A uniform rod has the length L, density ρ, specific heat capacity cp and thermal conductivity λ which are all assumed to be constant. Moreover, the sides of the rod are assumed to be insulated. In HeatConductionTI, one end is exposed to a fixed temperature while the other end is insulated. We considered a small portion of the rod which has a width of dx from a distance x, and by considering the conservation of energy the equations are defined. According to the conservation of energy, difference between the heat in from left boundary and heat out from the right boundary has to be equal to the heat change at the portion at Δx in time Δt.The discretized equations are described in the following form:
where i = 2,..,N−1 and they correspond to the temperature nodes along the rod excluding the temperature variables at the ends. In HeatConductionTI, TN has a constant temperature value and T1 is insulated. T1 has a boundary condition defined as:
The parameters for HeatConductionTI_FD are:
| Parameters |
Comment |
| L |
Length of the rod |
| N |
number of nodes |
| T0 |
Initial temperature |
| TN |
temperature at the last node |
| cp |
material specific heat capacity |
| lambda |
material thermal conductivity |
| rho |
material density |
| dx |
element length |
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