Heat Conduction is the flow of heat from one solid to another that has a different temperature when they come in contact with each other. For instance, we warm our hands when we touch hot water bottle, or when we rub our hands.

The principle of energy conservation and Fourier’s law of heat conduction are applied to derive different forms of the differential equation which govern the temperature distribution in a stationary medium. Fourier’s law of heat conduction is an empirical law based on the observation. The mathematical expression is given by

Q ∝ A dt / dx

Where,
Q is Heat flow through a body per unit time (in watts) W,
A is Surface area of heat flow m2,
dt is Temperature difference in oC or K
dx is Thickness of the body in the direction of flow, m.
Hence, we can express Heat Conduction formula by

Q = – k . A dt / dx

Where,
k = Constant of proportionality, known as the thermal conductivity of the body.

Example1

Asbestos layer whose thickness is 20 mm is used as an insulator over a boiler wall. Consider an area of 0.9m2 and calculate the rate of heat flow over this area if the temperatures on either side of the insulation are 400oC and 30oC. Given K = 0.116 W/mK

Solution:

To calculate heat flow, we need to find the heat flux.
Heat flux is given by,
q = – k dt / dx. m2

= – 0.116 × (30 – 400)/0.02

q = 1566 W/m2

Rate of heat flow Q is expressed by,

Q = Heat flux × Area

= 1566 × 0.9

Q = 1409.4 W

Example 2
Calculate the rate of heat transfer per square meter of surface of a cork board having 5 cm thickness, and a temperature difference of 85oC 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