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Erschienen in:
2015 | OriginalPaper | Buchkapitel
10. Conduction with Heat Sources
verfasst von : Roberto Mauri
Erschienen in: Transport Phenomena in Multiphase Flows
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Abstract
In this chapter we study problems of conduction combined with internal heat generation, that is the conversion of mechanical energy into internal energy. Here we list some examples of heat generation, specifying the energy “dissipated” per unit volume and unit time, \(\dot{q}\).First, in Sect. 10.1, we consider the general solution of this problem in plane, cylindrical and spherical geometries in the case of a uniform heat production. Then, in Sect. 10.2, we examine the case of a linear source term, using either regular or singular perturbation expansion methods to solve the limit cases corresponding to small and large heat generation, respectively.
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Dissipation of electrical energy \(\dot{q} = I^{2} /k_{e}\), where I is the current density, in amps cm−2, while k e is the electric conductivity, in Ω−1 cm−1.
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Dissipation of mechanical energy (viscous dissipation), \(\dot{q} = \mu \left| {{\nabla }v} \right|^{2}\), where μ is viscosity and \({\nabla }v\) the velocity gradient.
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Dissipation of chemical or nuclear energy.