The products of combustion from a burner are routed to an industrial application through a thin-walled metallic duct of diameter
Di=1 m and length L=100 m. The gas enters the duct at atmospheric pressure and a mean temperature and velocity of Tm,i=1600 K and Um,i=10 m/s, respectively. It must exit the duct at a temperature that is no less than Tm,o=1400 K. What is the minimum thickness of an alumina-silica insulation (Kins=0.125 W/m*K) needed to meet the outlet requirement under worst case conditions for which the duct is exposed to ambient air at T[infinity]=250 K and a cross-flow velocity of V=15 m/s? The properties of the gas may be approximated as those of air, and as a first estimate, the effect of the insulation thickness on the convection coefficient and the thermal resistance associated with the cross flow may be neglected.
1 answer:
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Explanation:
Consider a fluid of density, ρ moving with a velocity, U over a flat plate of length, L.
Let the Kinematic viscosity of the fluid be ν.
Let the flow over the fluid be laminar for a distance x from the leading edge.
Now this distance is called the critical distance.
Therefore, for a laminar flow, the critical distance can be defined as the distance from the leading edge of the plate where the Reynolds number is equal to 5 x
And Reynolds number is a dimensionless number which determines whether a flow is laminar or turbulent.
Mathematically, we can write,
Re =
or 5 x =
( for a laminar flow )
Therefore, critical distance
So x is defined as the critical distance upto which the flow is laminar.
Answer:
The function is and the constant of integration is
.
Explanation:
The resultant expression is equal to the sum of a constant multiplied by the integral of a given function and an integration constant. That is:
Where:
- Constant, dimensionless.
- Integration constant, dimensionless.
By comparing terms, ,
and
. Then,
is determined by deriving the cosine function:
The function is and the constant of integration is
.