Fourier heat transfer equation:
Conduction is
primarily a molecular phenomenon in which temperature gradient acts as a
driving force.
Experimental
evidence indicate that the study state one dimensional flow of heat by
conducting through a homogeneous material.
It is given
by
K=
proportionality factor.
q= The heat
flux (heat conducted per unit area).
Q= rate of
heat flow Kcal/hr (or)KJ/hr..
A= area
perpendicular to direction (m2).
dx = thickness
of material along the path of heat flow.
dt = temperature
difference between two surfaces(oK or oC).
The negative
sign indicates the heat flow is in the negative direction of temperature.
The proportionality
factor (K) is called the heat conductivity of material.
Fourier law is essentially based on the following assumptions:
*Steady state
conductivity which implies that the time rate of heat flow between any two
points is constant with time.
This also
means that the temperature of the fixed point within a heat conducting body
does not change time.
T ≠
f (τ)
*One dimensional heat flow :
Only one
space coordinate is required to describe the temperature distribution within
the heat conducting in the body.
t=f(x) in x
direction
similarly
t=f(y) in y
direction
t=f(z) in z
direction.
*Bounding surfaces
are isothermal in character (constant and uniform temperature) are maintained
at the two faces.
*Isotropic and
homogeneous material ie., thermal conductivity has a constant value in all the
directions.
*Constant temperature
gradient and the linear temperature profile.
*No internal
heat generation.
Some essential features of the Fourier equation relation are
enumerated below:
*Fourier law
predicts how heat is conducted through a medium form high temperature to low temperature
region.
*Fourier law
is valid for all matter (every object/Phases)
*Fourier law
is a vector expression that heat flow rate is normal to an isotherm and is in
direction of decreasing temperature.
*Fourier Law
cannot be derived from 1st principle. ie., it is based on experiment
evidence.
*Fourier law
helps to define transport property (K). ie., thermal conductivity in medium.
Assuming dx=
1m, A=1m2 and dt=1o,
then we
obtain Q=K
Hence
Thermal conductivity may be defined as amount of heat conducted per unit time
across unit area & through unit thickness.
When the
temperature difference of a unit degree is maintained across the boundary
surface.
The
magnitude of thermal Conductivity tells us how well a material transports
energy by conduction.
