# Heat Flow Rate Formula

Is the amount of heat that is transferred per unit of time in some material.

The rate of heat flow in a rod of material is proportional to the cross-sectional area of the rod and to the temperature difference between the ends and inversely proportional to the length.

Heat flow = - (heat transfer coefficient) * (area of the body) * (variation of the tem-perature) / (length of the material)

The equation is:

Q = -k (A/l) (ΔT)

We have:

Q: heat transfer per unit time

K: The thermal conductivity

A: area of the emitting body

l: the length of the material.

ΔT: Difference of temperature.

Heat transfer Formula Questions:

1) The wall of a house, 7 m wide and 6 m high is made from 0.3 m thick brick with k= 0.6 W/mK. The temperature on the inside of the wall is 16°C and that on the outside 6°C. Find the heat flux.

Answer:

The difference of temperature is ΔT = T_{i} - T_{O} = 16°C - 6°C = 10°C = 283 K.

The heat flow is given by the formula:

Q = -k (A/l) (ΔT)

Substituting the values of the heat conductivity coefficient, the area, the length and the difference of temperature between the inside and outside,

Q = -0.6 W/m K (7m*6 m/0.3 m) (283 K) =

Q = -840 W

2) A 20 mm diameter copper pipe is used to carry heated water, the external surface of the pipe has a k= 6 W /m K, it has a thick of 2 mm. Find the heat flux on the pipe when the external surface temperature is 80°C, and the surroundings are at 20°C.

Answer:

The difference of temperature is ΔT = T_{i} - T_{O} = 80°C - 20°C = 60°C = 333 K.

The heat flow is given by the formula:

Q = -k (A/l) (ΔT)

The area is given by π (0.02 m)^{2} = π 0.0004 = 0.0012 m^{2}.

Substituting the values of the heat conductivity coefficient, the area, the length and the difference of temperature between the inside and outside,

Q = -6 W/m K (0.0012 m^{2}/0.002 m) (333 K) = -1198.8 W

Q = -1198 W

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