How do I calculate the temperature at different layers within a cavity wall?

[ingram010]

Hi all

I have a revision question I am having some trouble with

A cold room has a wall measuring 5.2m by 2.5m. The wall is constructed of 120mm thick brick on the inside, a cork layer 80mm and a 30mm layer ow wood in the outside. the inside temperature is -4ºC and the outside temperature is 70ºC.

The thermal conductivities of the materials are:-

Brick,0.9Wm^-1K^-1, Cork, 0.04Wm^-1K^-1, and wood, 0.17Wm^-1K^-1


The formula for calculating for the rate of heat transfer through all the layers is:-

-Area/ (x1/k1) + (x2/k2) + (x3/k3) x (T1- T2)

so -13/ (0.12/0.9) + (0.08/0.04) + (0.03/0.17) x (-4 - 70) = 416.485 watts.

I am having a problem with the calculating the temperatures at the brick/cork and cork/wood interfaces.

If anyone could help I would be very grateful

Kindest regards

John

The Attempt at a Solution

 

[edgepflow]

Apply:

qT = Ts1 - Ts2 / Rs12

where,

qT = total heat transfer rate (you already calculated).
Ts1 = surface temperature at interface 1
Ts2 = surface temperature at interface 2
Rs12 = thermal resistance between surface 1 & 2 (for example: x1/k1)

So start at the surface with the known temperature (call it surface 1), and figure:

Ts2 = Ts1 - qT / Rs12

and work your way to the other end.

 

[ingram010]

Thanks edgepflow

much appreciated

 

[sourceinfrate]

thank you a lot this was the information i have been searching for last 2 days

 

[asteriatic]

:

To calculate the temperature at different layers within a cavity wall, you can use the heat transfer formula you have provided. However, in order to accurately determine the temperature at the interfaces between the materials, you will need to use the concept of thermal resistance. Thermal resistance is the measure of how resistant a material is to heat flow, and it is equal to the thickness of the material divided by its thermal conductivity.

In this case, you can calculate the thermal resistances for each layer as follows:

- Brick layer: 120mm / 0.9Wm^-1K^-1 = 133.33 m^2K/W
- Cork layer: 80mm / 0.04Wm^-1K^-1 = 2000 m^2K/W
- Wood layer: 30mm / 0.17Wm^-1K^-1 = 176.47 m^2K/W

Next, you can use these thermal resistances to calculate the temperature at the interfaces between the layers. For the brick/cork interface, the temperature can be calculated as follows:

T1 = T2 + (Q x R)

Where:
- T1 = temperature at the brick/cork interface
- T2 = temperature at the inside surface of the brick layer (-4ºC in this case)
- Q = rate of heat transfer calculated using the formula provided (-416.485 watts)
- R = thermal resistance of the brick layer (133.33 m^2K/W)

Plugging in the values, we get:

T1 = -4 + (-416.485 / 133.33) = -7.12ºC

Similarly, for the cork/wood interface, the temperature can be calculated as follows:

T2 = T3 + (Q x R)

Where:
- T2 = temperature at the cork/wood interface
- T3 = temperature at the outside surface of the wood layer (70ºC in this case)
- Q = rate of heat transfer calculated using the formula provided (-416.485 watts)
- R = thermal resistance of the wood layer (176.47 m^2K/W)

Plugging in the values, we get:

T2 = 70 - (-416.485 / 176.47) = 72.36ºC

Using these temperatures at the interfaces, you can then calculate the temperatures at any desired points within the cavity wall using the same formula, taking into