Determination of heat transfer coefficient using transient temperature response chart

An inverse finite element computer code is developed to predict surface heat flux and surface temperature in conjunction with the measured thermocouple temperature history. Determination of convective heat-transfer coefficient and combustion gas temperature is carried out employing transient temperature response chart. Examples are illustrated which are typical of those that arise in thermal design of rocket nozzle. The results demonstrate that the method is remarkable in its ability to estimate unknown boundary conditions.     

Comparison of interfacial heat transfer coefficient estimated by two different techniques during solidification of cylindrical aluminum alloy casting

The interfacial heat transfer coefficient (IHTC) is necessary for accurate simulation of the casting process. In this study, a cylindrical geometry is selected for the determination of the IHTC between aluminum alloy casting and the surrounding sand mold. The mold surface heat flux and temperature are estimated by two inverse heat conduction techniques, namely Beck’s algorithm and control volume technique. The instantaneous cast and mold temperatures are measured experimentally and these values are used in the theoretical investigations. In the control volume technique, partial differential heat conduction equation is reduced to ordinary differential equations in time, which are then solved sequentially. In Beck’s method, solution algorithm is developed under the function specification method to solve the inverse heat conduction equations. The IHTC was determined from the surface heat flux and the mold surface temperature by both the techniques and the results are compared.     

Temperature dependent viscosity and thermal conductivity effects on combined heat and mass transfer in MHD three-dimensional flow over a stretching surface with Ohmic heating

An analysis has been carried out to obtain the flow, heat and mass transfer characteristics of a viscous electrically conducting fluid having temperature dependent viscosity and thermal conductivity past a continuously stretching surface, taking into account the effect of Ohmic heating. The flow is subjected to a uniform transverse magnetic field normal to the plate. The resulting governing three-dimensional equations are transformed using suitable three-dimensional transformations and then solved numerically by using fifth order Runge–Kutta–Fehlberg scheme with a modified version of the Newton–Raphson shooting method. Favorable comparisons with previously published work are obtained. The effects of the various parameters such as magnetic parameter M, the viscosity/temperature parameter θ _r , the thermal conductivity parameter S and the Eckert number Ec on the velocity, temperature, and concentration profiles, as well as the local skin-friction coefficient, local Nusselt number, and the local Sherwood number are presented graphically and in tabulated form.     

Finite element analysis of conductive and radiative heating of a thin skin calorimeter

The main purpose of the present work is to investigate the influence of normal and lateral conduction on the temperature distribution and heat transfer coefficient on the surface of a typical sounding rocket. A two-dimensional heat conduction equation with a time dependent aerodynamic heating condition at one surface and a radiation boundary condition at the other end is solved using finite element method.     

Numerical nonlinear inverse problem of determining wall heat flux

The inverse problem of determining time-variable surface heat flux in a plane wall, with constant or temperature dependent thermal properties, is numerically studied. Different kinds of incident heat flux, including rectangular waveform, are assumed. The solution is numerically solved as a function estimation problem, so that no a priori information for the functional waveforms of the unknown heat flux is needed. In all cases, a solution in the form of a piece-wise function is used to approach the incident flux. Transient temperature measurements at the boundary, from the solution of the direct problem, served as the simulated experimental data needed as input for the inverse analysis. Both direct and inverse heat conduction problems are solved using the network simulation method. The solution is obtained step-by-step by minimising the classical functional that compares the above input data with those obtained from the solution of the inverse problem. A straight line of variable slope and length is used for each one of the stretches of the desired solution. The influence of random error, number of functional terms and the effect of sensor location are studied. In all cases, the results closely agree with the solution.     

A boundary identification method for an inverse heat conduction problem with an application in ironmaking

A boundary identification problem in inverse heat conduction is studied, based on data from internal measurement of temperature and heat flux. Formulated as a sideways heat conduction equation, a spatial continuation technique is applied to extend the solution to a known boundary condition at the desired boundary position. Recording the positions traversed in the continuation for each time instant yields the boundary position trajectory and hence the solution of the identification problem. A prospective application of the method can be found in the ironmaking blast furnace, where it is desired to monitor the thickness of the accreted refractory wall based on measurement of its internal state. Simulations featuring noisy measurement data demonstrate the feasibility of the identification method for blast furnace wall thickness estimation.     

Nodal predictive error model and Bayesian approach for thermal diffusivity and heat source mapping

This article aims at solving a two-dimensional inverse heat conduction problem in order to retrieve both the thermal diffusivity and heat source field in a thin plate. A spatial random heat pulse is applied to the plate and the thermal response is analysed. The inverse approach is based on the minimisation of a nodal predictive error model, which yields a linear estimation problem. As a result of this approach, the sensitivity matrix is directly filled with experimental data, and thus is partially noisy. Bayesian estimators, such as the Maximum A Posteriori and a Markov Chain Monte Carlo approach (Metropolis–Hastings), are implemented and compared with the Ordinary Least Squares solution. Simulated temperature measurements are used in the inverse analysis. The nodal strategy relies on the availability of temperature measurements with fine spatial resolution and high frequency, typical of nowadays infrared cameras. The effects of both the measurement errors and of the model errors on the inverse problem solution are also analysed.     

基于遗传算法的一种Tikhonov正则化改进方法

就Tikhonov正则化方法求解第一类算子方程进行了新的探讨,针对展平泛函的极值处理,采用了遗传算法来解决.结合遗传算法的优点,扩大了解决问题的范围.介绍了其基本原理及运算流程,作为此方法的应用,首先对一变截面悬臂梁模型进行截面积反求,另外解决了一个热传导反问题实例,证明了其方法的有效性.     

Thermoconductivity and thermoelasticity of thin isotropic shells heated by a moving heat pulse

The paper presents a solution to the problem of thermal conduction and thermoelasticity for a thin shallow spherical shell heated by a concentrated or local impulsive heat source moving over the shell surface. It is assumed that temperature is linearly distributed across the shell thickness and that the shell, on its sides, exchanges heat with the environment in accordance with Newton’s law of cooling. The Fourier and Laplace transforms are used to find an analytic solution. The dependence of the temperature field and stress/strain components on the type of heating and the form of heat source is studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 85–92, November 2006.     

Convective drying analysis of three-dimensional porous solid by mass lumping finite element technique

A numerical analysis of convective drying of a 3D porous solid of brick material is carried out using the finite element method and mass lumping technique. The energy equation and moisture transport equations for the porous solid are derived based on continuum approach following Whitaker’s theory of drying. The governing equations are solved using the Galerkin’s weighted residual method, which convert the governing equations into discretized form of matrix equations. The resulting capacitance matrices are made diagonal matrices by following the classical row-sum mass lumping technique. Hence with the use of the Eulerian time marching scheme, the final equations are reduced to simple algebraic equations, which can be solved directly without using an equation solver. The proposed numerical scheme is initially validated with experimental results for 1D drying problem and then tested by application to convective drying of 3D porous solid of brick material for four different aspect ratios obtained by varying the cross section of the solid. The mass lumping technique could correctly predict the wet bulb temperature of the solid under evaporative drying conditions. A parametric study carried out for three different values of convective heat transfer coefficients, 15, 30 and 45 W/m² K shows an increased drying rate with increase in area of cross section and convective heat transfer coefficient. The proposed numerical scheme could correctly predict the drying behavior shown in the form of temperature and moisture evolutions.     

Efficient reconstruction of local heat fluxes in pool boiling experiments by goal-oriented adaptive mesh refinement

In this paper, we consider the efficient estimation of local boiling heat fluxes from transient temperature measurements in the heater close to the heater surface. For accurate prediction, heat flux estimation is formulated as a transient three-dimensional (3D) inverse heat conduction problem (IHCP). This inverse problem is ill-posed and cannot be treated straightforwardly by established numerical methods. In order to obtain a regularized stable solution, a large-scale time-dependent PDE-constrained optimization problem has to be solved and an appropriate stopping criterion for the termination of the iterative solution process has to be chosen. Since the boiling heat flux is non-uniformly distributed on the heater surface due to the strong local activity of the boiling process, the use of a fixed uniform spatial discretization is not efficient. Instead, an adaptive mesh refinement strategy can be used to obtain an appropriate discretization which significantly reduces the total computational effort. In this work, we present an automatic algorithm incorporating an adaptive mesh refinement via a heat flux-based a-posteriori error estimation technique. The suggested algorithm can cope with both spatially point-wise or highly resolved temperature observations efficiently. It is applied to real measurement data obtained from two different types of pool boiling experiments. The numerical results show that the computational effort can be reduced significantly for given estimation quality. This adaptive IHCP solution technique can be also viewed as an efficient soft sensor to deduce unmeasurable local boiling heat fluxes.     

Correlation for frost properties on a cold cylinder surface in cross flow

An experimental study was reported earlier on the development of frost formation by humid flow passing over the cylinder. In this study, dimensionless correlations based on previous experimental data and reported empirical correlations of others for frost properties are proposed. The frost conduction coefficient is determined by using an analytical equation. Subsequently, correlations are sought for the heat conduction coefficient, dimensionless temperature, dimensionless thickness and density. The advantages of these correlations to any other proposed correlations are their explicit and dependency on time. Furthermore, an estimation of characteristics of the frost is followed by using the same approach and the established correlations.     

Inverse transient heat conduction problems and identification of thermal parameters

This work deals with the estimation of polymers properties. An inverse analysis based on finite element method is applied to identify simultaneously the constants thermal conductivity and heat capacity per unit volume. The inverse method algorithm constructed is validated from simulated transient temperature recording taken at several locations on the surface of the solid. Transient temperature measures taped with infrared camera on polymers were used for identifying the thermal properties. The results show an excellent agreement between manufacturer and identified values.     

The Domain-Boundary Element Method (DBEM) for hyperelastic and elastoplastic finite deformation: axisymmetric and 2D/3D problems

Summary  This paper presents the solution of geometrically nonlinear problems in solid mechanics by the Domain-Boundary Element Method. Because of the Total-Lagrange approach, the arising domain and boundary integrals are evaluated in the undeformed configuration. Therefore, the system matrices remain unchanged during the solution procedure, and their time-consuming computation needs to be performed only once. While the integral equations for axisymmetric finite deformation problems will be derived in detail, the basic ideas of the formulation in two and three dimensions can be found in [1]. The present formulation includes torsional problems with finite deformations, where additional terms arise due to the curvilinear coordinate system. A Newton–Raphson scheme is used to solve the nonlinear set of equations. This involves the solution of a large system of linear equations, which has been a very time-consuming task in former implementations, [1, 2]. In this work, an iterative solver, i.e. the generalized minimum residual method, is used within the Newton–Raphson algorithm, which leads to a significant reduction of the computation time. Finally, numerical examples will be given for axisymmetric and two/three-dimensional problems. Received 29 August 2000; accepted for publication 10 October 2000     

Optimum Suction Distribution for Transition Control

The optimum suction distribution which gives the longest laminar region for a given total suction is computed. The goal here is to provide the designer with a method of finding the best suction distribution subject to some overall constraints applied to the suction. We formulate the problem using the Lagrangian multiplier method with constraints. The resulting nonlinear system of equations is solved using the Newton–Raphson technique. The computations are performed for a Blasius boundary layer on flat-plate and crossflow cases. For the Blasius boundary layer, the optimum suction distribution peaks upstream of the maximum growth rate region and remains flat in the middle before it decreases to zero at the end of the transition point. For the stationary and travelling crossflow instability, the optimum suction peaks upstream of the maximum growth rate region and decreases gradually to zero. Received 8 May 1997 and accepted 5 November 1998     

变几何域传热的表面热流反演方法

变几何域的表面热流反演是一类特殊的热传导逆问题,在再入飞行器烧蚀型防热材料的表面热流反演中具有工程实用价值.本文首先对变几何域传热的正问题计算方法进行了校核验证,然后建立了求解变几何域表面热流反演问题的顺序函数法和共轭梯度法;给出了这两种反演方法的基本思想和算法推导,并针对典型算例进行了仿真.结果表明:两种反演方法都能计算出较好的反演结果,并且算法受测量噪声的影响较小,具有较好的鲁棒性;反演算法能适应不同的几何域变化函数,但几何域变化量的测量误差在表面热流的反演结果中会有较为直接的反映.     

Retrieving the heat transfer coefficient for jet impingement from transient temperature measurements

Algorithm of retrieving the heat transfer coefficient (HTC) from transient temperature measurements is presented. The unknown distributions of two types of boundary conditions: the temperature and heat flux are parameterized using a small number of user defined functions. The solutions of the direct heat conduction problems with known boundary temperature and flux are expressed as a superposition of auxiliary temperature fields multiplied by unknown parameters. Inverse problem is formulated as a least squares fit of calculated and measured temperatures and is cast in a form of a sum of two objective functions. The first results originates from an inverse problem for retrieving the boundary temperature the second comes from the inverse problem for reproducing the boundary heat flux. The final form of the objective function is obtained by enforcing constant in time value of the heat transfer coefficient. This approach leads to substantial regularization of the results, when compared with the standard technique, where HTC is calculated from separately reconstructed temperature and heat flux on the boundary. The validation of the numerical procedure is carried out by reconstructing a known distribution of the HTC using simulated measurements laden by stochastic error. The proposed approach is also used to reconstruct the distribution of the HTC in a physical experiment of heating a cylindrical sample using an impinging jet.     

Geometrical nonlinear analysis of thin-walled composite beams using finite element method based on first order shear deformation theory

Based on a seven-degree-of-freedom shear deformable beam model, a geometrical nonlinear analysis of thin-walled composite beams with arbitrary lay-ups under various types of loads is presented. This model accounts for all the structural coupling coming from both material anisotropy and geometric nonlinearity. The general nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed to solve the problem. Numerical results are obtained for thin-walled composite beam under vertical load to investigate the effects of fiber orientation, geometric nonlinearity, and shear deformation on the axial–flexural–torsional response.     

Determination of gun propellants erosivity: Experimental and theoretical studies

Requirements for higher and higher performances of contemporary guns intensify investigations concerning influence of various factors on barrel erosion. The most important parameter for the life of the gun is the type of the gun propellant. The device based on modification of 37 mm M39 gun for investigating influence of gun propellant on barrel erosion is used. The nozzle (main part of device) mass loss during firing was the measure of gun propellant erosivity. The theory of nozzle erosion includes basic thermal, chemical and metallurgical factors. The main thermal and chemical factors are maximum nozzle inside surface temperature and gun propellant composition. The maximum nozzle surface temperature was determined theoretically by developed interior ballistic model with heat transfer, and experimentally by micro thermocouples measurements and solution of inverse heat conduction problem. The coefficients of gun propellants erosivity are determined in experimental and theoretical way.     

Comparison of four different versions of the variable metric method for solving inverse heat conduction problems

In this study, four different versions of the variable metric method (VMM) are investigated in solving standard one-dimensional inverse heat conduction problems in order to evaluate their efficiency and accuracy. These versions include Davidon–Fletcher–Powell (DFP), Broydon–Fletcher–Goldfarb–Shanno (BFGS), Symmetric Rank-one (SR1), and Biggs formula of the VMM. These investigations are carried out using temperature data obtained from numerical simulations.