HEAT TRANSFER BY CONDUCTION
Fourier’s law of heat conduction
Fourier’s law of an heat conduction is an empirical law based on observation and states as follows.
“The rate of flow of heat through a simple homogenous solid is directly proportional to the area of the section at right angles to the direction of the heat flow, and to change of temperature with respect to the length of the path of the heat flow”
Mathematically,
Q A. Dt/dx
Where,
Q = heat flow through the body per unit time (watts)
A = surface area heat flow (perpendicular to the direction of flow, m2)
dt = temperature difference of the faces of block (homogenous solid)
of = Thickness ‘dx’ through which heat flows (oC or K) and
dx = thickness of body in the same direction of flow, (m)
Thus,
Q = -kA.dx/dx Watt
Where,
k = constant of proportionality and is known as conductivity of the body.
The negative sign of ‘k’ is to take care of the decreasing temperature along with in the direction of increasing thickness or the direction of heat flow. The temperature gradient dt/dx is always negative along positive x-direction and therefore the values as Q becomes + ve.
ASSUMPTIONS
The following are the assumption on which Fourier’s law is based on:
• Conduction of heat take place under steady state conditions.
• Heat flow is unidirectional
• The temperature gradient is constant and the temperature profile is linear.
• There is no internal heat generation.
• The bounding surfaces are isothermal in character.
• The material is homogenous and isotropic.