Conservation Equations for Mass, Momentum, and Energy

  • Tuncer Cebeci
  • Peter Bradshaw
Part of the Physical and Computational Aspects of Convective Heat Transfer book series (SSE)


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.


Conservation Equation Momentum Equation Viscous Stress Fluid Element Kinetic Energy Equation 
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  1. [1]
    Bradshaw, P.: Turbulence, in Science Progress, 67.: 185 Oxford, 1981.Google Scholar
  2. [2]
    Cebeci, T. and Smith, A. M. O.: Analysis of Turbulent Boundary Layers. Academic, New York, 1974.MATHGoogle Scholar
  3. [3]
    Hildebrand, F. B.: Advanced Calculus for Applications. Prentice-Hall, Englewood Cliffs, NJ, 1962.Google Scholar
  4. [4]
    Cebeci, T. and Bradshaw, P.: Momentum Transfer in Boundary Layers. Hemisphere, Washington, DC, 1977.MATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Tuncer Cebeci
    • 1
    • 2
  • Peter Bradshaw
    • 3
  1. 1.Douglas Aircraft CompanyLong BeachUSA
  2. 2.Department of Aerospace EngineeringCalifornia State University, Long BeachLong BeachUSA
  3. 3.Department of Mechanical EngineeringStanford UniversityStanfordUSA

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