Dynamic thermal networks: a methodology to account for time-dependent heat conduction

2020 ◽  
pp. 407-415
Author(s):  
J. Claesson
Keyword(s):  
Heat Conduction ◽  
Time Dependent

scholarly journals The role of heat conduction to the formation of [WC]-type planetary nebulae

2011 ◽  
Vol 7 (S283) ◽  
pp. 494-495
Author(s):  
Christer Sandin ◽  
Matthias Steffen ◽  
Ralf Jacob ◽  
Detlef Schönberner ◽  
Ute Rühling ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Chemical Composition ◽  
Physical Properties ◽  
Planetary Nebulae ◽  
Time Dependent ◽  
Diffuse Emission ◽  
Hydrodynamic Models ◽  
X Ray ◽  
Central Stars

AbstractX-ray observations of young Planetary Nebulæ (PNe) have revealed diffuse emission in extended regions around both H-rich and H-deficient central stars. In order to also reproduce physical properties of H-deficient objects, we have, at first, extended our time-dependent radiation-hydrodynamic models with heat conduction for such conditions. Here we present some of the important physical concepts, which determine how and when a hot wind-blown bubble forms. In this study we have had to consider the, largely unknown, evolution of the CSPN, the slow (AGB) wind, the fast hot-CSPN wind, and the chemical composition. The main conclusion of our work is that heat conduction is needed to explain X-ray properties of wind-blown bubbles also in H-deficient objects.

scholarly journals Analytical Solution of the Hyperbolic Heat Conduction Equation for Moving Semi-Infinite Medium under the Effect of Time-Dependent Laser Heat Source

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
R. T. Al-Khairy ◽  
Z. M. AL-Ofey
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Closed Form Solution ◽  
Infinite Medium ◽  
Form Solution ◽  
Time Dependent ◽  
Hyperbolic Heat Conduction ◽  
Laser Heat Source

This paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential) is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.

Multiquadric Collocation Method for Time-Dependent Heat Conduction Problems With Temperature-Dependent Thermal Properties

2006 ◽  
Vol 129 (2) ◽  
pp. 109-113 ◽  
Author(s):  
Somchart Chantasiriwan
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Collocation Method ◽  
Heat Conduction Problem ◽  
Piecewise Linear ◽  
Linear Functions ◽  
Time Dependent ◽  
Piecewise Linear Functions ◽  
Temperature Dependent ◽  
Kirchhoff Transformation

Abstract The multiquadric collocation method is a meshless method that uses multiquadrics as its basis function. Problems of nonlinear time-dependent heat conduction in materials having temperature-dependent thermal properties are solved by using this method and the Kirchhoff transformation. Variable transformation is simplified by assuming that thermal properties are piecewise linear functions of temperature. The resulting nonlinear equation is solved by an iterative scheme. The multiquadric collocation method is tested by a heat conduction problem for which the exact solution is known. Results indicate satisfactory performance of the method.

Long-Time Solutions to Heat-Conduction Transients with Time-Dependent Inputs

1980 ◽  
Vol 102 (1) ◽  
pp. 115-120 ◽  
Author(s):  
H. T. Ceylan ◽  
G. E. Myers
Keyword(s):  
Heat Conduction ◽  
Lower Cost ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Linear Functions ◽  
Time Dependent ◽  
Time Interval ◽  
Piecewise Linear Functions ◽  
One Dimensional ◽  
Long Time

An economical method for obtaining long-time solutions to one, two, or three-dimensional heat-conduction transients with time-dependent forcing functions is presented. The conduction problem is spatially discretized by finite differences or by finite elements to obtain a system of first-order ordinary differential equations. The time-dependent input functions are each approximated by continuous, piecewise-linear functions each having the same uniform time interval. A set of response coefficients is generated by which a long-time solution can be carried out with a considerably lower cost than for conventional methods. A one-dimensional illustrative example is included.

scholarly journals Exact Analytical Solution for 3D Time-Dependent Heat Conduction in a Multilayer Sphere with Heat Sources Using Eigenfunction Expansion Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Nemat Dalir
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Eigenfunction Expansion ◽  
Radial Direction ◽  
Exact Analytical Solution ◽  
Internal Heat ◽  
Expansion Method ◽  
Time Dependent ◽  
Heat Sources ◽  
Eigenfunction Expansion Method

An exact analytical solution is obtained for the problem of three-dimensional transient heat conduction in the multilayered sphere. The sphere has multiple layers in the radial direction and, in each layer, time-dependent and spatially nonuniform volumetric internal heat sources are considered. To obtain the temperature distribution, the eigenfunction expansion method is used. An arbitrary combination of homogenous boundary condition of the first or second kind can be applied in the angular and azimuthal directions. Nevertheless, solution is valid for nonhomogeneous boundary conditions of the third kind (convection) in the radial direction. A case study problem for the three-layer quarter-spherical region is solved and the results are discussed.

Sign in / Sign up

Export Citation Format

Share Document