| Summary: | 碩士 === 大同大學 === 化學工程學系(所) === 99 === Two-dimensional (2D) unsteady-state temperature profiles around a cylindrical heat source in an in vitro tissue have been studied. Comparison of the temperature profiles between the results of this study and that of previous one-dimensional (1D) unsteady-state model has also been investigated. Three heat transfer cases have been studied, including (1) heat transfer around a single cylindrical heat source, (2) heat transfer between two cylindrical heat sources, and heat transfer between a single cylindrical heat source and a parallel blood vessel.
A two-dimensional unsteady-state mathematical model has been developed for each of the above-mentioned case. Fourth-order finite difference was used to transfer the governing partial differential equation to simultaneous ordinary differential equations. Fourth-order Predictor- Corrector Method and Fortran program developed in this laboratory were then used to solve the 2D temperature profiles as function of time.
It has been found from the simulation results that the temperature decreases rapidly along the radial direction, due that the temperature increase in the tissue is resulted from heat conduction and the heat conductivity of the tissue is small. Temperature profiles of 2D model are similar to that of 1D model in radial direction. However, significant difference in axial temperature profiles is found between 1D and 2D models. When heat flux of the heat source is flat in axial direction, 2D simulation results show that temperature profiles are convex in axial direction, due to heat loss at the boundary. When heat flux is convex in axial direction, the temperature at the center point of heat source is even higher. However, when heat flux is concave in axial direction, the temperature profile becomes uniform. In addition, non-uniformity of temperature profile along axial coordinate increases with increasing temperature, indicating 1D model, which assumes uniform temperature in axial direction, might have significant error at high temperature.
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