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Laws of heat transfer
conduction
Fouriers law
It is an emperical law based on observation.
the rate of f low of heat through a simple homogeneoussolid is
directly proportional to the area of the section atright angles to
the direction of heat flow, and to change oftemperature with
respect to the length of path of the heatflow.
Q A dt\ dx.
where
Q =A=
dt=
dx=
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Q = - k A dt\ dx.
where k = thermal conductivity.
-ve sign of k is to take care of the decreasing temperature
along with the direction ofincreasing thickness or the direction of
heat glow.
The temperature gradient dt\dx is always negative along positive
x direction and,therefore the value as Q become +ve.
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Assumptions
The following are the assumptions on which Fourier's law.
Conduction takes place under steady state conditions.
The heat flow is unidirectional.
There is no internal heat generation.
The bounding surfaces are isothermal in character.
All the material is homogeneous and isotropic.
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Essential features of Fourier's law
It is applicable to all matters (may be solid, liquid or
gas.)
It is based on experimental evidence.
It is a vector expression indicating that heat flow rate is in
the direction of decreasingtemperature.
It helps to define thermal conductivity k of the medium through
which heat isconducting.
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Thermal conductivity
the amount of energy conducted through a body of unit area, and
unit thickness in unit time when thedifference in temperature
between the faces causing heat flow is unit temperature
difference.
Materials having good thermal conductivity are good conductors
of heat and vice-versa.
Thermal conductivity depends upon
Material structure.
Moisture contents.
Density of material.
Pressure and temperature.
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Points to be remember
Thermal conductivity of most of the metals decreases with
increase of temperature.
In most of the liquid thermal conductivity decreases with the
increase of temperature due to decreasein density with increase of
temperature.*(water being an exceptional.)
In gases thermal conductivity increases with temperature.
In most materials, thermal conductivity dependence almost linear
on temperature.
k = ko(1+ t)
where ko = thermal conductivity at 0 C,
= temperature coefficient of thermal conductivity,
t = temperature in C.
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General heat conduction equation in
Cartesian coordinates.
Cylindrical coordinates.
Spherical coordinates.
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Cartesian coordinates
parrallelopipide Volume = dx dy dzLet t = temperature of left
face.
dt\dx = temperature changes and rate ofchange along x
direction.
Net heat accumulated is
heat conducted + internal heat generated =energy stroed with in
the material.
