TAK 2000 Nodes - General

In order to develop a thermal network and solve it using numerical techniques, it is necessary to subdivide the thermal system into a number of finite subvolumes called nodes. The thermal properties of each node are concentrated at the central nodal point of each subvolume. Each node represents a capacitance and has a temperature.

The temperature assigned to a node represents the average mass temperature of the subvolume. The thermal capacitance assigned to a node is computed from the specific heat of the material evaluated at the temperature of the node. Because a node represents a lumping of parameters to a single point in space, the temperature distribution through the subvolume is linear. In a homogeneous material, the temperature at a point other than the nodal point may be approximated by interpolation between adjacent nodal points where the temperatures are known.

Types of Nodes

To this point, only nodes with finite thermal mass (capacitance) have been discussed. In many instances, two other types of nodes are required to define a thermal system. They are: (1) nodes having zero capacitance or, (2) nodes having an infinite capacitance. Thermal analyzers usually give these three nodes names as follows;

Finite Capacitance -> Diffusion
Zero Capacitance -> Arithmetic
Infinite Capacitance -> Boundary

Diffusion

A diffusion node is used to represent normal materials. Diffusion nodes have thermal mass (capacitance) and store and release energy with time. This process is characterized by a gain or loss of potential energy which depends on the capacitance value, the net heat flow, and the time over which the heat is flowing. In the transient solution routine, diffusion node temperatures are calculated by a finite difference representation of the partial differential heat transfer equation. Three items are stored for each diffusion node: temperature, thermal capacitance, and nodal heating (if any).

Thermal capacitance is the product of the mass of the node and the specific heat of the material that comprises the node.

Arithmetic

An arithmetic node can be used to represent the surface of a material. It could also represent the interface between two dissimilar materials, (for example a bondline). Arithmetic nodes have no thermal capacitance. They are sometimes called steady state nodes. Their temperatures are calculated by being brought into a steady state heat balance with the neighboring nodes. It can be used to represent nodes with very small capacitance relative to the rest of the model. In a transient analysis, this could result in a significant reduction in computer run time with only minor changes in overall accuracy.

Boundary

Boundary nodes are used to represent constant temperature sources or sinks. They have infinite thermal capacitance. Boundary conditions such as ambient air, electronic baseplates, or deep space can be simulated by using boundary nodes.

Boundary node temperatures are not altered by the solution routines. However, time varying boundary conditions can be modeled by using the TVS or PER node options.

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