H = heat flow

Q = heat

L = length

A = cross sectional area = temperature variation

k= constant that depends on the material

RELATED:

Specific heat capacity (theory)

Specific heat capacity (examples)

## Heat Flow

Heat flows at different rates, in different materials. Certain materials, like copper, are very good at transmitting heat. The dimensions of the material also have an influence: materials with larger cross sections will be more efficient a transmitting heat. The direction of heat flow is from hot to cold; the larger the difference in temperature between 2 places , the faster heat will flow. The formula below summarises all these ideas and more: The units are J/s = W

Examples:

1) What is the heat flow through a copper rod 1m long with a cross section of 0.05 m2 , if one end is at 350 K and the other is at 200 K?

What would it be the flow if the material was wood?

kcu = 380 W / mK and kwood = 0.1 W / mK

Solution:

Copper: H = 380 * 0.05*150 / 1 = 2850 W

Wood: 0.1 * 0.05*150 / 1 = 0.75 W

2) Two rods with cross sections of 10 cm2 are joined together. One is made of copper (1 m long) and the other is made of steel (2 m long). Their opposite ends are held at 400K (copper side ) and 300K (steel side). What is the temperature and the heat flow at the junction between the two? kcu = 380 W / mK and ksteel = 50 W / mK

Solution:

Heat will flow continuously from the copper side to the aluminium side, so that the heat flow must be the same in both rods. So, let's call Tj the temperature ate the junction:

380*(400-Tj) /1 = 50 * (Tj-300) /2

Tj=393.8 K

Calculating the flow :

copper rod = 380*(400-393.8)* 0.01/1 = 23.56 W

steel rod: 50*(393.8-300)*0.01/2 = 23.45 W

(the small difference is due to the rounding of the temperature to 393.8 K)