An analytical superposition approach to wall heat conduction under arbitrary temperature perturbations for air-conditioning applications |
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| Institution: | 1. School of Engineering, Mechanical Engineering Department, Iran University of Science and Technology, Narmak, Tehran, Iran;2. Universidad Católica Los Ángeles de Chimbote, Instituto de Investigación, Chimbote, Peru;3. Electronics Business Unit, Ansys, Inc, Austin, TX, 78746, USA;1. Department of Building Science, School of Architecture, Tsinghua University, Beijing, 100084, China;2. Beijing Key Laboratory of Indoor Air Quality Evaluation and Control, Tsinghua University, Beijing, 100084, China;1. School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China;2. Advanced Research Institute for Multidisciplinary Science (ARIMS), Beijing Institute of Technology, Beijing 100081, China;3. Beijing Key Laboratory of Energy Saving and Emission Reduction of Metallurgical Industry, University of Science and Technology Beijing, Beijing 100083, China;1. Center of Excellence in Design and Optimization of Energy Systems, School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran;2. Fuel Cell Research Lab (FCReL), Mechatronic System Engineering, Simon Fraser University (SFU), Vancouver, Canada |
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| Abstract: | An analytical solution is derived for the transient wall heat conduction problem under arbitrary outdoor air temperature perturbations. This is obtained by expanding the arbitrary perturbation in a Fourier series, consisting of a step function and an infinite sum of cosine and sine functions. The analytical solutions in the cases of step, cosine and sine temperature perturbations are derived separately from each other and are then superimposed to produce the resultant solution. Simple linear expressions are derived, which express the maximum indoor heat flow provoked by the arbitrary temperature perturbation in terms of parameters characterizing the perturbation. Such simple expressions are very useful in air-conditioning calculations for predicting peak loads and sizing heating or cooling equipment. |
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