{'fraction_non_alphanumeric': 0.026363636363636363, 'fraction_numerical': 0.0018181818181818182, 'mean_word_length': 5.049450549450549, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Thermally Developing Flow in an Annulus with a Boiling Boundary

Heat transfer from a liquid flowing in an annulus to a boiling fluid flowing in a tube was analyzed using four general formulations and several variations of them. The degree of complexity varied significantly among these analysis methods due primarily to the assumption of thermally fully developed flow applied in some methods and not in others. Measurements from a sodium-heated boiling water experiment provided the boundary conditions for the annulus heat-transfer problem. Finite-difference techniques were employed in some of the analyses, and an appropriate inverse heat-transfer technique was included in one of them. Comparisons of heat-transfer parameters calculated from the analysis methods are presented and the accuracies assessed. Three of these methods compared favorably with the most complete and complex of the analyses considered. Nomenclature Cp = specific heat, J/kg K D = diameter, m f(r) = initial sodium temperature distribution at z=0, °C h = heat transfer coefficient, W/m2 K k = thermal conductivity, W/m K