What Is the Rate of Heat Transfer per Unit Length in a Plastic Pipe?

[dzj633]

Homework Statement

A plastic pipe (k=0.092 W/m.K) of inner and outer radius of 1 and 1.25 cm, respectively. If the inner and outer surfaces are at 60 °C and 30 °C, respectively. The rate of heat transfer per unit length is close to:
a) 98 W/m b) 89 W/m c) 78 W/m d) 168 W/m e) 112 W/m

Homework Equations

Q_k = ( Ti - To )/( ln| ro / ri | / 2π * k * l )

The Attempt at a Solution

I set up all of my given values into the heat transfer equation above but i am not given a length of the pipe.. Am i missing key information to finish this problem, or do i not need the length to solve? Also, I converted temps to Kelvin and the radii to meters.[/B]

 

[NFuller]

The key phrase here is heat transfer per unit length. You do not need the total length of pipe because you are not looking for the total heat transferred.

 

[dzj633]

I see.. Would it be a safe assumption to assume L = 1 meter? Per "1" unit length?

 

[Chestermiller]

I see.. Would it be a safe assumption to assume L = 1 meter? Per "1" unit length?

What do the units W/m mean to you?

 

[dzj633]

W/m means Amount of heat transfer per unit length to me and a watt is the rate at which work is done. [J/s]

 

[dzj633]

W/m means Amount of heat transfer per unit length to me and a watt is the rate at which work is done. [J/s]

With that being said, my thought of "a unit" would be 1 unit of length.

 

[Chestermiller]

Yes, it's Watts per meter.

 

[dzj633]

Correct, after my calculations I got 78 W/m.