Thermal Solutions for a Plate With an Arbitrary Temperature Transient on One Surface and Convection on the Other: Direct and Inverse Formulations

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Albert E. Segall ◽  
Craig C. Schoof ◽  
Daniel E. Yastishock
Keyword(s):  
Thermal Stresses ◽  
The Other ◽  
Engineering Practice ◽  
Time Interval ◽  
Internal Heating ◽  
Surface Loading ◽  
Polynomial Coefficients ◽  
Loaded Surface ◽  
Walled Cylinder

Abstract Thick plates that are thermally loaded on one surface with convection on the other are often encountered in engineering practice. Given this wide utility and the limitations of most existing solutions to an adiabatic boundary condition, generalized direct thermal solutions were first derived for an arbitrary surface loading as modeled by a polynomial and its coefficients on the loaded surface with convection on the other. Once formulated, the temperature solutions were then used with elasticity relationships to determine the resulting thermal stresses. Additionally, the inverse thermal problem was solved using a least-squares type determination of the aforementioned polynomial coefficients based on the direct-solution and temperatures measured at the surface with convection. Previously published relationships for a thick-walled cylinder with internal heating/cooling and external convection are also included for comparison. Given the versatility of the polynomial solutions advocated, the method appears well suited for complicated thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties do not vary with temperature.

Thermal Solutions for a Plate With an Arbitrary Temperature Transient on One Surface and Convection on the Other: Direct and Inverse Formulations

2019 ◽  
Author(s):  
Albert E. Segall ◽  
Craig C. Schoof ◽  
Daniel E. Yastishock
Keyword(s):  
Thermal Stresses ◽  
The Other ◽  
Engineering Practice ◽  
Time Interval ◽  
Internal Heating ◽  
Surface Loading ◽  
Polynomial Coefficients ◽  
Loaded Surface ◽  
Walled Cylinder

Abstract Thick plates that are thermally loaded on one surface with convection on the other are often encountered in engineering practice. Given this wide utility and the limitations of most existing solutions to an adiabatic boundary condition, generalized direct thermal solutions were first derived for an arbitrary surface loading as modeled by a polynomial and its coefficients on the loaded surface with convection on the other. Once formulated, the temperature solutions were then used with elasticity relationships to determine the resulting thermal stresses. Additionally, the Inverse thermal problem was solved using a least-squares determination of the aforementioned polynomial coefficients based on the direct-solution and temperatures measured at the surface with convection. Previously published relationships for a thick-walled cylinder with internal heating/cooling and external convection are also included for comparison. Given the versatility of the polynomial solutions advocated, the method appears well suited for complicated thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties do not vary with temperature.

scholarly journals A combined methodology for the approximate estimation of the roots of the general sextic polynomial equation

2021 ◽  
Author(s):  
Giorgos P. Kouropoulos
Keyword(s):  
Mathematical Model ◽  
Regression Analysis ◽  
Polynomial Equation ◽  
Approximate Solutions ◽  
The Other ◽  
Polynomial Equations ◽  
Polynomial Coefficients ◽  
Approximate Estimation ◽  
Predetermined Interval

Abstract In this article we present the methodology, according to which it is possible to derive approximate solutions for the roots of the general sextic polynomial equation as well as some other forms of sextic polynomial equations that normally cannot be solved by radicals; the approximate roots can be expressed in terms of polynomial coefficients. This methodology is a combination of two methods. The first part of the procedure pertains to the reduction of a general sextic equation H(x) to a depressed equation G(y), followed by the determination of solutions by radicals of G(y) which does not include a quintic term, provided that the fixed term of the equation depends on its other coefficients. The second method is a continuation of the first and pertains to the numerical correlation of the roots and the fixed term of a given sextic polynomial P(x) with the radicals and the fixed term of the sextic polynomial Q(x), where the two polynomials P(x) and Q(x) have the same coefficients except for the fixed term which might be different. From the application of the methodology presented above, the following formulation is derived; For any given general sextic polynomial equation P with coefficients within the interval [a, b], a defined polynomial equation Q corresponds which has equal coefficients to P except for its fixed term which might be different and dependent on the other coefficients so that Q has radical solutions. If we assume a pair of equations P, Q with coefficients within a predetermined interval [a, b], the numerical correlation through regression analysis of the radicals of Q, the roots of P and the fixed terms of P, Q, leads to the derivation of a mathematical model for the approximate estimation of the roots of sextic equations whose coefficients belong to the interval [a, b].

scholarly journals A combined methodology for the approximate estimation of the roots of the general sextic polynomial equation

2021 ◽  
Author(s):  
Giorgos P. Kouropoulos
Keyword(s):  
Mathematical Model ◽  
Regression Analysis ◽  
Polynomial Equation ◽  
Approximate Solutions ◽  
The Other ◽  
Polynomial Equations ◽  
Polynomial Coefficients ◽  
Approximate Estimation ◽  
Predetermined Interval

Abstract In this article we present the methodology, according to which it is possible to derive approximate solutions for the roots of the general sextic polynomial equation as well as some other forms of sextic polynomial equations that normally cannot be solved by radicals; the approximate roots can be expressed in terms of polynomial coefficients. This methodology is a combination of two methods. The first part of the procedure pertains to the reduction of a general sextic equation H(x) to a depressed equation G(y), followed by the determination of solutions by radicals of G(y) which does not include a quintic term, provided that the fixed term of the equation depends on its other coefficients. The second method is a continuation of the first and pertains to the numerical correlation of the roots and the fixed term of a given sextic polynomial P(x) with the radicals and the fixed term of the sextic polynomial Q(x), where the two polynomials P(x) and Q(x) have the same coefficients except for the fixed term which might be different. From the application of the methodology presented above, the following formulation is derived; For any given general sextic polynomial equation P with coefficients within the interval [a, b], a defined polynomial equation Q corresponds which has equal coefficients to P except for its fixed term which might be different and dependent on the other coefficients so that Q has radical solutions. If we assume a pair of equations P, Q with coefficients within a predetermined interval [a, b], the numerical correlation through regression analysis of the radicals of Q, the roots of P and the fixed terms of P, Q, leads to the derivation of a mathematical model for the approximate estimation of the roots of sextic equations whose coefficients belong to the interval [a, b].

Thermoelastic Stresses in Thick-Walled Vessels Under Thermal Transients via the Inverse Route

2006 ◽  
Vol 128 (4) ◽  
pp. 599-604 ◽  
Author(s):  
A. E. Segall
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Thermal Stresses ◽  
Internal Surface ◽  
Time Interval ◽  
Unknown Boundary ◽  
Direct Solution ◽  
Thermal Transients ◽  
Thermoelastic Stresses ◽  
Walled Cylinder

A common threat to thick-walled vessels and pipes is thermal shock from operational steady state or transient thermoelastic stresses. As such, boundary conditions must be known or determined in order to reveal the underlying thermal state. For direct problems where all boundary conditions (temperature or flux) are known, the procedure is relatively straightforward and mathematically tractable as shown by many studies. Although more practical from a measurement standpoint, the inverse problem where the boundary conditions must be determined from remotely determined temperature and/or flux data is ill-posed and inherently sensitive to errors in the data. As a result, the inverse route is rarely used to determine thermal stresses. Moreover, most analytical solutions to the inverse problem rely on a host of assumptions that usually restrict their utility to time frames before the thermal wave reaches the natural boundaries of the structure. To help offset these limitations and at the same time solve for the useful case of a thick-walled cylinder exposed to thermal loading on the internal surface, the inverse problem was solved using a least-squares determination of polynomial coefficients based on a generalized direct solution to the heat equation. Once the inverse problem was solved in this fashion and the unknown boundary condition on the internal surface determined, the resulting polynomial was used with the generalized direct solution to determine the internal temperature and stress distributions as a function of time and radial position. For a thick-walled cylinder under an internal transient with external convection, excellent agreement was seen with known temperature histories. Given the versatility of the polynomial solutions advocated, the method appears well suited for many thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature.

Thermoelastic Stresses in Thick-Walled Vessels Under an Arbitrary Thermal Transient via the Inverse Route

2005 ◽  
Author(s):  
A. E. Segall
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Thermal Stresses ◽  
Thermal State ◽  
Time Interval ◽  
Unknown Boundary ◽  
Measured Temperature ◽  
Direct Solution ◽  
Thermoelastic Stresses ◽  
Walled Cylinder

A common threat to thick-walled vessels and pipes is thermal shock from operational steady-state or transient thermoelastic stresses. As such, boundary conditions must be known or determined in order to reveal the underlying thermal state. For direct problems where all boundary conditions are known, the procedure is relatively straightforward and mathematically tractable as shown by recent studies. Although more practical from a measurement standpoint, the inverse problem where boundary conditions must be determined from remotely determined temperature and/or flux data is ill-posed and inherently sensitive to errors in the data. As a result, the inverse route is rarely used to determine thermal-stresses. Moreover, most analytical solutions to the inverse problem rely on a host of assumptions that usually restrict their utility to timeframes before the thermal wave reaches the natural boundaries of the structure. To help offset these limitations and at the same time solve for the useful case of a thick-walled cylinder exposed to thermal loading on the ID, the inverse problem was solved using a least-squares determination of polynomial coefficients based on a generalized direct-solution to the Heat Equation. Once the inverse problem was solved in this fashion and the unknown boundary-condition on the ID determined, the resulting polynomial was used with the generalized direct solution to estimate the internal temperature and stress distributions as a function of time and radial position. For a thick-walled cylinder under an internal transient with external convection, excellent agreement was seen with various measured temperature histories. Given the versatility of the polynomial solutions advocated, the method appears well suited for many thermal scenarios provided the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature.

Determination of the lattice translation across {110} APBs in GaAs

1988 ◽  
Vol 46 ◽  
pp. 600-601
Author(s):  
D.R. Rasmussen ◽  
N.-H. Cho ◽  
C.B. Carter
Keyword(s):  
Grain Boundaries ◽  
Lower Energy ◽  
Antiphase Boundary ◽  
The Other ◽  
Boundary Structure ◽  
Interface Plane ◽  
Inversion Symmetry ◽  
High Angle ◽  
Equilibrium Distance

Domains in GaAs can exist which are related to one another by the inversion symmetry, i.e., the sites of gallium and arsenic in one domain are interchanged in the other domain. The boundary between these two different domains is known as an antiphase boundary [1], In the terminology used to describe grain boundaries, the grains on either side of this boundary can be regarded as being Σ=1-related. For the {110} interface plane, in particular, there are equal numbers of GaGa and As-As anti-site bonds across the interface. The equilibrium distance between two atoms of the same kind crossing the boundary is expected to be different from the length of normal GaAs bonds in the bulk. Therefore, the relative position of each grain on either side of an APB may be translated such that the boundary can have a lower energy situation. This translation does not affect the perfect Σ=1 coincidence site relationship. Such a lattice translation is expected for all high-angle grain boundaries as a way of relaxation of the boundary structure.

Determination of the Burgers vector of a dislocation in a Fe-Mn alloy by weak-beam image in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 330-331
Author(s):  
Y. Ishida ◽  
H. Ishida ◽  
K. Kohra ◽  
H. Ichinose
Keyword(s):  
High Order ◽  
Simulation Technique ◽  
The Other ◽  
Image Simulation ◽  
Diffraction Vector ◽  
Burgers Vector ◽  
Weak Beam ◽  
Beam Image ◽  
Edge Component

IntroductionA simple and accurate technique to determine the Burgers vector of a dislocation has become feasible with the advent of HVEM. The conventional image vanishing technique(1) using Bragg conditions with the diffraction vector perpendicular to the Burgers vector suffers from various drawbacks; The dislocation image appears even when the g.b = 0 criterion is satisfied, if the edge component of the dislocation is large. On the other hand, the image disappears for certain high order diffractions even when g.b ≠ 0. Furthermore, the determination of the magnitude of the Burgers vector is not easy with the criterion. Recent image simulation technique is free from the ambiguities but require too many parameters for the computation. The weak-beam “fringe counting” technique investigated in the present study is immune from the problems. Even the magnitude of the Burgers vector is determined from the number of the terminating thickness fringes at the exit of the dislocation in wedge shaped foil surfaces.

Procedures for the Quantitative Determination of Autoprothrombin C

1962 ◽  
Vol 08 (03) ◽  
pp. 434-441 ◽  
Author(s):  
Edmond R Cole ◽  
Ewa Marciniak ◽  
Walter H Seegers
Keyword(s):  
Quantitative Determination ◽  
Plasma Sample ◽  
Quantitative Measure ◽  
The Other ◽  
Clotting Time ◽  
Bovine Plasma ◽  
Autoprothrombin C

SummaryTwo quantitative procedures for autoprothrombin C are described. In one of these purified prothrombin is used as a substrate, and the activity of autoprothrombin C can be measured even if thrombin is in the preparation. In this procedure a reaction mixture is used wherein the thrombin titer which develops in 20 minutes is proportional to the autoprothrombin C in the reaction mixture. A unit is defined as the amount which will generate 70 units of thrombin in the standardized reaction mixture. In the other method thrombin interferes with the result, because a standard bovine plasma sample is recalcified and the clotting time is noted. Autoprothrombin C shortens the clotting time, and the extent of this is a quantitative measure of autoprothrombin C activity.

Determination of Factor XIII Activity and of Factor XIII Inhibitors Using an Ammonium-Sensitive Electrode

1983 ◽  
Vol 50 (02) ◽  
pp. 563-566 ◽  
Author(s):  
P Hellstern ◽  
K Schilz ◽  
G von Blohn ◽  
E Wenzel
Keyword(s):  
Factor Xiii ◽  
Normal Subjects ◽  
The Other ◽  
Activity Measurement ◽  
Factor Xiii Deficiency ◽  
Assay Procedure ◽  
Stabilization Factor ◽  
Release Method ◽  
Sensitive Electrode

SummaryAn assay for rapid factor XIII activity measurement has been developed based on the determination of the ammonium released during fibrin stabilization. Factor XIII was activated by thrombin and calcium. Ammonium was measured by an ammonium-sensitive electrode. It was demonstrated that the assay procedure yields accurate and precise results and that factor XIII-catalyzed fibrin stabilization can be measured kinetically. The amount of ammonium released during the first 90 min of fibrin stabilization was found to be 7.8 ± 0.5 moles per mole fibrinogen, which is in agreement with the findings of other authors. In 15 normal subjects and in 15 patients suffering from diseases with suspected factor XIII deficiency there was a satisfactory correlation between the results obtained by the “ammonium-release-method”, Bohn’s method, and the immunological assay (r1 = 0.65; r2= 0.70; p<0.01). In 3 of 5 patients with paraproteinemias the values of factor XIII activity determined by the ammonium-release method were markedly lower than those estimated by the other methods. It could be shown that inhibitor mechanisms were responsible for these discrepancies.

scholarly journals Thermal Stresses in Chemically Hardening Elastic Media With Application to the Molding Process

1974 ◽  
Vol 41 (3) ◽  
pp. 647-651 ◽  
Author(s):  
Myron Levitsky ◽  
Bernard W. Shaffer
Keyword(s):  
Residual Stress ◽  
Chemical Reaction ◽  
Thermal Stresses ◽  
Stress Component ◽  
Elastic Solid ◽  
Molding Process ◽  
Hardening Process ◽  
Exothermic Chemical Reaction ◽  
Component Parallel

A method has been formulated for the determination of thermal stresses in materials which harden in the presence of an exothermic chemical reaction. Hardening is described by the transformation of the material from an inviscid liquid-like state into an elastic solid, where intermediate states consist of a mixture of the two, in a ratio which is determined by the degree of chemical reaction. The method is illustrated in terms of an infinite slab cast between two rigid mold surfaces. It is found that the stress component normal to the slab surfaces vanishes in the residual state, so that removal of the slab from the mold leaves the remaining residual stress unchanged. On the other hand, the residual stress component parallel to the slab surfaces does not vanish. Its distribution is described as a function of the parameters of the hardening process.

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