Hybrid differential transform and finite difference method to solve the nonlinear heat conduction problem

2008 ◽  
Vol 13 (8) ◽  
pp. 1605-1614 ◽  
Author(s):  
Hsin-Ping Chu ◽  
Chieh-Li Chen
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Heat Conduction Problem ◽  
Nonlinear Heat Conduction ◽  
Differential Transform

Prediction of Temperature Fields in the System “Casting and a Damp Sandy-Argillaceous Mold”

2018 ◽  
Vol 284 ◽  
pp. 640-646
Author(s):  
V.M. Kolokoltsev ◽  
A.S. Savinov ◽  
A.S. Tuboltseva
Keyword(s):  
Heat Capacity ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Moisture Content ◽  
Difference Method ◽  
Silicon Oxide ◽  
Heat Conduction Problem ◽  
Initial Moisture Content ◽  
Temperature Fields

The function of the equivalent heat capacity that takes into account the heat consumption for heating and evaporation of water in the layer of sand with initial moisture content 2 - 10% has been obtained in the work. The function found allows taking into consideration the temperature change of the specific heat capacity of silicon oxide of sandy - argillaceous molds (SAM) and can be applied in the numerical solution of the heat conduction problem by a finite difference method.

scholarly journals Entropy production in a heat conduction problem

2016 ◽  
Vol 38 (4) ◽  
Author(s):  
Enrique N. Miranda
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Entropy Production ◽  
Difference Method ◽  
Heat Conduction Problem ◽  
Equilibrium System ◽  
Transient Behaviour ◽  
Different Temperatures

Heat conduction along an isolated bar placed between two reservoirs at different temperatures is studied. The entropy production is considered in detail with two different approaches. In the first one, the whole system (the bar and the two reservoirs) is analysed in the steady state with the help of standard thermodynamics. In the second one, the bar is divided into n cells and a simple finite difference method is used to evaluate the time evolution of the entropy production. This approach is useful because the transient behaviour can be studied. In this way, it is shown a simple example of a non-equilibrium system where the entropy production (even its transient behaviour) can be evaluated with tools at hand of a motivated undergraduate.

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