The heat resistance theory of heat sink

As shown figure 1, the heat flow ∅_0 goes through the bottom of heat sink and then goes into its root. In the root, the heat flow will be divided into two shares ∅_1and∅_2, and then through the root and environment air, start convection and heat exchange. Finally, the heat flow goes into the environment by heat exchange with fins. The heat resistance network model is shown in figure 1.

Fig 1. The heat flow schematic diagram of heat sink dissipation

Fig 2. The heat resistance network model of fins

As the lateral area of heat sink base is much smaller than the root cross-sectional area, the heat dissipated from side can be omitted. The whole heat flow enters the bottom and side of heat sink by heat conduction. The heat transfer thermal resistance  on the surface of fins is much larger than the heat conduction thermal resistance  in the fins. So on the cross section at the constant height, the fin temperature can be considered uniform. The top of the fins can be regarded as insulation. The heat conduction coefficient , the surface heat transfer coefficient h and the cross section area Ac along the fin height are all constant.

According to the above simplification, the model established is a one-dimensional steady state heat conduction model and the equivalent thermal resistance of the rib fin is

Where, Rr— heat resistance of the heat dissipation part at the root, K / W;
Rf—heat resistance of the heat dissipation part in the side, K / W.

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