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4. (30 Points) Pollutant concentration and heat transport equations are given by
Let
∂c
∂t
+ u
j
∂c
∂x
j
c = C +
2
∂ c
= α
∂x
∂x
c'
j
j
T = T +
T'
∂T
∂t
+ u
j
∂T
∂x
u = U + u
a. Find the equation governing the average concentration C and average temperature .
b. Find the transport equation for concentration-temperature correlation c' T'
c. Identify the terms in the equation for .
i
c' T'
j
2
∂ T
= α
∂x
∂x
i
'
i
j
j
T