modelOneDHeatTransferTI_FD

One end at a fixed temperature, one end is insulated; 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 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

Parameters

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

Components

TypeNameDefaultDescription
SIunits.Temperature[N]Ttemperature of the nodes
SIunits.Temperature[N - 1]Ttildestate variables