Why Does the Convection Heat Transfer Coefficient Vary with Temperature?

[theBEAST]

Homework Statement

I have a question about part b for this question:

In the solution apparently h1 and h2 are a function of temperature as shown here:

However, I thought the convection heat transfer coefficient is a constant. I have done some problems where it is constant but in this case it is not. Does anyone know why? When is it constant and when is it not?

 

[Redbelly98]

Moderator's note: thread moved from Intro Physics to Engineering.

(Hopefully somebody can help out.)

 

[Chestermiller]

In real world situations, the convective heat transfer coefficient is not going to be constant unless the flow is constant. Maybe you can cite some examples of where it was treated as constant.

Chet