Thermal convection scaling analysis

The thermal convection scaling analysis for this system is based on the thermal Grashof number (6), shown in Equation 1,... 

Heat-Transfer Analysis Thermal-Capillary Models. Numerous analyses of various aspects of heat transfer in the CZ system have been reported many of these are cited by either Kobayashi (143) or Derby and Brown (144). The analyses vary in complexity and purpose, from the simple one-dimensional or fin approximations designed to give order-of-magni-tude estimates for the axial temperature gradient in the crystal (98) to complex system-oriented calculations designed to optimize heater design and power requirements (145,146). The system-oriented, large-scale calculations include radiation between components of the heater and the crucible assemblies, as well as conduction and convection. 

On the other hand, the heat fransfer literatiue of the last decade has demonstrated a vivid and growing interest in thermal analysis of flows in micro-channels, botii tiirough experimental and analytical approaches, in connection with cooling techniques of micro-electronics and witii tiie development of micro-electromechanical sensors and actuators (MEMS), as also pointed out in recent reviews [12-16]. Since tiie available analytical information on heat fransfer in ducts could not be directly extended to flows witiiin microch mels with wall slip, a number of contributions have been recentiy directed towards the analysis of internal forced convection in the micro-scale. In the paper by Barron et al. 

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