scholarly journals Inverse Approach for the Average Convection Coefficient Induced by a Forced Fluid Flow Over an Annular Fin of Rectangular Profile Using Tip Temperature Measurements

2021 ◽  
Vol 16 ◽  
pp. 106-114
Author(s):  
Antonio Campo

The objective of the present paper is to develop a simple algebraic computational procedure for the estimation of the average convection coefficient of a forced fluid flow over an annular fin of rectangular profile within the platform of inverse heat conduction problems. The data required is the tip temperatures of an annular fin of rectangular profile, which are measured in an experimental setup. Based on nonlinear regression analysis, an empirical correlation equation is constructed for the dimensionless average tip temperature depending upon the dimensionless thermo–geometrical parameter and the radius ratio. When compared against the outcome of a direct heat conduction problem, the good quality of the estimated average convection coefficient for the annular fin of rectangular profile demonstrates the feasibility of the simple algebraic computational procedure.

1989 ◽  
Vol 111 (2) ◽  
pp. 218-224 ◽  
Author(s):  
E. P. Scott ◽  
J. V. Beck

Various methods have been proposed to solve the inverse heat conduction problem of determining a boundary condition at the surface of a body from discrete internal temperature measurements. These include function specification and regularization methods. This paper investigates the various components of the regularization method using the sequential regularization method proposed by Beck and Murio (1986). Specifically, the effects of the regularization order and the influence of the regularization parameter are analyzed. It is shown that as the order of regularization increases, the bias errors decrease and the variance increases. Comparatively, the zeroth regularization has higher bias errors and the second-order regularization is more sensitive to random errors. As the regularization parameter decreases, the sensitivity of the estimator to random errors is shown to increase; on the other hand, the bias errors are shown to decrease.


2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Y. Hwang ◽  
S. Deng

The primary cause of gun barrel erosion is the heat generated by the shell as its travels along the barrel. Therefore, calculating the heat flux input to the gun bore is very important when investigating wear problems in the gun barrel and examining its thermomechanical properties. This paper employs the continuous-time analog Hopfield neural network (CHNN) to compute the temperature distribution in various forward heat conduction problems. An efficient technique is then proposed for the solution of inverse heat conduction problems using a three-layered backpropagation neural network (BPN). The weak generalization capacity of BPN networks when applied to the solution of nonlinear function approximations is improved by employing the Bayesian regularization algorithm. The CHNN scheme is used to calculate the temperature in a 155mm gun barrel and the trained BPN is then used to estimate the heat flux of the inner surface of the barrel. The results show that the proposed neural network analysis method successfully solves forward heat conduction problems and is capable of predicting the unknown parameters in inverse problems with an acceptable error.


2016 ◽  
Vol 831 ◽  
pp. 33-43
Author(s):  
Rafał Gałek

The paper investigates the possibility of applying a heuristic algorithm to solve an inverse heat conduction problem encountered in Temperature Oscillation IR Thermography method. The idea of TOIRT [24] is to infer about convection coefficient in given point h(x,y) from phase delay φ(x,y) of the temperature signal measured by means of thermography on the opposite side of heat conducting wall in steady-periodic conditions. Since the exact solution for inverse 3D heat conduction problem defined by TOIRT method is not available, there is a need to employ some kind of optimisation scheme to find the distribution h(x,y). In [22] it has been done by iterative solution of associated direct problem with finite difference method and updating the distribution h(x,y) in every iteration according to relative error between measured and computed values of φ(x,y) on the surface of the conducting wall. This paper presents an alternative approach based on symbolic regression with Genetic Algorithm to find an explicit formula relating amplitude as well as phase shift angle of temperature signal and the value of convection coefficient. Proposed procedure involves an offline training of the model with data previously generated with Finite Element Method which assures that time-consuming part of the calculation is carried out once and since then obtained explicit formula may be used in fast and straightforward manner. The results show that proposed approach gives solution with at least comparable accuracy to that obtained in [22], but requires careful selection of training data mainly in terms of their diversity and values of gradient of h(x,y).


2017 ◽  
Vol 139 (7) ◽  
Author(s):  
M. Tadi

This note is concerned with a new method for the solution of an elliptic inverse heat conduction problem (IHCP). It considers an elliptic system where no information is given at part of the boundary. The method is iterative in nature. Starting with an initial guess for the missing boundary condition, the algorithm obtains corrections to the assumed value at every iteration. The updating part of the algorithm is the new feature of the present algorithm. The algorithm shows good robustness to noise and can be used to obtain a good estimate of the unknown boundary condition. A number of numerical examples are used to show the applicability of the method.


2018 ◽  
Vol 40 (3) ◽  
pp. 91-96
Author(s):  
E.N. Zotov ◽  
A.A. Moskalenko ◽  
O.V. Razumtseva ◽  
L.N. Protsenko ◽  
V.V. Dobryvechir

The paper presents an experimental-computational study of the results of using the IQLab program to solve inverse heat conduction problem and restore the surface temperature of cylindrical thermosondes from heat-resistant chromium-nickel alloys while cooling them in liquid media. The purpose of this paper is to verify the correct operation of the IQLab program when restoring the surface temperature of thermosondes with 1-3 thermocouples. The IQLab program is also designed to solve one-dimensional nonlinear direct lines and inverse heat conduction problems with constant initial and boundary conditions specified as a function of time in a tabular form with a constant and variable time step. A finite-difference method is used to solve the heat equation. Experiments were carried out on samples D = 10-50 mm in liquids with different cooling capacities such as aqueous solutions of  NaCl and Yukon-E polymer, rapeseed oil and I-20A mineral oil. For the calculation we used the readings of thermocouples installed at internal points of cylindrical thermosondes. The advantages of solving inverse heat conduction problems with the IQLab program include the possibility of restoring the surface temperature for cylindrical samples with a diameter of 10 mm to 50 mm with practical accuracy according to the indications of a single thermocouple located in the geometrical center of the thermosonde, which simplifies the manufacture of the probe. For larger dimensions with a diameter D ≥ 50 mm, it is necessary to install control intermediate thermocouples and perform additional tests. The solution of inverse heat conduction problems and restoration of the surface temperature of the sample makes it possible to calculate other important characteristics of the cooling process: the heat flux density and the heat transfer coefficient.


2003 ◽  
Vol 125 (6) ◽  
pp. 1197-1205 ◽  
Author(s):  
Sun Kyoung Kim ◽  
Woo Il Lee

A solution scheme based on the maximum entropy method (MEM) for the solution of two-dimensional inverse heat conduction problems is established. MEM finds the solution which maximizes the entropy functional under the given temperature measurements. The proposed method converts the inverse problem to a nonlinear constrained optimization problem. The constraint of the optimization problem is the statistical consistency between the measured temperature and the estimated temperature. Successive quadratic programming (SQP) facilitates the numerical estimation of the maximum entropy solution. The characteristic feature of the proposed method is investigated with the sample numerical results. The presented results show considerable enhancement in resolution for stringent cases in comparison with a conventional method.


2011 ◽  
Vol 308-310 ◽  
pp. 890-893
Author(s):  
Miao Cui ◽  
Xiao Wei Gao ◽  
Hai Geng Chen

A new inverse algorithm is proposed for the reconstruction of the total heat exchange factor, which is concerned with transient heat conduction problems. The unknown total heat exchange factor is treated as the optimization variable, and the errors to be minimized are the differences between the calculated temperatures and the measured ones. The sensitivity coefficients are obtained by the complex-variable-differentiation method. The effectiveness, efficiency and accuracy of the inverse approach are demonstrated in few test cases.


Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3313
Author(s):  
Sun Kyoung Kim

This work examines the effects of the known boundary conditions on the accuracy of the solution in one-dimensional inverse heat conduction problems. The failures in many applications of these problems are attributed to inaccuracy of the specified constants and boundary conditions. Since the boundary conditions and material properties in most thermal problems are imposed with uncertainty, the effects of their inaccuracy should be understood prior to the inverse analyses. The deviation from the exact solution has been examined for each case according to the errors in material properties, boundary location, and known boundary conditions. The results show that the effects of such errors are dramatic. Based on these results, the applicability and limitations of the inverse heat conduction analyses have been evaluated and discussed.


2013 ◽  
Vol 749 ◽  
pp. 131-136
Author(s):  
Hong Fen Gao ◽  
Gao Feng Wei

In this paper the meshless manifold method is used to obtain the solution of an inverse heat conduction problem with a source parameter. Compared with the numerical methods based on mesh, such as finite element method and boundary element method, the meshless manifold method only needs the scattered nodes instead of meshing the domain of the problem when the trial function is formed. The meshless manifold method is used to discretize the governing partial differential equation, and boundary conditions can be directly enforced without numerical integration in the problem domain. This reduces the computation cost greatly. A numerical example is given to show the effectiveness of the method.


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