Arithmetic Nodes

Arithmetic nodes have a number of uses which are consequences of the fact that such nodes serve as an engineering model of the proverbial "wafer of thickness dx, where dx approaches zero". A typical application lies in the modeling of exterior surfaces of reentry vehicles which are often subjected to severe, rapidly changing, boundary conditions. In the physical system, the surface temperature remains very close to radiation equilibrium with the surface heating rate ,indicating that this system can be accurately simulated by the use of a surface arithmetic node. This application is illustrated in the figure.

Use of Arithmetic Nodes to Model Surfaces

The case where heat flows from a surface by conduction is usually one in which two structures are bonded together and a bondline temperature is sought. When the structures are homogeneous, a bondline temperature may be established by simple linear interpolation between the nearest node centers. When the materials are dissimilar, it is more appropriate to use an arithmetic node at the bondline, leaving to the computer the process of performing a conductance weighted average of the adjoining diffusion node temperature which, in essence, is the result of finding the steady state (heat in = heat out) temperature for an arithmetic node.

Arithmetic nodes may also be used advantageously in place of diffusion nodes which have a capacitance that is small when compared to the great majority of nodes in the system. This often occurs when modeling a small quantity of gas in a tube or other enclosure, or when modeling small structural parts, such as wires, bolts, fillets, films, and sheets, where detailed temperatures are desired (which precludes lumping such items along with larger nearby nodes). The correct use of arithmetic nodes in these cases generally results in a considerable saving of computer time when the model is processed.

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