Heat Conduction Formula and Sample Examples

Heat Conduction Formula :

Heat flow through a body Q (w) in watt is proportional to the Surface area of heat flow A(m2) 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(m2) * (dt(k) / dx(m))

Where,

Q → heat flow through a body per unit time (in watts W)
A → Surface area of heat flow in ( m2)
dt→ Temperature difference in ( oC )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(m2) 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(m2) (dt(k) / dx(m))

Where,

k → thermal conductivity of the body and it is a Constant of proportionality (Wm-1K-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 80oC 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 0C

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 85oC 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 0C

By Substituting in the corresponding formula, we get

Q = – k . A (dt / dx)

= – (- 0.6) (7) (85)

Hence, Q = 357 W.

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