modelOneDHeatTransferTT_FD

Both ends are exposed to a fixed temperature, implemented by FD method

Information

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 HeatConductionTT, both ends are exposed to a fixed temperature. 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 HeatConductionTT, T1 and TN have constant temperature values.

The parameters for HeatConductionTT_FD are:

Parameters Comment
L Length of the rod
N number of nodes
T0 Initial temperature
T1 temperature at the first node
TN temperature at the last node
cp material specific heat capacity
lambda material thermal conductivity
rho material density
dx element length

Parameters

TypeNameDefaultDescription
SIunits.LengthLlength
IntegerN2number of nodes
SIunits.TemperatureT0Initial temperature
SIunits.TemperatureT1Initial temperature at first node
SIunits.TemperatureTNInitial temperature at the last node
SIunits.SpecificHeatCapacitycpMaterial Heat Capacity
SIunits.ThermalConductivitylambdaMaterial thermal conductivity
SIunits.DensityrhoMaterial Density
Modelica.Units.SI.LengthdxL/(N - 1)Element length

Components

TypeNameDefaultDescription
SIunits.Temperature[N]Ttemperature of the nodes
SIunits.Temperature[N - 2]Ttildestate variables