A HEAT TRANSFER TEXTBOOK - THIRD EDITION Episode 3 Part 1 potx

9.6 Transition boiling and system influences Many system features influence the pool boiling behavior we have dis-cussed thus far.. It makes it clear that a change in the surface chemistry

§9.6 Transition boiling and system influences 489

or

qmin= 18, 990 W/m2From Fig 9.2 we read 20,000 W/m2, which is the same, within the

accuracy of the graph

9.6 Transition boiling and system influences

Many system features influence the pool boiling behavior we have

dis-cussed thus far These include forced convection, subcooling, gravity,

surface roughness and surface chemistry, and the heater configuration,

among others To understand one of the most serious of these—the

influ-ence of surface roughness and surface chemistry—we begin by thinking

about transition boiling, which is extremely sensitive to both

Surface condition and transition boiling

Less is known about transition boiling than about any other mode of

boiling Data are limited, and there is no comprehensive body of theory

The first systematic sets of accurate measurements of transition boiling

were reported by Berenson [9.30] in 1960 Figure9.14shows two sets of

his data

The upper set of curves shows the typical influence of surface

chem-istry on transition boiling It makes it clear that a change in the surface

chemistry has little effect on the boiling curve except in the transition

boiling region and the low heat flux film boiling region The oxidation of

the surface has the effect of changing the contact angle dramatically—

making it far easier for the liquid to wet the surface when it touches it

Transition boiling is more susceptible than any other mode to such a

change

The bottom set of curves shows the influence of surface roughness on

boiling In this case, nucleate boiling is far more susceptible to roughness

than any other mode of boiling except, perhaps, the very lowest end of the

film boiling range That is because as roughness increases the number

of active nucleation sites, the heat transfer rises in accordance with the

Yamagata relation, eqn (9.3)

It is important to recognize that neither roughness nor surface

chem-istry affects film boiling, because the liquid does not touch the heater

490

§9.6 Transition boiling and system influences 491

Figure 9.15 The transition boiling regime.

The fact that both effects appear to influence the lower film boiling range

means that they actually cause film boiling to break down by initiating

liquid–solid contact at low heat fluxes

Figure9.15shows what an actual boiling curve looks like under the

influence of a wetting (or even slightly wetting) contact angle This figure

is based on the work of Witte and Lienhard ([9.32] and [9.33]) On it are

identified a nucleate-transition and a film-transition boiling region These

are continuations of nucleate boiling behavior with decreasing liquid–

solid contact (as shown in Fig 9.3c) and of film boiling behavior with

increasing liquid–solid contact, respectively

These two regions of transition boiling are often connected by abrupt

jumps However, no one has yet seen how to predict where such jumps

take place Reference [9.33] is a full discussion of the hydrodynamic

theory of boiling, which includes an extended discussion of the transition

boiling problem and a correlation for the transition-film boiling heat flux

by Ramilison and Lienhard [9.34]

Figure9.14also indicates fairly accurately the influence of roughness

and surface chemistry on qmax It suggests that these influences mally can cause significant variations in qmax that are not predicted inthe hydrodynamic theory Ramilison et al [9.35] correlated these effects

nor-for large flat-plate heaters using the rms surface roughness, r in µm, and the receding contact angle for the liquid on the heater material, β r

in radians:

qmax

qmaxZ = 0.0336 (π − β r ) 3.0 r 0.0125 (9.36)This correlation collapses the data to±6% Uncorrected, variations from

the predictions of hydrodynamic theory reached 40% as a result of ness and finish Equivalent results are needed for other geometries

rough-Subcooling

A stationary pool will normally not remain below its saturation ature over an extended period of time When heat is transferred to thepool, the liquid soon becomes saturated—as it does in a teakettle (recallExperiment9.1) However, before a liquid comes up to temperature, or if

temper-a very smtemper-all rtemper-ate of forced convection continuously repltemper-aces wtemper-arm liquidwith cool liquid, we can justly ask what the effect of a cool liquid bulkmight be

Figure 9.16 shows how a typical boiling curve might be changed if

Tbulk < Tsat: We know, for example, that in laminar natural convection,

q will increase as (T w − Tbulk) 5/4 or as [(T w − Tsat) + ∆Tsub] 5/4, where

∆Tsub ≡ Tsat− Tbulk During nucleate boiling, the influence of subcooling

on q is known to be small The peak and minimum heat fluxes are known

to increase linearly with ∆Tsub These increases are quite significant The film boiling heat flux increases rather strongly, especially at lower

heat fluxes The influence of ∆Tsub on transitional boiling is not welldocumented

Gravity

The influence of gravity (or any other such body force) is of concern cause boiling processes frequently take place in rotating or acceleratingsystems The reduction of gravity has a significant impact on boiling

be-processes aboard space vehicles Since g appears explicitly in the tions for qmax, qmin, and qfilm boiling, we know what its influence is Both

equa-qmax and qmin increase directly as g 1/4 in finite bodies, and there is an

additional gravitational influence through the parameter L  However,

when gravity is small enough to reduce R below about 0.15, the

hydrody-§9.6 Transition boiling and system influences 493

Figure 9.16 The influence of subcooling on the boiling curve.

namic transitions deteriorate and eventually vanish altogether Although

Rohsenow’s equation suggests that q is proportional to g 1/2in the

nucle-ate boiling regime, other evidence suggests that the influence of gravity

on the nucleate boiling curve is very slight, apart from an indirect effect

on the onset of boiling

Forced convection

The influence of superposed flow on the pool boiling curve for a given

heater (e.g., Fig.9.2) is generally to improve heat transfer everywhere But

flow is particularly effective in raising qmax Let us look at the influence

of flow on the different regimes of boiling

Influences of forced convection on nucleate boiling Figure9.17showsnucleate boiling during the forced convection of water over a flat plate.Bergles and Rohsenow [9.36] offer an empirical strategy for predictingthe heat flux during nucleate flow boiling when the net vapor generation

is still relatively small (The photograph in Fig.9.17 shows how a stantial buildup of vapor can radically alter flow boiling behavior.) Theysuggest that

• qFCis the single-phase forced convection heat transfer for the heater,

as one might calculate using the methods of Chapters6and7

• q B is the pool boiling heat flux for that liquid and that heater from

eqn (9.4)

• q iis the heat flux from the pool boiling curve evaluated at the value

of (T w −Tsat) where boiling begins during flow boiling (see Fig.9.17)

An estimate of (T w − Tsat)onset can be made by intersecting the

forced convection equation q = hFC(T w − T b ) with the following

con-Peak heat flux in external flows The peak heat flux on a submerged

body is strongly augmented by an external flow around it Althoughknowledge of this area is still evolving, we do know from dimensionalanalysis that

qmax

ρ g h fg u ∞ = fnWeD , ρ f ρ g

(9.39)

§9.6 Transition boiling and system influences 495

Figure 9.17 Forced convection boiling on an external surface.

where the Weber number, We, is

Kheyrandish and Lienhard [9.38] suggest fairly complex expressions

of this form for qmax on horizontal cylinders in cross flows For a

cylin-drical liquid jet impinging on a heated disk of diameter D, Sharan and

Lienhard [9.39] obtained

qmax

ρ g h fg ujet =0.21 + 0.0017ρ f ρ g

djet D

range of the data

The influence of fluid flow on film boiling Bromley et al [9.40] showedthat the film boiling heat flux during forced flow normal to a cylindershould take the form

for u2∞ /(gD) ≥ 4 with h  fg from eqn (9.29) Their data fixed the constant

at 2.70 Witte [9.41] obtained the same relationship for flow over a sphereand recommended a value of 2.98 for the constant

Additional work in the literature deals with forced film boiling onplane surfaces and combined forced and subcooled film boiling in a vari-ety of geometries [9.42] Although these studies are beyond our presentscope, it is worth noting that one may attain very high cooling rates usingfilm boiling with both forced convection and subcooling

9.7 Forced convection boiling in tubes

Flowing fluids undergo boiling or condensation in many of the cases inwhich we transfer heat to fluids moving through tubes For example,such phase change occurs in all vapor-compression power cycles and

refrigerators When we use the terms boiler, condenser, steam generator,

or evaporator we usually refer to equipment that involves heat transfer

within tubes The prediction of heat transfer coefficients in these systems

is often essential to determining U and sizing the equipment So let us

consider the problem of predicting boiling heat transfer to liquids flowingthrough tubes

Figure 9.18 The development of a two-phase flow in a vertical

tube with a uniform wall heat flux (not to scale)

497

Relationship between heat transfer and temperature difference

Forced convection boiling in a tube or duct is a process that becomes veryhard to delineate because it takes so many forms In addition to the usualsystem variables that must be considered in pool boiling, the formation

of many regimes of boiling requires that we understand several boilingmechanisms and the transitions between them, as well

Collier and Thome’s excellent book, Convective Boiling and tion [9.43], provides a comprehensive discussion of the issues involved

Condensa-in forced convection boilCondensa-ing Figure9.18 is their representation of the

fairly simple case of flow of liquid in a uniform wall heat flux tube in

which body forces can be neglected This situation is representative of a

fairly low heat flux at the wall The vapor fraction, or quality, of the flow

increases steadily until the wall “dries out.” Then the wall temperaturerises rapidly With a very high wall heat flux, the pipe could burn outbefore dryout occurs

Figure9.19, also provided by Collier, shows how the regimes shown inFig.9.18are distributed in heat flux and in position along the tube Noticethat, at high enough heat fluxes, burnout can be made to occur at any sta-

tion in the pipe In the subcooled nucleate boiling regime (B in Fig.9.18)

and the low quality saturated regime (C), the heat transfer can be

pre-dicted using eqn (9.37) in Section 9.6 But in the subsequent regimes

of slug flow and annular flow (D, E, and F ) the heat transfer mechanism

changes substantially Nucleation is increasingly suppressed, and ization takes place mainly at the free surface of the liquid film on thetube wall

vapor-Most efforts to model flow boiling differentiate between

nucleate-boiling-controlled heat transfer and convective boiling heat transfer In

those regimes where fully developed nucleate boiling occurs (the later

parts of C), the heat transfer coefficient is essentially unaffected by the

mass flow rate and the flow quality Locally, conditions are similar to poolboiling In convective boiling, on the other hand, vaporization occursaway from the wall, with a liquid-phase convection process dominating

at the wall For example, in the annular regions E and F , heat is convected

from the wall by the liquid film, and vaporization occurs at the interface

of the film with the vapor in the core of the tube Convective boilingcan also dominate at low heat fluxes or high mass flow rates, where wallnucleate is again suppressed Vaporization then occurs mainly on en-trained bubbles in the core of the tube In convective boiling, the heattransfer coefficient is essentially independent of the heat flux, but it is

§9.7 Forced convection boiling in tubes 499

Figure 9.19 The influence of heat flux on two-phase flow behavior.

strongly affected by the mass flow rate and quality

Building a model to capture these complicated and competing trends

has presented a challenge to researchers for several decades One early

effort by Chen [9.44] used a weighted sum of a nucleate boiling heat

trans-fer coefficient and a convective boiling coefficient, where the weighting

depended on local flow conditions This model represents water data to

an accuracy of about ±30% [9.45], but it does not work well with most

other fluids Chen’s mechanistic approach was substantially improved

in a more complex version due to Steiner and Taborek [9.46] Many other

investigators have instead pursued correlations built from dimensional

analysis and physical reasoning

To proceed with a dimensional analysis, we first note that the liquid

and vapor phases may have different velocities Thus, we avoid

intro-ducing a flow speed and instead rely on the the superficial mass flux, G,

through the pipe:

Physical arguments then suggest that the dimensional functional

equa-tion for the flow boiling heat transfer coefficient, hfb, should take the following form for saturated flow in vertical tubes:

hfb= fnhlo, G, x, h fg , q w , ρ f , ρ g , D

(9.45)

It should be noted that other liquid properties, such as viscosity and

con-ductivity, are represented indirectly through hlo This functional tion has eight dimensional variables (and one dimensionless variable, x)

equa-in five dimensions (m, kg, s, J, K) We thus obtaequa-in three more

dimension-less groups to go with x, specifically

Bo≡ q w

§9.7 Forced convection boiling in tubes 501

Table 9.4 Fluid-dependent parameter F in the Kandlikar

cor-relation for copper tubing Additional values are given in [9.47]

When the convection number is large (Co  1), as for low quality,

nucleate boiling dominates In this range, hfb /hlorises with increasing Bo

and is approximately independent of Co When the convection number

is smaller, as at higher quality, the effect of the boiling number declines

and hfb /hloincreases with decreasing Co

Correlations having the general form of eqn (9.49) were developed

by Schrock and Grossman [9.48], Shah [9.49], and Gungor and

Winter-ton [9.50] Kandlikar [9.45, 9.47, 9.51] refined this approach further,

obtaining good accuracy and better capturing the parametric trends His

method is to calculate hfb/hlofrom each of the following two correlations

and to choose the larger value:

where “nbd” means “nucleate boiling dominant” and “cbd” means

“con-vective boiling dominant”

In these equations, the orientation factor, f o, is set to unity for

ver-tical tubes4 and F is a fluid-dependent parameter whose value is given

4 The value for horizontal tubes is given in eqn (9.52).

in Table9.4 The parameter F arises here for the same reason that

fluid-dependent parameters appear in nucleate boiling correlations: surfacetension, contact angles, and other fluid-dependent variables influencenucleation and bubble growth The values in Table9.4are for commer-cial grades of copper tubing For stainless steel tubing, Kandlikar recom-

mends F = 1 for all fluids Equations (9.50) are applicable for the

satu-rated boiling regimes (C through F ) with quality in the range 0 < x ≤ 0.8.

For subcooled conditions, see Problem9.21

Example 9.9

0.6 kg/s of saturated H2O at T b = 207 ◦C flows in a 5 cm diameter

ver-tical tube heated at a rate of 184,000 W/m2 Find the wall temperature

at a point where the quality x is 20%.

Solution. Data for water are taken from Tables A.3–A.5 We first

compute hlo

G = A m˙

pipe = 0.001964 0.6 = 305.6 kg/m2sand

Relo= GD

µ f = (305.6)(0.05) 1.297 × 10 −4 = 1.178 × 105From eqns (7.42) and (7.43):

in Table9.4 The parameter F arises here for the same reason that

fluid-dependent parameters appear in...

497

Relationship between heat transfer and temperature difference

Forced... flow and annular flow (D, E, and F ) the heat transfer mechanism

changes substantially Nucleation is increasingly suppressed, and ization takes place mainly at the free surface of the