Page 245 - Fluid mechanics, heat transfer, and mass transfer

8

DIMENSIONLESS NUMBERS, TEMPERATURE
MEASUREMENT, AND CONDUCTION HEAT TRANSFER

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8.1 Important Dimensionless Groups in Heat Transfer 225 & Grashof number (N Gr ): L r bg Dt/m is the ratio of
8.2 Temperature Measurement 226 buoyancy force to viscous force acting on a fluid. L is
8.3 Conduction Heat Transfer 232 characteristic length. It is generally used to model
8.3.1 Thermal Insulation 236 natural convection.
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& Rayleigh number (N Ra ): N Gr N Pr ¼ L r gbC p DT/
ma is the quantity that governs natural convection
heat transfer.

& Graetz number (N Gz ): WC p /kL ¼ D i /LN Re N Pr
characterizes laminar flow in a conduit. Ratio of the
sensible heat change of the flowing fluid to the rate of
8.1 IMPORTANT DIMENSIONLESS GROUPS IN
heat conduction through a film of thickness D or L.
HEAT TRANSFER
& Biot number (N Bi ): hL/k is the ratio of the internal
. Name dimensionless groups of importance in heat
thermal resistance to the external thermal resistance.
transfer and state their physical significance (other than
It represents the relative importance of the thermal
those mentioned in Chapter 1).
resistance within a solid body.
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& Fourier number (N Fo ): ku/rC p L is the ratio of the rate
of heat transfer by conduction to the rate of energy & Stanton number (N St ): h/C p Vr ¼ N Nu /N Re N Pr
measures the ratio of the heat transferred into a fluid
storage in the system.
to the thermal capacity of the fluid. Used in forced
& Prandtl number (N Pr ): C p m/k is the ratio of momen-
convection.
tum diffusivity (m) and thermal diffusivity. Since it is
2
1/3
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& Condensation number (N Co ): (h/k)(m /r g) .
a material property, Prandtl number depends only on
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& Vapor condensation number (N Cv ): L r gl/kDt.
the physical conditions (temperature and pressure)
that a material is held at, not on the system in which it & Bond number, B d , is the ratio of gravity forces to
is placed. surface tension forces and is significant in drainage of
& Peclet number (N Re N Pr ): DVrC p /k is the convec- condensate from heat exchanger surfaces and is
tive transport/diffusive transport. useful in the design of finned surfaces for efficient
drainage of condensate.
& Nusselt number (N Nu ): hD/k is the ratio of convective
heat transfer to conductive heat transfer in the fluid & Bond number at the base of a fin can be approximated
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perpendicular to flow direction. Measures enhance- by B d ¼ (r l r g )ge /su m , where r l and r g are the
ment of heat transfer from a surface that occurs in a liquid and vapor densities, e is the fin height, s is
real situation compared to heat transferred if only surface tension, and u m is fin angle.
conduction occurred. Nusselt number conveys how ➢ If the surface tension forces are dominant over
important convection is compared to conduction. It gravity forces, the condensate drainage is deter-
involves a heat transfer coefficient and a character- mined by surface tension.
istic length, both of which depend on the type of ➢ B d ¼ 1 implies that surface tension forces are equal
system one is using. to gravity forces at the end of the fin and that
Fluid Mechanics, Heat Transfer, and Mass Transfer: Chemical Engineering Practice, By K. S. N. Raju
Copyright Ó 2011 John Wiley & Sons, Inc.

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