A Rigorous Series Solution for Diamond Heat Spreaders with Temperature-Dependent Thermal Conductivity Used in Microwave Power Devices

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In this paper we derive a rigorous series solution of the nonlinear heat transfer equation using the modified Kirchhoff transformation for a cylindrical diamond heat spreader with temperature-dependent thermal conductivity, situated on the top of a copper heat sink. We point out what we believe to be errors in two analytical approaches applied to the same problem which were published recently [Proc. R. Soc. Lond. A 441 (1993) 181; Proc. R. Soc. Lond. A 445 (1995) 375; and IEEE Trans. Microwave Theor. & Technol. 42 (1994) 573]. The basic difference between our work and these previous studies lies in the boundary condition (b.c.) of the transformed heat potential over the spreader-sink interface-we use nonlinear b.c. whereas the boundary conditions in the previous studies have been assumed to be linear. Calculations of change in the thermal resistance with the geometrical dimensions of the spreader, the input power, and the ambient temperature show up the profound influence which the assumed b.c. have on the problem. Our study has also revealed errors in numerical results presented in another paper [IEEE Semi-Therm Proc. (4th Annu. Semiconductor Thermal and Temperature Measurement Symp.), p. 113].
社団法人応用物理学会の論文
1996-11-15