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Cooling and Warming Laws: An Exact Analytical Solution

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Title: Cooling and Warming Laws: An Exact Analytical Solution
Language: English
Authors: Besson, Ugo
Source: European Journal of Physics. Sep 2010 31(5):1107-1121.
Availability: Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP
Peer Reviewed: Y
Physical Description: PDF
Page Count: 15
Publication Date: 2010
Document Type: Journal Articles
Reports - Descriptive
Education Level: Higher Education
Descriptors: Radiation, Heat, Climate, Physics, Science Instruction, College Science, Science Experiments, Scientific Principles, Energy, Scientific Concepts
DOI: 10.1088/0143-0807/31/5/013
ISSN: 0143-0807
Abstract: This paper deals with temperature variations over time of objects placed in a constant-temperature environment in the presence of thermal radiation. After a historical introduction, the paper discusses cooling and warming laws, by taking into account first solely object-environment energy exchange by thermal radiation, and then adding object-environment heat exchange by convection. These processes are usually evaluated by approximating the law of exchange of thermal radiation by a linear relationship between power exchange and temperature difference. In contrast, in this paper an exact analytical solution considering Stefan's fourth power law is provided, under some general hypotheses, for both cases. A comparison with exponential approximations and with a historical law proposed by Dulong and Petit in 1817 is presented. Data of an experiment are used to test the analytical solution: the test has allowed evaluating the heat transfer coefficient h of the experiment and has shown that our solution provides a better fit with the measured values than any exponential function. The topic is developed in a way which can be suitable both for undergraduate students and for general physicists. (Contains 6 footnotes and 6 figures.)
Abstractor: As Provided
Number of References: 18
Entry Date: 2010
Accession Number: EJ901530
Database: ERIC
FullText Text:
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  Data: Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP
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  Data: This paper deals with temperature variations over time of objects placed in a constant-temperature environment in the presence of thermal radiation. After a historical introduction, the paper discusses cooling and warming laws, by taking into account first solely object-environment energy exchange by thermal radiation, and then adding object-environment heat exchange by convection. These processes are usually evaluated by approximating the law of exchange of thermal radiation by a linear relationship between power exchange and temperature difference. In contrast, in this paper an exact analytical solution considering Stefan's fourth power law is provided, under some general hypotheses, for both cases. A comparison with exponential approximations and with a historical law proposed by Dulong and Petit in 1817 is presented. Data of an experiment are used to test the analytical solution: the test has allowed evaluating the heat transfer coefficient h of the experiment and has shown that our solution provides a better fit with the measured values than any exponential function. The topic is developed in a way which can be suitable both for undergraduate students and for general physicists. (Contains 6 footnotes and 6 figures.)
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