## Heat Conduction Formula :

Heat flow through a body Q _{(w) }in watt is proportional to the Surface area of heat flow A_{(m}^{2}_{)} in meter square is multiply by Temperature difference dt_{(k)} in kelvin and the Thickness of the body in the direction of flow dx_{(m)} in meter. Hence the Fourie’s law of conduction of heat has been written as,

**Q _{(w) }**

**∝**

**A**

_{(m}^{2}_{)}* (dt_{(k)}/ dx_{(m)})Where,

Q → heat flow through a body per unit time (in watts W)

A → Surface area of heat flow in ( m^{2})

dt→ Temperature difference in ( ^{o}C )or (K)

dx→ Thickness of the body in the direction of flow in (m)

Hence, we can express the Heat Conduction formula by,

Heat flow through a body Q _{(w) }in watt is equal to the product of the thermal conductivity of the body – k _{(Wm-1K-1)} watt per meter Kelvin is multiply by Surface area of heat flow A_{(m}^{2}_{) }in meter square is multiply by Temperature difference dt_{(k)} in kelvin and the Thickness of the body in the direction of flow dx_{(m)} in meter. Hence the Heat Conduction formula has been written as,

**Q _{(w)} = – k _{(Wm-1K-1)} * A_{(m}^{2}_{)} (dt_{(k)} / dx_{(m)})**

Where,

k → thermal conductivity of the body and it is a Constant of proportionality (Wm^{-1}K^{-1}) .

## Sample Problems :

### Example 1:

Calculate the rate of heat transfer per square meter of the surface of a cork board having 6 cm thickness, and a temperature difference of 80^{o}C is applied across the board. The value of thermal conductivity (k) is -0.5 W/mc.

### Solution :

Given parameters are,

k = – 0.5

A = 6 cm

(dt / dx) = 80 ^{0}C

By Substituting in the corresponding formula, we get

Q = – k . A (dt / dx)

= – (- 0.5) (6) (80)

Hence,

Q = 240 W.

### Example 2:

Calculate the rate of heat transfer per square meter of the surface of a cork board having 7 cm thickness, and a temperature difference of 85^{o}C is applied across the board. The value of thermal conductivity (k) is -0.6 W/mc.

### Solution :

Given parameters are,

k = – 0.6

A = 7 cm

(dt / dx) = 85 ^{0}C

By Substituting in the corresponding formula, we get

Q = – k . A (dt / dx)

= – (- 0.6) (7) (85)

Hence, Q = 357 W.