Doubt in Fourier's Law of Heat conduction

[R Power]

Hello friends
Fourier law of heat conduction states that:

Q ~ A.(Dt/Dx) where A= area normal to direction of heat flow.
Dt/Dx= temp gradient in same direction.

Now, obviously rate of heat flow will depend upon temp gradient but my doubt is how/why rate of heat flow is affected by this NORMAL area A ?

Thnx

 

[Coto]

Back in the 1800s they used to think heat was a fluid... called a caloric fluid. The reason they thought this was because it's behaviour was similar to that of a fluid.

Using the ideas of a fluid, in particular let's use water, if we maintain a *constant* pressure gradient on a pipe from one end to another and change its diameter, would you say more water now flows? It's the same idea for heat.

 

[cjl]

Hello friends
Fourier law of heat conduction states that:

Q ~ A.(Dt/Dx) where A= area normal to direction of heat flow.
Dt/Dx= temp gradient in same direction.

Now, obviously rate of heat flow will depend upon temp gradient but my doubt is how/why rate of heat flow is affected by this NORMAL area A ?

Thnx

Because the total heat flow depends on the size of the cross section. Think about it - will a wire conduct as much heat from one point to another as a large rod of the same material?

 

[R Power]

yeah, I get it now after a bit of thinking. If source of heat is placed at one end then more the area of cross section more the medium is available for flow so more heat will flow. It was simple.
Thnx coto and cj.

 

[sardar]

for your question. The reason why the area A is included in Fourier's Law of Heat Conduction is because it represents the cross-sectional area through which heat is flowing. This area is important because it determines the amount of heat that can pass through it. For example, if you have a larger area, more heat can flow through it compared to a smaller area. This is why the area A is included in the equation. Additionally, the normal direction of the area A is important because it represents the direction in which the heat is flowing. The temperature gradient, represented by Dt/Dx, is also in the same direction as the area A. This is because the temperature gradient is the change in temperature over a certain distance in the direction of heat flow. So, to summarize, the area A and the normal direction play a crucial role in determining the rate of heat flow according to Fourier's Law. I hope this helps to clarify any doubts you may have.