Answer:
a)In Q= - 200 W
Out Q = 0 W
b)h = 2.89 W/m²·K
Explanation:
T(x) = a + bx + cx²
T(x) = 350 -100 x + 50 x²
[tex]\dfrac{dT}{dx} = -100 + 100 x[/tex]
a)
We know that
[tex]Q=-K\dfrac{dT}{dx}[/tex]
In condition : x= 0
[tex]\dfrac{dT}{dx} = -100 + 100 x[/tex]
Put x= 0
[tex]\dfrac{dT}{dx} = -100[/tex]
[tex]Q=-K\dfrac{dT}{dx}[/tex]
K= 2 W/m·K
Q = -100 x 2 = - 200 W
Exit condition : x= 1
[tex]\dfrac{dT}{dx} = -100 + 100 x[/tex]
Put x= 1
[tex]\dfrac{dT}{dx} = -100 + 100\times 1[/tex]
[tex]\dfrac{dT}{dx} = 0[/tex]
It means that right side of wall is insulated.
b)
Lets take h is the convection coefficient of fluid
Q= h ΔT
T(x) = 350 -100 x + 50 x²
At x = 0 , T= 350 K
So
ΔT = 350 - (273+10) = 350 - 283 K
ΔT = 67 K
Q= h ΔT
200 = h x 67
h = 2.89 W/m²·K
