Transient Heat Conduction in a Heat Generating Layer Between Two Semi-Infinite Media

2001 ◽  
Vol 124 (2) ◽  
pp. 299-306 ◽  
Author(s):  
Leendert van der Tempel
Keyword(s):  
Thermal Analysis ◽  
Heat Conduction ◽  
Thermal Model ◽  
Series Solution ◽  
Transient Heat Conduction ◽  
One Dimensional ◽  
Optical Disks ◽  
The One ◽  
Infinite Media ◽  
Lateral Heat

The problem of transient heat conduction in a heat generating layer between two semi-infinite media has been solved. The one-dimensional thermal model is Laplace transformed. Three analytical temperature solutions are derived: two approximation solutions and an exact series solution. They are compared with respect to accuracy, convergence and computational efficiency. The approximations are computationally more efficient, and the series converge to the exact solution. The presented accurate solutions enable quick thermal analysis in terms of just 2 parameter groups, but overestimate the temperature during initialization of rewritable optical disks due to lateral heat conduction.

Simple Explicit Equations for Transient Heat Conduction in Finite Solids

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
A. G. Ostrogorsky
Keyword(s):  
Fourier Series ◽  
Heat Conduction ◽  
Biot Number ◽  
Series Solution ◽  
Transient Heat Conduction ◽  
Simple Equation ◽  
Lower Error ◽  
Transient Conduction ◽  
The One ◽  
Cylinders And Spheres

Abstract Based on the one-term Fourier series solution, a simple equation is derived for low Biot number transient conduction in plates, cylinders, and spheres. In the 0<Bi<0.3 range, the solution gives approximately three times less error than the lumped capacity solution. For asymptotically low values of Bi, it approaches the lumped capacity solution. A set of equations valid for 0<Bi<1 is developed next. These equations are more involved but give approximately ten times lower error than the lumped capacity solution. Finally, a set of broad-range correlations is presented, covering the 0<Bi<∞ range with less than 1% error.

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.

Enhanced Explicit Scheme to Solve Transient Heat Conduction Problem

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Ganesh Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Conduction ◽  
Correction Factor ◽  
Truncation Error ◽  
Transient Heat Conduction ◽  
Explicit Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Time Step ◽  
One Dimensional ◽  
Partial Derivatives

Improvement in accuracy without sacrificing stability and convergence of the solution to unsteady diffusion heat transfer problems by computational method of enhanced explicit scheme (EES), has been achieved and demonstrated, through transient one dimensional and two dimensional heat conduction. The truncation error induced in the explicit scheme using finite difference technique is eliminated by optimization of partial derivatives in the Taylor series expansion, by application of interface theory developed by the authors. This theory, in its simple terms gives the optimum values to the decision vectors in a redundant linear equation. The time derivatives and the spatial partial derivatives in the transient heat conduction, take the values depending on the time step chosen and grid size assumed. The time correction factor and the space correction factor defined by step sizes govern the accuracy, stability and convergence of EES. The comparison of the results of EES with analytical results, show decreased error as compared to the result of explicit scheme. The paper has an objective of reducing error in the explicit scheme by elimination of truncation error introduced by neglecting the higher order terms in the expansion of the governing function. As the pilot examples of the exercise, the implementation is aimed at solving one-dimensional and two-dimensional problems of transient heat conduction and compared with the results cited in the referred literature.

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.

One-Dimensional Transient Heat Conduction in Composite Living Perfuse Tissue

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
S. M. Becker
Keyword(s):  
Heat Conduction ◽  
Initial Conditions ◽  
Separation Of Variables ◽  
Composite Layer ◽  
Circulatory System ◽  
Transient Heat Conduction ◽  
Bioheat Equation ◽  
Perfusion Rate ◽  
One Dimensional ◽  
Perfuse Tissue

Modeling the conduction of heat in living tissue requires the consideration of sudden spatial discontinuities in property values as well as the presence of the body's circulatory system. This paper presents a description of the separation of variables method that results in a remarkably simple solution of transient heat conduction in a perfuse composite slab for which at least one of the layers experiences a zero perfusion rate. The method uses the natural analytic approach and formats the description so that the constants of integration of each composite layer are expressed in terms of those of the previous layer's eigenfunctions. This allows the solution to be “built” in a very systematic and sequential manner. The method is presented in the context of the Pennes bioheat equation for which the solution is developed for a system composed of any number of N layers with arbitrary initial conditions.

scholarly journals Fractional Heat Conduction Models and Thermal Diffusivity Determination

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Monika Žecová ◽  
Ján Terpák
Keyword(s):  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Numerical Methods ◽  
Fractional Order ◽  
Experimental Verification ◽  
Heat Conduction Equation ◽  
Historical Overview ◽  
One Dimensional ◽  
The One ◽  
Fractional Heat Conduction

The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.

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