A series of experiments were conducted by passing 40°C air over a long 25-mm-diameter cylinder with an embedded electrical heater. The objective of these experiments was to determine the power per unit length required to maintain the surface temperature of the cylinder at 300°C for different air velocities (V). The results of these experiments are given in the following table:

Question

(a) Assuming a uniform temperature over the cylinder, negligible radiation between the cylinder surface and surroundings, and steady-state conditions, determine the convection heat transfer coefficient (h) for each velocity (V). Plot the results in terms of h (W/m2•K)?vs. V (m/s). Provide a computer-generated graph for the display of your results, and tabulate the data used for the graph.



(b) Assume that the heat transfer coefficient and velocity can be expressed in the form h = CVn. Determine the values of the constants C and n from the results of part (a) by plotting h vs. V on log-log coordinates and choosing a C value that assures a match at V = 1 m/s and then varying n to get the best fit.

Answer 1

Power required to maintain the surface temperature of a long, 25 mm diameter cylinder with an imbedded electrical heater for different air velocities.

Assumptions 1 Temperature is uniform over the cylinder surface. 2 Negligible radiation exchange between the cylinder surface and the surroundings. 3 Steady state conditions.

Analysis (a) From an overall energy balance on the cylinder, the power dissipated by the electrical heater is transferred by convection to the air stream. Using Newton’s law of cooling on a per unit length basis,



where is the electrical power dissipated per unit length of the cylinder. For the V = 1 m/s condition, using the data from the table given in the problem statement, find



Repeating the calculations for the rest of the V values given, find the convection coefficients for the remaining conditions in the table. The results are tabulated and plotted below. Note that h is not linear with respect to the air velocity.



(b) To determine the constants C and n, plot h vs. V on log-log coordinates. Choosing C = 22.12 W/m2.K(s/m)n, assuring a match at V = 1, we can readily find the exponent n from the slope of the h vs. V curve. From the trials with n = 0.8, 0.6 and 0.5, we recognize that n = 0.6 is a reasonable choice. Hence, the best values of the constants are: C = 22.12 and n = 0.6. The details of these trials are given in the following table and plot.