Abstract
This chapter presents derivations of the differential equations that, with corresponding boundary conditions, describe convective heat transfer processes. Since convective heat transfer always involves transfer of mass and momentum, the derivations of the corresponding equations are also presented and serve as an introduction to the heat-transfer equations, which are conceptually rather similar. The derivations in Sections 2.1 to 2.3 lead to equations that represent conservation of mass, momentum, and energy—including thermal energy—for unsteady two-dimensional flows. These derivations use control-volume analysis, together with the laws for heat- and momentum-flux rates in a viscous conducting fluid that were introduced in Chapter 1. The equations for three-dimensional flows contain extra terms but no new principles (see Problems 2.1 and 2.4). Since most practical cases of convective heat transfer involve turbulent flow, the usual decomposition of the velocity and fluid properties into mean and fluctuating quantities, with subsequent averaging of the equations, is described in Section 2.4.
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References
Bradshaw, P.: Turbulence, in Science Progress, 67.: 185 Oxford, 1981.
Cebeci, T. and Smith, A. M. O.: Analysis of Turbulent Boundary Layers. Academic, New York, 1974.
Hildebrand, F. B.: Advanced Calculus for Applications. Prentice-Hall, Englewood Cliffs, NJ, 1962.
Cebeci, T. and Bradshaw, P.: Momentum Transfer in Boundary Layers. Hemisphere, Washington, DC, 1977.
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© 1988 Springer-Verlag New York Inc.
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Cebeci, T., Bradshaw, P. (1988). Conservation Equations for Mass, Momentum, and Energy. In: Physical and Computational Aspects of Convective Heat Transfer. Physical and Computational Aspects of Convective Heat Transfer. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3918-5_2
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DOI: https://doi.org/10.1007/978-1-4612-3918-5_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96821-6
Online ISBN: 978-1-4612-3918-5
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