Kevin asked in Science & MathematicsEngineering · 2 months ago

# Heat equation 1 dimensional meaning of thin rod?

A thin rod is used to model the heat equation, what is the meaning of this?

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• 2 months ago

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.

• Vaman
Lv 7
2 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.

• 2 months ago

which heat equation? can you provide a reference or example?

edit:

partial differential equations are beyond my knowledge.

the thin rod is an attempt to show a simple example of the equation.

• Kevin2 months agoReport

https://en.wikipedia.org/wiki/Heat_equation