Heat equation 1 dimensional meaning of thin rod?
A thin rod is used to model the heat equation, what is the meaning of this?
- 2 months agoFavorite Answer
A "thin rod" has a "small" cross sectional area, so that diffusion doesn't need to be modeled throughout the cross-section and at the boundary around the rod. That is, heat only varies with the x and t variables.
If you want to model a wire-like rod, you would have to use different assumptions than if you wanted to model a very thick rod.
Simplifying assumptions and experimental physical laws are used in deriving different PDEs.
- VamanLv 72 months ago
It is Q dT/dx= - K T. T is the temperature. K and Q are constants. Make it dT/dx = - m T. This gives the temperature distribution at a given time. Any mathematical method will have such equation.
- billrussell42Lv 72 months ago
which heat equation? can you provide a reference or example?
partial differential equations are beyond my knowledge.
the thin rod is an attempt to show a simple example of the equation.