cubic spline collocation method. Eringen has applied the spline alternating direction implicit (SADI) procedure to solve the governing momentum, angular momentum, and energy equations those formulated. Along the wavy surface, the velocity, temperature, and microrotation profiles are presented. The influences of micropolar parameters R, u , geometry, and Gr/Re 2 number on the skin friction coefficient and Nusselt number have been studied in this work. The results demonstrate that the skin friction coefficient consists of a mixture of two harmonics in micropolar fluids and in Newtonian fluids. As the vortex viscosity parameter (R) increases, the heat transfer rate decreases, but the skin friction increases. In addition, when the spin gradient viscosity parameter ( u ) increases, the skin friction decreases. Comparisons between a Newtonian fluid and a micropolar fluid are also discussed.     

Mean Overall Heat Transfer Coefficient in Heat Exchangers Allowing for Temperature-Dependent Fluid Properties

For temperature-dependent heat transfer coefficients and heat capacities, fast approximation methods are presented for the estimation of the effective overall heat transfer coefficient. The heat transfer coefficients are calculated for two, three, or four reference temperatures. For the parallel and countercurrent flow a known method is described that uses a hypothetical fluid temperature for the iteration-free consideration of variable heat capacities. For the mixed–unmixed cross flow a previous method for temperature-dependent heat transfer coefficients is refined to allow also for variable heat capacities. For the mixed–mixed cross flow a new iterative fast design and rating method is developed that is a suitable model for special multipass shell-and-tube heat exchangers. The accuracy of the methods is tested against numerical calculations with good results.     

Use of CFD to Determine Effect of Wire Matrix Inserts on Crude Oil Fouling Conditions

Crude oil fouling rates are strongly affected by both local surface temperature and local surface shear stress. The use of in-tube inserts (such as hiTRAN) in heat exchangers has been shown to be effective in mitigating crude oil fouling while at the same time enhancing heat transfer. However, the introduction of inserts means that there will be axial and radial distributions of both local shear stress and local heat transfer coefficient between the repeating insert–wall contact points, which could mean that there will be local variations in fouling rate. While estimation of local shear stresses and film heat transfer coefficients is facile for bare round tubes, this is no longer the case for tubes fitted with inserts. Accordingly, this article describes a possible solution to the design challenge using computational fluid dynamics (CFD) simulation, the output of which is the temperature and velocity distributions in a three-dimensional geometry of the fluid flow in a tube fitted, for example, with a hiTRAN insert. A simple algorithm is then described for calculating the overall heat transfer coefficient based on the resulting temperature distribution along the wall of the tube. Simulated values of the overall heat transfer coefficient are then compared with those obtained by experiment, showing that there is good agreement, thereby indicating that predicted local values are accurate. Use of CFD in fouling applications now allows the prediction of local conditions when inserts are used and hence can be used to predict whether, and where, fouling might occur.     

An estimation for velocity and temperature profiles of nanofluids in fully developed turbulent flow conditions

Theoretically convective heat transfer coefficient depends on velocity and temperature profiles. In this work friction factor and convection coefficient are used in order to compare both profiles for nanofluids and base fluids. For this purpose Al₂O₃/water (due to its present vast experimental study) and carbon nanotube/water (manufactured and examined with our group) are selected. The results show that velocity profile of a nanofluid is similar to the velocity profile of its base fluid. It is proposed that the change of temperature profile for nanofluids compared to the base fluids is the only variable responsible for unpredictable convective heat transfer coefficient of nanofluids using available correlations.     

Toward the thermohydrodynamic behavior of a nanofluid containing C-MWCNTs flowing through a 3D annulus channel under constant imposed heat flux

The heat transport and friction factor in a three-dimensional horizontal concentric annular duct filled with nanofluids comprising clove-treated multiwalled carbon nanotubes are investigated numerically in this paper. The cylinder's outer surface is thermally insulated, while uniform heat flux is imposed on the cylinder's inner surface. The problem is formulated in dimensionless cylindrical coordinates. The numerical solutions were obtained based on the finite volume technique with second-order precision, and cover a range of the Reynolds number 1000 ≤ Re ≤ 2000 and nanoparticle weight fractions 0.075, 0.125, and 0.175 wt%. To describe the results for both heat exchange and fluid flow performance, the temperature profile, Nusselt number, heat transfer coefficient, and friction factor are represented. The findings state that heat transport increases as Reynolds is increased and nanoparticles are introduced. The friction factor was also observed to improve as the concentration of nanoparticles increased. In addition, two new Nusselt number and friction factor correlations were established.     

Sensitivity analysis and numerical experiments on transient test of compact heat exchanger surfaces

A single-blow transient testing technique considering the effect of longitudinal heat conduction is suggested for determining the average convection heat transfer coefficient of compact heat exchanger surface. By matching the measured outlet fluid temperature variation with similar theoretical curves, the dimensionless longitudinal conduction parameter ?_l, the time constant of the inlet fluid temperature ?⁺, and the number of heat transfer units N_tu can be determined simultaneously using the Levenberg-Marquardt nonlinear parameter estimation method. Both sensitivity analysis and numerical experiments with simulated measurements containing random errors show that the method in the present investigation provides satisfactory accuracy of the estimated parameter N_tu, which characterizes the heat transfer performance of compact heat exchanger surfaces.     

Heat transfer coefficient of wheel rim of large capacity steam turbines

A way of calculating the overall equivalent heat transfer coefficient of wheel rims of large capacity steam turbines is presented. The method and formula to calculate the mean forced convection heat-transfer coefficient of the surface of the blade and for the bottom wall of the blade passage, are introduced. The heat transmission from the blade to the rim was simplified by analogy to heat transmission in the fins. A fin heat transfer model was then used to calculate the equivalent heat transfer coefficient of the blade passage. The overall equivalent heat transfer coefficient of the wheel rim was then calculated using a cylindrical surface model. A practical calculation example was presented. The proposed method helps determine the heat transfer boundary conditions in finite element analyses of temperature and thermal stress fields of steam turbine rotors. __________ Translated from Journal of Power Engineering, 2007, 27(2): 153–156 [틫自: 뚯솦릤돌]     

Conjugate natural convection about a vertical cylindrical fin with lateral mass flux in a saturated porous medium

The problem of conjugate natural convection about a vertical cylindrical fin with uniform lateral mass flux in a fluid-saturated porous medium has been studied numerically. Solutions based on the third level of truncation are obtained by the local nonsimilarity method. The effects of the surface mass flux, the conjugate convection-conduction parameter, and the surface curvature on fin temperature distribution, local heat transfer coefficient, local heat flux, average heat transfer coefficient, and total heat transfer rate are presented. A comparison with finite-difference solutions for the case of constant wall temperature was made, and found in a good agreement.     

Numerical study of the inlet/outlet arrangement effect on microchannel heat sink performance

In this study, fluid flow and heat transfer in microchannel heat sinks are numerically investigated. The three-dimensional governing equations for both fluid flow and heat transfer are solved using the finite-volume scheme. The computational domain is taken as the entire heat sink including the inlet/outlet ports, inlet/outlet plenums, and microchannels. The particular focus of this study is the inlet/outlet arrangement effects on the fluid flow and heat transfer inside the heat sinks.The microchannel heat sinks with various inlet/outlet arrangements are investigated in this study. All of the geometric dimensions of these heat sinks are the same except the inlet/outlet locations. Because of the difference in inlet/outlet arrangements, the resultant flow fields and temperature distributions inside these heat sinks are also different under a given pressure drop across the heat sink. Using the averaged velocities and fluid temperatures in each channel to quantify the fluid flow and temperature maldistributions, it is found that better uniformities in velocity and temperature can be found in the heat sinks having coolant supply and collection vertically via inlet/outlet ports opened on the heat sink cover plate. Using the thermal resistance, overall heat transfer coefficient and pressure drop coefficient to quantify the heat sink performance, it is also found these heat sinks have better performance among the heat sinks studied. Based on the results from this study, it is suggested that better heat sink performance can be achieved when the coolant is supplied and collected vertically.