EXPERIMENT # 1
INVESTIGATION OF FOURIER’S LAW FOR LINEAR CONDUCTION IN ONE DIMENSION ALONG A SINGLE BAR
Theory:
Fourier’s Law of Heat Conduction:
It states that,
“Flow of heat per unit is proportional to the temperature difference per unit length.”
i.e.
Q ̇/A=-k(dT/dx)
By re-writing above relation,
Q=dT/(dx/kA)
Where, dx/kA=Conductive Resistance of the material
Properties of “K”: It is a material property and a function of temperature. It may be different in different orientations.
Observation and Calculations:
Sr. No. Heat Supplied
(Watts) T1
(oC) T2
(oC) T3
(oC) T4
(oC) T5
(oC) T6
(oC) T7
(oC) T8
(oC) T9
(oC)
1 9.9 64 63.5 59.2 53.1 49.6 48.8 29.1 33.9 33.1
2 8.4 49.8 48.6 47.8 43.5 42.4 37.6 32.8 32.4 32.1
3 5.1 49.9 43.5 42.8 43.4 42 42.7 32.8 31.3 32.1 …show more content…
The heat exchanger has main application in thermal power plant and engines. A shell and tube heat exchanger has two concentric tubes the inner tube contains the hot fluid whereas the outer tube has cold fluid flowing in it. The heat exchange takes place from hot fluid to cold fluid and this heat exchange is governed mainly by conduction.
As we know,
Q=UA ∆T
For the parallel flow heat exchanger shown the heat transfer is given by, dq= -m_h c_h dT_h= m_c c_c dT_c
The heat transfer is also given as, dq=U(T_h-T_c )dA dT_h=(-dq)/(m_h c_h ) dT_c=dq/(m_c c_c ) dT_h- dT_c=d(T_h-T_c )= -dq(1/(m_h c_h )-1/(m_c c_c ))
Putting the value of dq from previous equation,
(dT_h- dT_c)/(T_h-T_c )=-U(1/(m_h c_h )-1/(m_c c_c ))dA ln (T_h2-T_c2)/(T_h1-T_c1 )=-UA(1/(m_h c_h )-1/(m_c c_c ))
m_h c_h=q/(T_h1-T_h2 ) m_c c_c=q/(T_c2-T_c1 )
Putting these values in the above
INVESTIGATION OF FOURIER’S LAW FOR LINEAR CONDUCTION IN ONE DIMENSION ALONG A SINGLE BAR
Theory:
Fourier’s Law of Heat Conduction:
It states that,
“Flow of heat per unit is proportional to the temperature difference per unit length.”
i.e.
Q ̇/A=-k(dT/dx)
By re-writing above relation,
Q=dT/(dx/kA)
Where, dx/kA=Conductive Resistance of the material
Properties of “K”: It is a material property and a function of temperature. It may be different in different orientations.
Observation and Calculations:
Sr. No. Heat Supplied
(Watts) T1
(oC) T2
(oC) T3
(oC) T4
(oC) T5
(oC) T6
(oC) T7
(oC) T8
(oC) T9
(oC)
1 9.9 64 63.5 59.2 53.1 49.6 48.8 29.1 33.9 33.1
2 8.4 49.8 48.6 47.8 43.5 42.4 37.6 32.8 32.4 32.1
3 5.1 49.9 43.5 42.8 43.4 42 42.7 32.8 31.3 32.1 …show more content…
The heat exchanger has main application in thermal power plant and engines. A shell and tube heat exchanger has two concentric tubes the inner tube contains the hot fluid whereas the outer tube has cold fluid flowing in it. The heat exchange takes place from hot fluid to cold fluid and this heat exchange is governed mainly by conduction.
As we know,
Q=UA ∆T
For the parallel flow heat exchanger shown the heat transfer is given by, dq= -m_h c_h dT_h= m_c c_c dT_c
The heat transfer is also given as, dq=U(T_h-T_c )dA dT_h=(-dq)/(m_h c_h ) dT_c=dq/(m_c c_c ) dT_h- dT_c=d(T_h-T_c )= -dq(1/(m_h c_h )-1/(m_c c_c ))
Putting the value of dq from previous equation,
(dT_h- dT_c)/(T_h-T_c )=-U(1/(m_h c_h )-1/(m_c c_c ))dA ln (T_h2-T_c2)/(T_h1-T_c1 )=-UA(1/(m_h c_h )-1/(m_c c_c ))
m_h c_h=q/(T_h1-T_h2 ) m_c c_c=q/(T_c2-T_c1 )
Putting these values in the above