Derive a differential equation whose solution allows calculating the temperature of the fin at any point on the x axis.
Allowable terms: d²/dx², dT/dx, At(x), dAt(x)/dx, h, k, dAs/dx, T(x), T[infinity]
Considerations:
1- Unidirectional conduction T=T(x)
2- Surroundings: T=T[infinity]
3- Parameters for heat transfer: h, k
4- Surface area: As
5- Cross-sectional area: At
6- Steady state.
Strategy: Start with energy balance for a differential element.