Question

Air at a pressure of 6000 N/m^2 and a temperature of 300C flows with a velocity of 10 m/sec over a flat plate of length 0.5 m. Estimate the rate of cooling per unit width of the plateneeded to maintain it at a surface temperature of 27C.

Answer 1

`Q=hA(T_(w)-T_(inf))=16.97*0.5(27-300)=-2316.4J`

Step-by-step explanation:

To solve this problem we use the expression for the temperature film

`T_(f)=(T_(\inf)+T_(w))/(2)=(300+27)/(2)=163.5`

Then, we have to compute the Reynolds number

`Re=(uL)/(v)=\frac{10(m)/(s)*0.5m}{16.96*10^(-6)\rfac{m^(2)}{s}}=2.94*10^(5)`

Re<5*10^{5}, hence, this case if about a laminar flow.

Then, we compute the Nusselt number

`Nu_(x)=0.332(Re)^{(1)/(2)}(Pr)^{(1)/(3)}=0.332(2.94*10^(5))^{(1)/(2)}(0.699)^{(1)/(3)}=159.77`

but we also now that

`Nu_(x)=(h_(x)L)/(k)\\h_(x)=(Nu_(x)k)/(L)=(159.77*26.56*10^(-3))/(0.5)=8.48\\`

but the average heat transfer coefficient is h=2hx

h=2(8.48)=16.97W/m^{2}K

Finally we have that the heat transfer is

`Q=hA(T_(w)-T_(inf))=16.97*0.5(27-300)=-2316.4J`

In this solution we took values for water properties of

v=16.96*10^{-6}m^{2}s

Pr=0.699

k=26.56*10^{-3}W/mK

A=1*0.5m^{2}

I hope this is useful for you

regards