Conduction with Generation
Thermal energy may be generated or consumed due to conversion from some other energy form.
* If thermal energy is generated in the material at the expense of some other energy form:
–Deceleration and absorption of neutrons in a nuclear reactor
–Exothermic reactions
–Conversion of electrical to thermal energy:
information : where I is the current, Re the electrical resistance, V the volume of the medium
* If thermal energy is consumed we have a sink: is -ve
–Endothermic reactions
In The Plane Wall
Consider one-dimensional, steady-state conduction in a plane wall of constant k, with uniform generation, and asymmetric surface conditions:
- General Solution:
- Boundary Conditions:
Temperature Profile
assumptions :
Profile is parabolic.
Heat flux not independent of x Symmetrical Distribution
Note that at the plane of symmetry :
* Equivalent to adiabatic surface
Calculation of surface temperature Ts
Boundary condition at the wall:
Substituting (dT/dx)x=L from equation:
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