The principle of energy conservation and Fourier’s law of heat conduction is applied to derive different forms of the differential equation which govern the temperature distribution in a stationary medium. Fourier’s law of conduction of heat is an empirical law based on the observation.
Fourier’s law of conduction of heat is expressed as
Q ∝ A × (dt / dx)
Where,
Q = heat flow through a body per unit time (in watts W)
A = Surface area of heat flow m2,
dt = Temperature difference in oC or K
dx = Thickness of the body in the direction of flow, m.
Hence, we can express the Heat Conduction formula by
Q = – k × A (dt / dx)
Where
k = thermal conductivity of the body and it is a Constant of proportionality
Example 1
Calculate the rate of heat transfer per square meter of the surface of a cork board having 5 cm thickness, and a temperature difference of 75oC is applied across the board. The value of thermal conductivity (k) is -0.4 W/mc.
Solution:
Given parameters are,
k = – 0.4
A = 5 cm
(dt / dx) = 75oC
By Substituting in the corresponding formula, we get
Q = – k . A (dt / dx)
= – (- 0.4) (5) (75)
Hence, Q = 150 W
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