Heat Conduction Formula

Heat Conduction is the heat transfer from one solid to another which has different temperature as they come into contact with each otherFor example, when we touch hot water bottle, or when we rub our hands, we warm our hands.

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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