scholarly journals A Modified Method to Solve the One-Dimensional Heat Conduction Problem

2018 ◽  
Vol 6 (2) ◽  
Author(s):  
Ilmars Kangro
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
One Dimensional ◽  
Modified Method ◽  
The One

Investigation of the one-dimensional transient heat conduction problem of a coated high strength steel plate

2019 ◽  
Vol 24 (11) ◽  
pp. 3472-3484 ◽  
Author(s):  
Yang Yang ◽  
Hong-Liang Dai ◽  
Chao Ye ◽  
Wei-Li Xu ◽  
Ai-Hui Luo
Keyword(s):  
Heat Conduction ◽  
High Strength Steel ◽  
Heat Conduction Problem ◽  
Thermal Relaxation ◽  
High Strength ◽  
Transient Heat Conduction ◽  
One Dimensional ◽  
Temperature Increment ◽  
Transient Heat Conduction Problem ◽  
The One

In this paper, the one-dimensional transient heat conduction problem is investigated of a coated high strength steel (HSS) plate which is composed of two coating layers and a HSS layer. As the coating is extremely thin, non-Fourier heat conduction is applied to this part, while the steel part is analyzed by Fourier conduction. Then the temperature increment equations are obtained, which can be calculated by the Newmark method. The effects of thermal relaxation time, temperature boundary conditions, and coating parameters on temperature increment distribution of the coated HSS plate are also presented. Thus, the one-dimensional transient heat conduction problem of a coated HSS plate can be solved, which contributes to practical application and engineering design.

An Initial Value Approach to the Inverse Heat Conduction Problem

1986 ◽  
Vol 108 (2) ◽  
pp. 248-256 ◽  
Author(s):  
E. Hensel ◽  
R. G. Hills
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Noisy Data ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Initial Value ◽  
Surface Conditions ◽  
One Dimensional ◽  
The One

The one-dimensional linear inverse problem of heat conduction is considered. An initial value technique is developed which solves the inverse problem without need for iteration. Simultaneous estimates of the surface temperature and heat flux histories are obtained from measurements taken at a subsurface location. Past and future measurement times are inherently used in the analysis. The tradeoff that exists between resolution and variance of the estimates of the surface conditions is discussed quantitatively. A stabilizing matrix is introduced to the analysis, and its effect on the resolution and variance of the estimates is quantified. The technique is applied to “exact” and “noisy” numerically simulated experimental data. Results are presented which indicate the technique is capable of handling both exact and noisy data.

scholarly journals Simplified Grinding Temperature Model Study

2019 ◽  
Vol 6 (2) ◽  
pp. a1-a7
Author(s):  
N. V. Lishchenko ◽  
V. P. Larshin ◽  
H. Krachunov
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Heat Source ◽  
Boundary Conditions ◽  
Grinding Temperature ◽  
Temperature Model ◽  
One Dimensional ◽  
Heating And Cooling ◽  
Equation Of Heat Conduction ◽  
The One

A study of a simplified mathematical model for determining the grinding temperature is performed. According to the obtained results, the equations of this model differ slightly from the corresponding more exact solution of the one-dimensional differential equation of heat conduction under the boundary conditions of the second kind. The model under study is represented by a system of two equations that describe the grinding temperature at the heating and cooling stages without the use of forced cooling. The scope of the studied model corresponds to the modern technological operations of grinding on CNC machines for conditions where the numerical value of the Peclet number is more than 4. This, in turn, corresponds to the Jaeger criterion for the so-called fast-moving heat source, for which the operation parameter of the workpiece velocity may be equivalently (in temperature) replaced by the action time of the heat source. This makes it possible to use a simpler solution of the one-dimensional differential equation of heat conduction at the boundary conditions of the second kind (one-dimensional analytical model) instead of a similar solution of the two-dimensional one with a slight deviation of the grinding temperature calculation result. It is established that the proposed simplified mathematical expression for determining the grinding temperature differs from the more accurate one-dimensional analytical solution by no more than 11 % and 15 % at the stages of heating and cooling, respectively. Comparison of the data on the grinding temperature change according to the conventional and developed equations has shown that these equations are close and have two points of coincidence: on the surface and at the depth of approximately threefold decrease in temperature. It is also established that the nature of the ratio between the scales of change of the Peclet number 0.09 and 9 and the grinding temperature depth 1 and 10 is of 100 to 10. Additionally, another unusual mechanism is revealed for both compared equations: a higher temperature at the surface is accompanied by a lower temperature at the depth. Keywords: grinding temperature, heating stage, cooling stage, dimensionless temperature, temperature model.

METHOD OF FUNDAMENTAL SOLUTION FOR AN INVERSE HEAT CONDUCTION PROBLEM WITH VARIABLE COEFFICIENTS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341009 ◽  
Author(s):  
MING LI ◽  
XIANG-TUAN XIONG ◽  
YAN LI
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Fundamental Solutions ◽  
Variable Coefficients ◽  
Inverse Heat Conduction Problem ◽  
Method Of Fundamental Solutions ◽  
Inverse Heat Conduction ◽  
Modified Method ◽  
On Line ◽  
Ill Posed

In this paper, we consider an inverse heat conduction problem with variable coefficient a(t). In many practical situations such as an on-line testing, we cannot know the initial condition for example because we have to estimate the problem for the heat process which was already started. Based on the method of fundamental solutions, we give a numerical scheme for solving the reconstruction problem. Since the governing equation contains variable coefficients, modified method of fundamental solutions was used to solve this kind of ill-posed problems. Some numerical examples are given for verifying the efficiency and accuracy of the presented method.

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