fourierslaw

Fouriers law of heat conduction;

Rate of heat conduction through uniform material ids directly proportional to area which is normal to the direction of heatflow and the temperature gradient which is in the direction of heat flow

Q α a dt/dy

Q= -k a dt/dy
Q /a = -k dt /dy
Q’ = -k dt /dy

Q = heat flow
A = area of crosssection
,dt/dy = temperature gradient

K= thermal conductivity



Thermal conductivity :

It is the rate of heat transfer per unit area

K = Q’ dy/dt



Q’ = heat flux

Units of thermal conductivity

Watt /m.kelvin



Fouriers law of heat conduction for a plane wall

Let the thermal conductivity be = k
Let the thickness of the wall be = x m
Let the hot surface temperature be = t1
Let the temperature of cold surface be = t2

Assuming the steady state
According to fouriers law of heat conduction



q/a = -k dt /dx



x t2
∫dx = -ka /q ∫dt
0 t1

x-0 = -ka /q(t2-t1)

q = t1-t2/(x/ka)
q= ^t/R
r = x/ka
thermal conductivity is the function of property of the material and its temperature or themal energy
k of solids > liquids>gases

keywords: thermal conductivity , fouriers law of heat conduction, fouriers law of heat conduction in plane wall,