{'fraction_non_alphanumeric': 0.008, 'fraction_numerical': 0.0, 'mean_word_length': 5.310924369747899, '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}}
Explicit Matrix Solution of the Discretized Thermal Regenerator Model

A matrix approach to the discretized model of the thermal regenerator is used to develop an explicit analytical expression, which calculates both the transients and the periodic steady state temperatures. The cyclic steady state solution is reduced to a system of linear equations for the initial temperatures in each of the compartments. This methodology can be applied to the cases of cocurrent or countercurrent flow directions as well as symmetric or asymmetric lengths and switching times. An eigenvalue analysis using this model shows the approach of the thermal regenerator toward the cyclic steady state. Results are also compared to previous data of other investigators.