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I am interested in learning how to calculate the equivalent resistance between two points in a wye circuit for application to thermal networks (i.e. I'd like to calculate the equivalent thermal resistance between nodes with two conductive paths). enter image description here

Say I am interested in calculating the equivalent resistance between the following nodes: (1) Node 1 and Node 4; (2) Node 1 and Node 3; (3) Node 3 and Node 4 for arbitrary values of R1, R2, and R3. Is there an analytical expression for such a calculation, or a way to determine the equivalent resistances? If you could also provide a link to some reference for my review, that would also be appreciated. Thanks!

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Ohm's thermal law used by electronics engineers for the sizing of radiators is a law formulated by "analogy" of electrical and thermal equations.

As soon as the correspondence is established between analogous quantities, it is therefore possible to use electronic tools to solve thermal problems.

In this case, the heat sources (temperature °K) are analogous to the voltage sources, the current corresponds to the heat flow (amount of heat calculated on the basis of the electrical power W to be removed) ... and the resistance is the quotient of the two (analogy between thermal Fourier law and electrical Ohm's law)

Pouillet's law has an equivalent in thermal.

Rt = L / k / A ... where Rt is the thermal resistance (unit °K/W), L (m) is the thickness of the heat conducting layer, k (unit W/m/°K) is the conductivity of the material, A (m^2) is the area of the zone.

In your case (if there is "no thermal coupling" between the equal "resistances", temperature of node2 is the mean of the temperature of node1, node3 and node4. At node2, sum of the tree "currents" (heat transfer) equal zero.

Note that there is a resistance from a point (anywhere) at Tx ... to "free air" ! So if "convection" or "radiation" of heat occurs, it must be taken also in account. A "thermal" program may be helpfull.

Some electronic card production software allows this thermal simulation to be carried out at the same time as the electrical simulation ...

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