Recently the computational speed and the functions of the numerical methods are advancing rapidly. It is the future trend that using the computational fluid dynamics (CFD) to perform simulation for making up the experimental deficiency, reducing the risk, improving the quality of the product, and saving the cost of research and development. A two-dimensional simulation was employed to study the melt/air and melt/solid interface shapes of the miniature molten zone formed in the laser-heated pedestal growth (LHPG) system. Using non-orthogonal body-fitting grid system with control-volume finite difference method, the interface shape can be determined both efficiently and accurately. During stable growth, the dependence of the molten-zone length and shape on the heating CO2 laser is examined in detail under both the maximum and the minimum allowed powers with various growth speeds. The effect of gravity for the miniature molten zone is also simulated, which reveals the possibility for a horizontally oriented LHPG system. Such a horizontal system is good for the growth of long crystal fibers. After comparing with the shape of the molten zone in terms of the experiment and the analysis of the simulation shown as above. Heat transfer and fluid flow in the LHPG system are analyzed near the deformed interfaces. The global thermal distributions of the crystal fiber, the melt, and the source rod are described by temperature and its axial gradient within length of ~10 mm. As compared with the growth of bulk crystal of several centimeters in dimension, natural convection drops six orders in magnitude due to smaller melt volume; therefore, conduction rather than convection determines the temperature distribution in the molten zone. Moreover, thermocapillary convection rather than mass-transfer convection becomes dominant. The symmetry and mass flow rate of double eddy pattern are significantly influenced by the molten-zone shape due to the diameter reduction and the large surface-tension-temperature coefficient in the order of 10-4~10-3. According to the analysis shown as above, the results could be further extended for the analysis of the concentration profile and study of horizontal growth.