The law of heat conduction is also known as Fourier’s law. It states that “the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and the area.”
`Q=-k\times A\frac{dt}{dx} ...(1)`
Where, Q is the heat flow
rate by conduction (W), k is the thermal conductivity of body material (W/m.K),
A is the cross-sectional area normal to the direction of heat flow (m2
) and dt/dx is the temperature gradient (K/m).
The negative sign in
Fourier’s equation indicates that the heat flow is in the direction of negative
gradient temperature and that serves to make heat flow positive. Thermal conductivity
is one of the transport properties. Other properties include viscosity
associated with the transport of momentum and diffusion coefficient associated
with the transport of mass. Thermal conductivity provides an indication of the
rate at which heat energy is transferred through a medium by conduction
process.
The assumptions of the Fourier
equation include steady-state heat conduction, one-directional heat flow, isothermal
bounding surfaces with constant and uniform temperatures at the two faces,
isotropic and homogeneous material and thermal conductivity constant, constant
temperature gradient, and linear temperature profile, and no internal heat
generation.
The unique features of the
Fourier equation are that this equation is valid for all matter solid, liquid,
or gas. The vector expression indicates that the heat flow rate is normal to an
isotherm and is in the direction of decreasing temperature. It cannot be
derived from the first principle and helps to define the transport property
‘k’.
Thermal resistance is
reciprocal of thermal conductance and is associated with the conduction of
heat. Consider a plane wall of thickness L and average thermal conductivity k.
The two surfaces of the wall are maintained at constant temperatures of T1
and T2. For one-dimensional steady heat conduction through the wall,
we have Tx. Then Fourier’s law of heat conduction for the wall with
two surfaces is expressed as:
`Q_{wall}=-kA\frac{T_2-T_1}L ...(2)`
`=-\frac{T_2-T_1}L ...(3)`
Where, Qwall
is the heat flux through the plane (W), k is the conductivity of the material
(W/m.K), L is the plane thickness (m) and A is the plane area (m2).
Thermal resistance is a heat property and is a measurement of a temperature
difference by which an object or material resists a heat flow. The thermal
resistance (Rt) for conduction in a plane wall is defined as:
`R_t=\frac L{kA} ...(4)`
Where, k is the conductivity
of the material (W/m.K), L is the plane thickness (m) and A is the plane area
(m2).
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