modelOneDHeatTransferTT_Check
analytical solution for TT models
Information
In the verification of OneDHeatTransferTT_FD and OneDHeatTransferTT_Modelica, mid-nodes of the models are selected, and verified by the analytical solution. The temperature at the middle of the model implemented by analytical solution, the temperature at the mid-node of the model implemented by equations and the temperature of the heat capacitor at the middle of the model implemented by Modelica.Thermal library, are compared.Analytical solutions are based on the solutions in “Handbook of Linear Partial Differential Equations for Engineers and Scientists” by Andrei D. Polyanin. If we consider one dimensional partial differential heat equation in the form:
| Parameters | Comment |
|---|---|
| L | length of the rod |
| N | number of nodes |
| T0 | Initial temperature of the heat capacitors |
| T1 | fixed temperature at the first node |
| TN | fixed temperature at the last node |
| cp | material specific heat capacity |
| lambda | material thermal conductivity |
| rho | material density |
| A | cross section area of the rod |
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| SIunits.Length | L | 0.2 | Length of the rod |
| Integer | N | 30 | Number of nodes |
| SIunits.Temperature | T0 | 273.15 | Initial temperature |
| SIunits.Temperature | T1 | 330 | Fixed temperature at first node |
| SIunits.Temperature | TN | 300 | Fixed temperature at the last node |
| SIunits.SpecificHeatCapacity | cp | 910 | Material Heat Capacity |
| SIunits.ThermalConductivity | lambda | 237 | Material thermal conductivity |
| SIunits.Area | A | 0.05 | Area |
| Modelica.Units.SI.Density | rho | 2712 | Material Density |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Units.SI.Temperature | T_mid_exact | Temperature value that function returns | |
| Modelica.Units.SI.Temperature | T_mid_numerical | Temperature value that discretized equation returns | |
| Modelica.Units.SI.Temperature | T_mid_modelica | Temperature value that heat capacitor returns | |
| Models.OneDHeatTransferTT_FD | example | ||
| Models.OneDHeatTransferTT_Modelica | example2 |
Contents
| Name | Description |
|---|---|
| f |