Engine oil at
flows over a
-m-long flat plate whose temperature is
with a velocity of
. Determine the total drag force and rate of heat transfer over the entire plate per unit width.
Solution:
Firstly we find the film temperature, which is the average of the temperature of the surface and the temperature of the free stream medium.
.
The fluid properties of oil are then evaluated at this temperature. For this we turn to our data tables, and since they normally have intervals of
, we would linearly interpolate between the values to get our constants. That is we would use
, which since we're going to need four constants means we have to do this four times (this is the annoying part -.-).
So we're given this for the properties of Engine Oil from the data table.
Interpolating gives
Now to find out the behavior of the flow (that is whether it is Laminar, Transitional or Turbulent), we need to find the Reynolds number, which is a dimensionless constant given by
.
We are told that the critical Reynolds number is
, since this is less than that we have a Laminar Flow.
Now to find the rate of heat transfer, we need the heat transfer coefficient,
, but to find this we need to find another dimensionless constant, the Nusselt Number, Nu. The relationship between Nu and Re, Pr will change depending on the flow. We look at the formula sheet which has three relationships for Laminar, Transitional and Turbulent flows, which as we know the flow is turbulent comes out to be
given that
, which is true.
Now we can find the rate of heat transfer, using
.