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Thermal energy transfer
Thermal resistance test bench
Ref : 253 118
In a Cartesian system, Fourier's rapport thus applied is expressed by:
With �� ⃗ unit vector oriented according to the flow
�� : Temperature
Note: �� is always positive. The sign « - » translates the heat flows orientation towards low
temperatures.
In our case, the wall is homogeneous, then: �� = ��������
Also, the wall is flat, giving: S=S' (see diagram).
Consequently, we can write:
Equation 1
In a steady state case, the temperatures Ɵ
and Ɵ is a constant physical quantity of the system.
By applying this so-called Fourier's law, we can determine the relation involved.
2.2.2 Determination of the Relation Involved
Application of the Fourier's law given by the above equation 1:
Φ = ����
Applying the Fourier's law:
Φ . �� ( �� ) = −��. �� . ��(��)
Φ .
Φ. | �� |
Φ. ( �� − �� ) = −��. ��. (�� − �� )
Φ. ( �� − �� ) = ��. ��. (�� − �� ) where ( �� − �� ) = e (wall thickness)
Being Φ. e = ��. ��. (�� − �� )
The flow is then equal to:
with
ENGLISH
=> Φ ���� = −��������
��(��) = −�� . �� .
��(��)
= −�� . �� . | �� |
(
wall thermal resistance
.
����
Φ = ����
����
and Ɵ
are considered equal to constants;
1
2
��. ��. (�� − �� )
Φ =
��
).
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