A theoretical and experimental study of a natural circulation loop is presented. The analysis is based on a one-dimensional model in which the continuity, momentum, and energy equations are given and solved. Expressions for the steady-state and transient flow rates and temperature distributions are derived. The apparatus consisted of an electricallyheated section and two parallel loops with heat exchangers. Steady-state and transient experiments were conducted to study the effects of core flow resistance, power distribution and upper plenum design. Flow oscillations were observed under certain conditions, which were accompanied by instabilities and flow reversals. Reasonable agreement (±30 percent) is obtained between the analytical and experimental results.

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Finite difference numerical models based on bioheat transfer [H. H. Pennes, J. Appl. Physiol. 1, 93–122 (1948)] and incomplete countercurrent heat exchange [S. Weinbaum and L. M. Jiji, J. Biomech. Eng. 107, 121–139 (1985)] have been developed and tested. Predicted performance of hyperthermia phantoms heated by ultrasound applicators will be compared with actual performance to validate the models. The models will then be used as aids in designing ultrasound applicators to produce heat deposition patterns believed advantageous for hyperthermia treatment of experimental animals and patients. The 3D models admit adiabatic or isothermal boundaries and arrays of paired, straight tubules for counter current heat exchange. Results of parametric variations will be shown. Preliminary results obtained by using as inputs the design parameters for a proposed kidney phantom perfused at 110 ml/100 g (of tissue-equivalent gel) per minute have yielded satisfactory time constants on the order of 150 s. When the simulated ultrasound applicator emitted 56 acoustic watts at 1 MHz, applied as an 8-cm-diam, unfocused Gaussian beam, the predicted steady-state, spatial maximum temperature rise was 6 °C. [Work supported by PHS Grant No. R01 CA33749 awarded by the National Cancer Institute, DHHS.]