Heat transfer through 5" light weight concrete 1

[austin1015]

Hope you guys can help me out. Its been awhile since I have done any sort of heat transfer seeing as how I am a Civil. I am trying to determine the temperature on the bottom side of a lightweight concrete bridge deck if the top side is being heated to an average temp of 57 degrees F with insulating blankets placed on top. The thickness of the deck is 5" and has a steel grid within it as reinforcement. This seems like a really easy problem to solve, I just dont know how to get started. Thanks for your help.

 

[ione]

First of all there must be a temperature gradient amongst the two surfaces to acts as the driving force for thermal flux to take place.

Assume we have air on both sides of the wall.

You know that air temperature on top side is 57 °F. You should know air temperature on the other side.

Then……
Q1 = htc1 * (Ti – Twi)
Q2 = k/s * (Twe – Twi)
Q1 = htc2 * (Te – Twe)

Where:

htc1 = convection heat transfer coefficient at film temperature (top side)

htc2 = convection heat transfer coefficient at film temperature (bottom side)

k = light weight concrete wall thermal conductivity

s = light weight concrete wall thickness

Ti = air temperature (top side)

Te = air temperature (bottom side)

Twi = wall temperature (top side)

Twe = wall temperature (bottom side)


Choose a trial temperature Twi, compute htc1 (trial), put Q1 = Q2 and compute Twe (trial)

Then you put Q2 = Q3 and solve for htc2 and check whether it matches the value of htc2 you have separately calculated for the relevant geometry and with Te and Twe (trial). Iterate until results converge.

You may find of some help this calculator:

http://www.thermal-wizard.com/tmwiz/default.htm

One last note (to be more precise you should include also the radiation heat transfer component)