Before being injected into a furnace, pulverized coal is preheated by passing it through a cylindrical tube whose surface is maintained at T sur = 1000 ° C . The coal pellets are suspended in an airflow and are known to move with a speed of 3 m/s. If the pellets may be approximated as spheres of 1-mm diameter and it may be assumed that they are heated by radiation transfer from the tube surface, how long must the tube be to heat coal entering at 25 ° C to a temperature of 600 ° C? Is the use of the lumped capacitance method justified?
Before being injected into a furnace, pulverized coal is preheated by passing it through a cylindrical tube whose surface is maintained at T sur = 1000 ° C . The coal pellets are suspended in an airflow and are known to move with a speed of 3 m/s. If the pellets may be approximated as spheres of 1-mm diameter and it may be assumed that they are heated by radiation transfer from the tube surface, how long must the tube be to heat coal entering at 25 ° C to a temperature of 600 ° C? Is the use of the lumped capacitance method justified?
Solution Summary: The author explains how to calculate the required time to heat the coal.
Before being injected into a furnace, pulverized coal is preheated by passing it through a cylindrical tube whose surface is maintained at
T
sur
=
1000
°
C
.
The coal pellets are suspended in an airflow and are known to move with a speed of 3 m/s. If the pellets may be approximated as spheres of 1-mm diameter and it may be assumed that they are heated by radiation transfer from the tube surface, how long must the tube be to heat coal entering at
25
°
C
to a temperature of
600
°
C?
Is the use of the lumped capacitance method justified?
A long and wide heated plate is maintained at uniform temperature. You have to calculate the
flux from the plate if a fluid is flowing over the plate at 1 m/s. The length of the plate in the direction of the
flow is 10 m. The fluid is air. Temperature of the plate is 60°C and temperature of
average
heat
81-3 u 10°C.
Water at 45.0oC flows over a large plate at a velocity of 30.0 cm/s. The plate is 1.0 m long (in the flow direction), and its surface is maintained at a uniform temperature of 5.0oC. Calculate the steady rate of heat transfer per unit width of the plate.
Properties The properties of air at 1 atm and the film temperature of (Ts+T∞)/2 = (5+45)/2 = 25°C are:
ρ = 996.6 kg/m3, k = 0.610 W/m.oC, μ = 0.854x10-3 kg/m.s, Pr = 5.85
Merrill et al. (1965) in a series of classic experiments studied the flow of blood in capillary tubes of various diameters. The blood had a hematocrit of 39.3 and the temperature was 20°C. They measured the pressure drop as a function of the flow rate for five tube diameters ranging from 288 to 850 μm. When they expressed the measured pressure drops in terms of the wall shear stress, and the volumetric flow rates in terms of the reduced average velocity, all of the data for the various tube sizes formed, within the experimental accuracy, a single line as predicted by the Rabinowitsch equation expressed in terms of reduced average velocity. From their results they provide the following values of the Casson parameters at 20°C: τy = 0.0289 dynes cm−2 and s = 0.229 (dynes s cm−2)1/2. Using these values for τy and s, show that the equation below for reduced average velocity provides an excellent fit to their data summarized in the following table.
(Wall shear stress) τw , dynes cm-2…
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