Inverse Solution of a Heat Conduction Problem Using Evolutionary Data Segregation Techniques

2003 ◽  
Author(s):  
Peter E. Johnson ◽  
Kenneth M. Bryden ◽  
Daniel A. Ashlock
Keyword(s):  
Boundary Conditions ◽  
Temperature Profile ◽  
Heat Conduction Problem ◽  
Inverse Solution ◽  
Problem Definition ◽  
Direct Solution ◽  
Novel Technique ◽  
Squared Error ◽  
Engineering Design Problem ◽  
Engineering Problems

Engineering problems are typically solved by direct solution. For the direct solution of engineering problems the boundary conditions and physical properties of the domain are given, and the dependent variable is calculated throughout the domain. In contrast to this, for inverse engineering problems the dependent variable is known at select locations in the domain, and the material properties and/or the boundary conditions need to be determined. This paper will present a novel technique for the inverse solution of a heat transfer engineering design problem in which the temperature profile and materials are known, but the placement of these materials and the heat flux on the boundaries are unknown. This technique uses evolutionary optimization in the form of the Adaptive Modeling by Evolving Blocks Algorithm (AMoEBA) to determine the material configurations. The material configurations, geometry, and properties are defined by evolving binary trees. The evolved domains are solved directly and then compared with the known temperature profile. Fitness of the new designs is determined by the least squared error between the proposed and the known profile. When this fitness reaches a defined level, the material placement scheme of the real system is found, and boundary conditions matching the problem definition are identified.

scholarly journals Constraints on glacier flow from temperature-depth profiles in the ice. Application to EPICA Dome C.

2016 ◽  
Author(s):  
Ignacio Hermoso de Mendoza ◽  
Jean-Claude Mareschal ◽  
Hugo Beltrami
Keyword(s):  
Heat Flux ◽  
Velocity Profile ◽  
Boundary Conditions ◽  
Temperature Profile ◽  
East Antarctica ◽  
Surface Velocity ◽  
Function Parameter ◽  
Unknown Parameters ◽  
Conduction Model ◽  
Ice Flow

Abstract. A one-dimensional (1-D) ice flow and heat conduction model is used to calculate the temperature and heat flux profiles in the ice and to constrain the parameters characterizing the ice flow and the thermal boundary conditions at the Dome C drilling site in East Antarctica. We use the reconstructions of ice accumulation, glacier height and air surface temperature histories as boundary conditions to calculate the ice temperature profile. The temperature profile also depends on a set of poorly known parameters, the ice velocity profile and magnitude, basal heat flux, and air-ice surfaces temperature coupling. We use Monte Carlo methods to search the parameters' space of the model, compare the model output with the temperature data, and find probability distributions for the unknown parameters. We could not determine the sliding ratio because it has no effect on the thermal profile, but we could constrain the flux function parameter p that determines the velocity profile. We determined the basal heat flux qb = 49.0  ± 2.7 (2σ)m W m−2, almost equal to the apparent value. We found an ice surface velocity of vsur = 2.6 ± 1.9 (2σ)m y−1 and an air-ice temperature coupling of 0.8 ± 1.0(2σ)K. Our study confirms that the heat flux is low and does not destabilize the ice sheet in east Antarctica.

A Method for Applying Automatic Temperature Control to the Transient Finite Element Analysis of a Pressure Vessel Undergoing Postweld Heat Treatment

2004 ◽  
Author(s):  
Michael Sciascia
Keyword(s):  
Heat Treatment ◽  
Finite Element ◽  
Boundary Conditions ◽  
Temperature Profile ◽  
Pressure Vessel ◽  
Postweld Heat Treatment ◽  
Transient Temperature ◽  
Element Analysis ◽  
Heater Power ◽  
Postweld Heat

For complex finite element problems it is often desirable to prescribe boundary conditions that are difficult to quantify. The analysis of a pressure vessel undergoing postweld heat treatment (PWHT) is an example of such a problem. The PWHT process is governed by Code rules, but the temperature and gradient requirements they impose are not sufficient to precisely describe the complete vessel temperature profile. The imposition of such a profile in the analysis results in uncertainty and errors. A suitable but difficult approach is to specify heater power instead of temperatures, letting the solver determine the temperature profile. Unfortunately, the individual heater power levels necessary to meet the Code requirements are usually not known in advance. Determining the power levels necessary is particularly difficult if a transient solution is required. A means of actively controlling the heaters during the FEA solution is requirement for this approach. A simple and adaptive control algorithm was incorporated into the FEA solver via its scripting capability. Heat flux boundary conditions (heater power) were applied instead of transient temperature boundary conditions. Heater power levels were optimized to achieve predetermined time/temperature goals as the solution proceeded. The algorithm described was successfully applied to a pressure vessel PWHT with 14 zones of control. The approach may be adapted to other problems and boundary conditions.

scholarly journals Direct and Inverse Solutions with Geodetic Latitude in Terms of Longitude for Rhumb Line Sailing

2012 ◽  
Vol 65 (3) ◽  
pp. 549-559 ◽  
Author(s):  
Wei-Kuo Tseng ◽  
Michael A. Earle ◽  
Jiunn-Liang Guo
Keyword(s):  
Information System ◽  
Complete Solution ◽  
Oblate Spheroid ◽  
Original Data ◽  
Inverse Solution ◽  
Direct Solution ◽  
Electronic Chart ◽  
Inverse Solutions ◽  
Computer Based ◽  
High Degree

In this paper, equations are established to solve problems of Rhumb Line Sailing (RLS) on an oblate spheroid. Solutions are provided for both the inverse problem and the direct problem, thereby providing a complete solution to RLS. Development of these solutions was achieved in part by means of computer based symbolic algebra. The inverse solution described attains a high degree of accuracy for distance and azimuth. The direct solution has been obtained from a solution for latitude in terms of distance derived with the introduction of an inverse series expansion of meridian arc-length via the rectifying latitude. Also, a series to determine latitude at any longitude has been derived via the conformal latitude. This was achieved through application of Hermite's Interpolation Scheme or the Lagrange Inversion Theorem. Numerical examples show that the algorithms are very accurate and that the differences between original data and recovered data after applying the inverse or direct solution of RLS to recover the data calculated by the direct or inverse solution are very small. It reveals that the algorithms provided here are suitable for programming implementation and can be applied in the areas of maritime routing and cartographical computation in Graphical Information System (GIS) and Electronic Chart Display and Information System (ECDIS) environments.

scholarly journals Relaxation methods applied to engineering problems. VIII. Plane-potential problems involving specified normal gradients

1943 ◽  
Vol 182 (989) ◽  
pp. 129-151 ◽  
Keyword(s):  
Harmonic Function ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Boundary Values ◽  
Approximate Computation ◽  
Relaxation Methods ◽  
Potential Problems ◽  
Engineering Problems ◽  
Direct Attack

Since every plane-harmonic function is associated with a conjugate, problems in which normal gradients are specified on the boundary can be transformed into problems in which boundary values are specified. There then remains, however, the problem of deducing a function ψ from its conjugate ϕ, and this, when the conjugate has been determined only approximately, entails uncertainties which were exemplified in Part V. To minimize the errors of approximate computation ψ and ϕ should be determined severally and independently, consequently a method of direct attack is still needed on problems in which normal gradients are specified. Recent applications have, moreover, presented cases in which the boundary conditions are ‘mixed’, i.e. values are specified at some parts of the boundary, gradients at others. Here, two methods are propounded for the satisfaction of mixed boundary conditions, the first applicable also to cases in which normal gradients alone are specified. Test examples indicate that the wanted extension of method is now available.

Evaluation of Boundary Conditions for CFD Simulation of Liquid Food Thermal Process in Glass Bottles

2012 ◽  
Vol 7 (6) ◽  
Author(s):  
Pedro Esteves Duarte Augusto ◽  
Marcelo Cristianini
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Temperature Profile ◽  
Thermal Process ◽  
Cfd Simulation ◽  
Convective Heat Transfer Coefficient ◽  
Food Products ◽  
Food Preservation ◽  
Heating Water ◽  
Experimental Values

The growing demand for safer and high-quality food products creates the need for better knowledge of the processes involved in food production. The computational fluid dynamics (CFD) have been widely used to better understand food thermal process, one of the safest and most frequently used methods for food preservation. However, no consistency in mathematical models has been observed, especially on the boundary conditions definition. The present study has evaluated four methodologies for the definition of boundary conditions for heating water in two commercial bottles: (M1) temperature profile of heating water (T∞) and convective heat transfer coefficient (h), (M2) T∞ as boundary condition for the outside package wall, (M3) T∞ as boundary condition for the outside heated liquid edge, and (M4) internal temperature profile (T=T(x,y,z,t)), previously measured in the inner package wall, as boundary condition for the outside heated liquid edge. Models that considered the measured value of h e T∞ as boundary condition showed good agreement with experimental values, compared by thermal history and sterilization value (F). The models that considered the temperature profile of the heating water or the inner package wall as boundary conditions, showed faster heating. By over-estimating the product heating rate, those models are not appropriated for thermal process modelling, as it compromises the safety and preservation of food products.

scholarly journals Benchmark Studies for the Generalized Streamwise Periodic Heat Transfer Problem

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Steven B. Beale
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Transfer Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Wall Boundary Conditions ◽  
Engineering Problems ◽  
Complex Engineering ◽  
The Common ◽  
Periodic Heat

This is a comparison of calculations performed with a scheme for handling streamwise-periodic boundary conditions with known solutions to the common problem of fully developed heat transfer in a plane duct. Constant value, constant flux, mixed boundary conditions, and linear wall flux (conjugate heat transfer) are all considered. Agreement is, in every case, near exact showing that the methodology may be applied with confidence to complex engineering problems with a variety of thermal wall boundary conditions.

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