Differential equation for temperature distribution inside a geometry having variable thermal
conductivity and cross-sectional area
L
&
Qx
system
x
x
x+x
Insulated surface
&
Q x + x
k=thermal conductivity
Ac=cross-sectional area
Apply first law of thermody
Heat and Mass Transfer (ENGG*3430)
Winter 2014 (Useful Math)
Useful Information:
&
&
First Law of Thermodynamics for closed system: Ein Eout = dE
dt
=
system
dU
dt
= mCv
system
dT
dT
= (V )Cv
dt
dt
Useful Integration:
x n +1
x dx = n + 1 + C1
1
ln(ax + b