Modern Engineering Thermodynamics

4.13 Heat Transfer Modes 129
Table 4.7 Thermal Conductivity of Various Materials
Thermal Conductivity k t
Material
Temperature (°C/°F) Btu/(h ·ft ·R) W/(m·K)
Air (14.7 psia) 27/81 0.015 0.026
Hydrogen (14.7 psia) 27/81 0.105 0.182
Saturated water vapor (14.7 psia) 100/212 0.014 0.024
Saturated liquid water (14.7 psia) 0/32 0.343 0.594
Engine oil 20/68 0.084 0.145
Mercury 20/68 5.02 8.69
Window glass 20/68 0.45 0.78
Glass wool 20/68 0.022 0.038
Aluminum (pure) 20/68 118.0 204.0
Copper (pure) 20/68 223.0 386.0
Carbon steel (1% carbon) 20/68 25.0 43.0
4.13.2 Convection
Convective heat transfer occurs whenever an object is either hotter or colder than the surrounding fluid. The
basic equation of convection heat transfer is Newton’s law of cooling:
_Q conv = hAðT ∞ − T s Þ (4.76)
where _Q conv is the convection heat transfer rate, h is the convective heat transfer coefficient, A is the surface area
of the object being cooled or heated, T ∞ is the bulk temperature of the surrounding fluid, and T s is the surface
temperature of the object. The algebraic sign of Newton’s law of cooling has been chosen to be positive for
T ∞ > T s (i.e., for heat transfer into the object). This corresponds to our thermodynamic sign convention for heat
transfer when the object is the system. The convective heat transfer coefficient h is always a positive, empirically
determined value. Table 4.8 lists typical heat transfer coefficients.
4.13.3 Radiation
All electromagnetic radiation is classified as radiation heat transfer. Infrared, ultraviolet, visible light, radio and
television waves, X rays, and so on are all forms of radiation heat transfer. The radiation heat transfer between
two objects situated in a nonabsorbing or emitting medium is given by the Stefan-Boltzmann law:
_Q rad = F 1−2 ε 1 A 1 σðT 4 2 − T4 1 Þ (4.77)
where _Q rad is the radiation heat transfer rate, F 1–2 is called the view factor between objects 1 and 2 (it describes how
well object 1 “sees” object 2), ε 1 is the dimensionless emissivity or absorptivity (the hotter object is said to emit
energy while the colder object absorbs energy) of object 1, A 1 is the surface area of object 1, σ is the Stefan-
Boltzmann constant (5.69 × 10 −8 W/m 2 · K 4 or 0.1714 × 10 −8 Btu/h · ft 2 · R 4 ), and T 1 and T 2 are the surface
temperatures of the objects. A black object is defined to be any object whose emissivity is ε = 1.0. Table 4.9 lists
some typical emissivity values. Also, if object 1 is completely enclosed by object 2, then F 1–2 = 1.0. For a completely
enclosed black object, the Stefan-Boltzmann law reduces to
ð _Q rad Þ black
= A 1 σðT2 4 − T4 1 Þ (4.78)
enclosed
Table 4.8 Typical Values of the Convective Heat Transfer Coefficient
Convective Heat Transfer Coefficient h
Type of Convection
Btu/(h · ft 2 · R)
W/(m 2 ·k)
Air, free convection 1–5 2.5–25
Air, forced convection 2–100 10–500
Liquids, forced convection 20–3000 100–15,000
Boiling water 500–5000 2500–25,000
Condensing water vapor 1000–20,000 5000–100,000