Abstract
An analytical expression is developed for transient thermal spreading resistance from an isothermal circular source in a cylindrical flux tube as a function of constriction ratio and time. The flux tube is semi-infinite. The spreading resistance expression is obtained from the temperature expression by solving the heat equation. For short times, the dimensionless transient spreading resistance is proportional to dimensionless time based on the square root of the source area. For long times, the dimensionless spreading resistance approaches the values of the corresponding steady-state expression in the literature. For small constriction ratios, dimensionless spreading resistance approaches the classic isothermal half-space limit. A numerical analysis is presented which shows excellent agreement with the analytical solution. Approximate correlations for dimensionless resistance are also presented for both the isothermal and the isoflux cases.
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