Consider the oil flowing in a pipe in Problem 10. The inlet temperature is (300 mathrm{~K}) and

Question:

Consider the oil flowing in a pipe in Problem 10.

The inlet temperature is \(300 \mathrm{~K}\) and the pipe is now heated electrically at a rate of \(76 \mathrm{~W} / \mathrm{m}^{2}\). Plot the wall temperature, the center temperature, and the bulk temperature as a function of position using the asymptotic solution for large length.

Verify that the cup mixing temperature in dimensionless units is equal to \(4 \zeta\).

Problem 10:

A pipe of diameter \(2 \mathrm{~cm}\) with an oil flow rate of \(0.02 \mathrm{~kg} / \mathrm{s}\) heated by a wall temperature of \(400 \mathrm{~K}\). The inlet temperature is \(300 \mathrm{~K}\).
Find and plot the radial temperature profile at a distance of \(5 \mathrm{~cm}\) from the entrance.
Find and plot the radial temperature profile at a distance of \(100 \mathrm{~cm}\) from the entrance.
If an outlet temperature of \(380 \mathrm{~K}\) is needed, what is the length of the heat exchanger needed? Use an average Nusselt-number value of 3.66 .
The following values for the physical properties are applicable: \(v=4 \times 10^{-5}, c_{p}=2120\), \(k=0.14\), and \(ho=1000\). All are in SI units.