{'fraction_non_alphanumeric': 0.01713859910581222, 'fraction_numerical': 0.0, 'mean_word_length': 5.395238095238096, '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': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A Multi-Parametric Mathematical Approach on the Selection of Optimum Insulation Thicknesses in Buildings

Detailed simulations have indicated optimum insulation thicknesses of walls’ insulation for a variety of cases. Simplified analytical relations have also been proposed to the same aim, allowing the extraction of more general results, with limited accuracy however, as imposed by mathematical simplicity requirements. In this sense, a variety of important parameters are ignored, such as: the existence of any glazing at the wall, the absorptance of the wall, the base temperature of the heated space which the referred to wall belongs to and its variation with insulation, the thermal characteristics (thermal capacitance, total heat losses coefficient) and the heat and solar gains of the heated space. An alternative analytical approach is consequently developed here, incorporating all above parameters and in this context accessing the wall as part of the whole heated space, instead of considering it solely as an isolated fabric element. The approach consists of a set of two implicit equations which are easily solved, and enables the investigation of the effects of all principal and secondary parameters on the optimum thickness. The ignorance even of the secondary of these parameters has proved to lead to significant errors.