.ScalableTestSuite.Thermal.HeatConduction.Verification.OneDHeatTransferTT_Check

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:

In HeatConductionTT, the ends are maintained at fixed temperatures. Therefore, the following conditions are prescribed:

Solution:

where where Rn(t) can be written according to our boundary conditions:

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

Contents

NameDescription
 f
Generated at 2024-11-21T19:25:40Z by OpenModelicaOpenModelica 1.24.2 using GenerateDoc.mos