Finite differencing TAK 2000 is a finite differencing analyzer. The user defines a thermal network in a manner analogous to an electrical system composed of resistors, voltages, capacitances, and currents. A thermal system is divided into nodes and connected by conductors. These conductors can represent conduction, convection, radiation, or mass flow. Constant and time/temperaturevarying heat sources can be applied to the nodes. Examples of heat sources are: heaters, electrical dissipation, solar radiation, albedo, or earth IR. The network can be analyzed with a steady state and/or transient solution technique. When running a steady state analysis, TAK 2000 computes the temperatures for all the nodes, the heat flows through all the conductors, and reports on any heaters and flow conductors that were modeled. When running a transient analysis, TAK 2000 computes the temperatures of each node as a function of time. The output can include temperature, incident heating, and values of time or temperature varying quantities.
The temperature, T, assigned to a node represents the average mass temperature of the subvolume. The capacitance, C, assigned to a node is computed from the thermophysical properties of the subvolume material evaluated at the temperature of the node. Capacitance is assumed to be concentrated at the nodal center of the subvolume. Because a node represents a lumping of parameters to a single point in space, the subvolume implied by the nodal temperature is linear as shown in Figure C and not a step function as illustrated in Figure B.
The error introduced by dividing a system into finite size nodes rather than volumes dx3 where dx approaches zero is dependent on numerous considerations: material thermal properties, boundary conditions, node size, node center placement, and time increment of transient calculations.
