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# 3b-r - One-Dimensional Steady-State Conduction with Thermal...

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One-Dimensional, Steady-State One-Dimensional, Steady-State Conduction with Conduction with Thermal Energy Generation Thermal Energy Generation Chapter Three Chapter Three Section 3.5, Appendix C Section 3.5, Appendix C

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Implications Implications Implications of Energy Generation Involves a local (volumetric) source of thermal energy due to conversion from another form of energy in a conducting medium. The source may be uniformly distributed , as in the conversion from electrical to thermal energy (Ohmic heating): 2 g e E I R q = = 2200 2200 (3.38) or it may be non-uniformly distributed , as in the absorption of radiation passing through a semi-transparent medium. ( 29 exp q x α - Generation affects the temperature distribution in the medium and causes the heat rate to vary with location, thereby precluding inclusion of the medium in a thermal circuit. For a plane wall,
The Plane Wall The Plane Wall The Plane Wall Consider one-dimensional, steady-state conduction in a plane wall of constant k , uniform generation , and asymmetric surface conditions : Heat Equation : 2 2 0 0 d dT d T q k q dx dx dx k + = + = (3.39) Is the heat flux independent of x? q ′′ General Solution : ( 29 2 1 2 / 2 T x q k x C x C = - + + What is the form of the temperature distribution for 0? q = > 0? q < 0? q How does the temperature distribution change with increasing ? q

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Plane Wall (Cont.) Plane Wall (Cont.) Symmetric Surface Conditions or One Surface Insulated: What is the temperature gradient at the centerline or the insulated surface?
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3b-r - One-Dimensional Steady-State Conduction with Thermal...

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