Heat 1D

Suppose we want to simulate the heating of a bar. The equation governing this phenomenon is the transient heat equation (Reddy 1993), which is :

Heat equation

Where r is the density, c is the specific heat of the material, A is the cross-sectional area of the material, T is the temperature, k is the thermal conductivity of the material, t is time, and q is the heat energy generated per unit of volume.

We could use a plot for vectors to view the temperature at every time interval. The vector will be plotted at time intervals of PLdelta.

It is possible to show a three dimensional plot, with the following axes: the dimension of the bar (X axis), the time (Y axis), and the temperature (Z axis).

Let q be a function of time. We could visualize this function in a two dimensional plot, and also obtain other information, for example, the total heat in the bar. We are going to put this last plot in a different form, because the scales of q(t) and the total heat could be quite different.

Finally, we want to put a listing of the total heat along time in a sepparate window. This can be done by means of the PRINT command.

Theory pages:
Main page
FEM (i)
FEM (ii)
FDM (i)
Example pages:
1-d Heat Equation
2-d steady state Heat Equation
2-d Heat Equation
1-d non diffusive transport equation
1-d diffusive transport equation
2-d Non diffusive transport equation
Mesh generation with OOCSMP
Moving grids
Application pages:
Heating of two beams
Heating of two moving beams
Solving the equation Ut+Uxx+Uxy+Uyx=0
Solving the equation Ut+Uxx+Uxy+Uyx=0 using MGEN
Heat 1d using several outputs
Solving the Heat equation with a CA
Comparing a CA with the FEM
Gordon's sine equation

Other courses
Other pages

Last modified 22/12/99 by Juan de Lara ( Juan.Lara@ii.uam.es, http://www.ii.uam.es/~jlara) need help for using this courses?.

The OOCSMP code - The SODA code