Page 380 - Bird R.B. Transport phenomena

362 Chapter 11 The Equations of Change for Nonisothermal Systems

11A.3. Transpiration cooling.
(a) Calculate the temperature distribution between the two shells of Example 11.4-4 for radial
mass flow rates of zero and 10"° g/s for the following conditions:

R = 500 microns T R = 300°C
KR = 100 microns T = 100°C
K
к = 6.13 X 10~ cal/cm -s -C
5
C p = 0.25 cal/g • С
(b) Compare the rates of heat conduction to the surface at KR in the presence and absence of
convection.
11A.4. Free-convection heat loss from a vertical surface. A small heating panel consists essentially
of a flat, vertical, rectangular surface 30 cm high and 50 cm wide. Estimate the total rate of
heat loss from one side of this panel by free convection, if the panel surface is at 150°F, and
the surrounding air is at 70°F and 1 atm. Use the value С = 0.548 of Lorenz in Eq. 11.4-51 and
the value of С recommended by Whitaker, and compare the results of the two calculations.
Answer: 8.1 cal/sec by Lorenz expression

11A.5. Velocity, temperature, and pressure changes in a shock wave. Air at 1 atm and 70°F is flow-
ing at an upstream Mach number of 2 across a stationary shock wave. Calculate the following
quantities, assuming that у is constant at 1.4 and that C p = 0.24 Btu/lb m • F:
(a) The initial velocity of the air.
(b) The velocity, temperature, and pressure downstream from the shock wave.
(c) The changes of internal and kinetic energy across the shock wave.
Answer: (a) 2250 ft/s
(b) 844 ft/s; 888 R; 4.48 atm
(c) AU = +61.4 Btu/lb ; AK - 86.9 Btu/lb
w m
11A.6. Adiabatic frictionless compression of an ideal gas. Calculate the temperature attained by
compressing air, initially at 100°F and 1 atm, to 0.1 of its initial volume. It is assumed that у =
1.40 and that the compression is frictionless and adiabatic. Discuss the result in relation to the
operation of an internal combustion engine.
Answer: 950°F

11 A.7. Effect of free convection on the insulating value of a horizontal air space. Two large parallel
horizontal metal plates are separated by a 2.5 cm air gap, with the air at an average temperature
of 100°C. How much hotter may the lower plate be (than the upper plate) without causing the
onset of the cellular free convection discussed in Example 11.5-2? How much may this tempera-
ture difference be increased if a very thin metal sheet is placed midway between the two plates?
Answers: Approximately 3 and 48°C, respectively.
11B.1. Adiabatic frictionless processes in an ideal gas.
(a) Note that a gas that obeys the ideal gas law may deviate appreciably from C p = constant.
Hence, rework Example 11.4-6 using a molar heat capacity expression of the form

(b) Determine the final pressure, p , required if methane (CH ) is to be heated from 300K and
2
4
1 atm to 800K by adiabatic frictionless compression. The recommended empirical constants 1

1
O. A. Hougen, K. M. Watson, and R. A. Ragatz, Chemical Process Principles, Part 1,2nd edition, Wiley,
New York (1958), p. 255. See also Part II, pp. 646-653, for a fuller discussion of isentropic process calculations.