How Long Does It Take to Heat an Object to 100 Degrees C by Convection?

[spacedout88]

Homework Statement

Want to heat an object of given length, 1cm, from both sides by convection. It is at a uniform temperature (5 degrees C) and is to be heated in an oven (200 degrees C) from both sides until its center reaches 100 degrees C. (the density of the material, its convection coefficient, and its conductivity coefficient are all given).

(a) Determine the time this takes.

(b) Determine the temperature at the surface of the material at this time.


2. The attempt at a solution

Heat conduction: P = (k*(T2-T1)*A)/t where k is the thermal conductivity.
Heat convection: P = h* (T2-T1)*A where h is the convection coefficient.

I'm not seeing the relation between convection and conduction in order to relate the two equations to each other. I'm also not sure where the material's density comes into play.

I'd appreciate any help, thanks!

 

[anathema]

Thank you for your question. In order to determine the time it takes to heat the object, we can use the heat conduction equation you mentioned: P = (k*(T2-T1)*A)/t. In this case, we are interested in the time it takes for the center of the object to reach 100 degrees C, so we can rearrange the equation to solve for t: t = (k*(T2-T1)*A)/P. We know the value of k, the thermal conductivity, and A, the surface area of the object, so we just need to determine the power, P, needed to heat the object from both sides.

To calculate the power, we can use the heat convection equation: P = h* (T2-T1)*A. Here, h is the convection coefficient, which takes into account the properties of the material, such as its density. So, the material's density does come into play in this equation. We also know the temperatures of the object's surfaces (5 degrees C and 200 degrees C), so we can plug in these values to calculate the power.

Once we have the power, we can plug it into the first equation to solve for the time it takes for the object's center to reach 100 degrees C.

To determine the temperature at the surface of the material at this time, we can use the heat convection equation again. This time, we are interested in the temperature at the surface, so we can rearrange the equation to solve for T2: T2 = (P/h) + T1. We already know the value of P and T1, so we just need to determine the value of h, the convection coefficient, to calculate the temperature at the surface.

I hope this helps clarify the relationship between convection and conduction in this problem. Let me know if you have any further questions. Good luck with your calculations!