BOILING HEAT TRANSFER

Boiling occurs at the solid liquid interface when a liquid brought into a contact with a surface maintained at a temperature Tw sufficiently above the saturation temperature Tsat of the liquid.

OR, when a surface is exposed to a liquid and is maintained at a temperature above the saturation temperature of the liquid, boiling occurs & the heat flux will depend on the difference of the temp. between the surface and the saturation temperature.

Boiling heat flux:-

qboiling=h(Tw-Tsat)=h∆Texcess --------------- (1) ∆Texcess = excess temp.

Boiling heat transfer depends on:

µ, ķ, ρ, Cp, hfg and σ (surface tension)

If T↑ then σ ↓

Bubbles are their existence to the surface tension σ at the liquid vapor interface.

Surface Tension: Attraction force on the molecules at the interface towards the liquid phase.

Force balance on the vapour bubble:

Consider a spherical bubble. Pressure force =∏r2(pv-pl)

Surface tension force =2∏r σ pv= vapor pressure inside bubble

Pl=liquid pressure

σ =surface tension of the vapor liquid interface

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Force balance,

∏r2(pv-pl) =2∏r σ

Or, pv-pl = -----------(2)

Bubble in pressure equilibrium.

When vapor collapse:

Temperature of the vapor inside the bubble = saturation temp. corresponding to vaqpour pressure pv

Temperature of the liquid = saturation temp. corresponding to liquid pressure pl

Tsat at pv > Tsat at pl

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=>Heat is conducted out of bubble.

=> vapor outside the bubble condense(collaspse)

Classification of boiling:- Depending of bulk fluid motion

I. Pool boilingII. Flow boiling (forced convection boiling)

Pool boiling: the heated surface is submerged below a free surface of liquid. No bulk fluid flow. Any motion of the fluid is due to natural convection currents and the motion of the bubbles under the influence of the buoyancy.

Examples of pool boiling:- Boiling of the tap water in a pan on the top of the stove. At the early stages of boiling , some bubbles that stick to the surface of the pan are caused by the release of the air molecules dissolved in liquid water.

Flow boiling: it occurs under the action of presence of bulk fluid flow. In flow boiling the fluid is forced to move by an external source such as a pump as it undergoes a phase change process.

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Flow boiling →1. External flow boiling (fire tube boiler)

2. Internal flow boiling (water tube boiler)

1. External flow boiling: External flow boiling over a flay plate or cylinder is simslar to pool boiling , but the added motion increases both the nuclute boiling heat flux and the critical heat flux considerably.

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Fig: External flow boiling

2. Internal flow boiling: Internal flow boiling is much more complicated in nature because there is no free surface for the vapor to collapse, and thus both the liquid and the vapor are forced to flow together. The two phase flow in a tube exhibits different flow boiling regimes, de3pending on the relative components of the liquid and the vapor phases.

Depending of bulk liquid temperature:I. Sub cooled or local boiling.

II. Saturated or bulk boiling

Sub cooled or local boiling: the temp. of the liquid is below the saturation temp. Saturated or bulk boiling : the temp. of the liquid is maintained at the saturation temp.

Sub cooled or local boiling → Saturated boiling Bubbles as energy movers.

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Examples of Forced convection(liquid):

Bubble flow Slug flow Annular flow Transition flow Mist flow

Boiling Heat Transfer curve:-

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The general shape of the boiling heat transfer curve remains the same for different fluids. The specific shape of the curve depends on the fluid heating surface material combination and the fluid pressure but it is practically dependent of the geometry of the heating surface.

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1Region 1:

1?? Page 7 of 13

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Free convection currents are responsible for motion of the fluid near the surface. The liquid near the surface is superheated slightly(no bubbles until liquid temperature is few degrees above the saturation temperature)&is subsequently evaporates when it rises to the surface.

Region 2:

Bubbles begin to form on the surface of the wire and are dissipated in the liquid after breaking away from the surface. this region indicates the beginning of nucleate boiling.

The space vacated by the rising bubbles is filled by the liquid in the vicinity of the heater surface. The stirring& agitation caused by the entrainment of the liquid to the heater surface is primarily responsible for the increased heat transfer coefficient & heat flux in this region. Page 6of 11

Region 3:

The heater temperature is further increased & bubbles form at such great rates at such a large number of nucleation sites that they form numerous continuous columns of vapor in the liquid. These bubbles move all the way up to the free surface, where they break up & release their vapor content. The large heat fluxes & heat transfer coefficient in this region are caused by the combined effect of liquid entrainment & evaporation.

Region 4:

When the heater temperature is further increased, bubbles form more rapidly that they blanket the heating surface & prevent the inflow of fresh liquid from taking their place.At this point the bubbles coalesce& form a vapor film which covers the surface. The heat must be conducted through this film causes a reduction in heat flux. This region is a transition from nucleate boiling to film boiling & is unstable.

Region 5:

Stable film boiling regime.

Region 6:

The surface temperature required to maintain stable film boiling are high& once this condition .

Critical or maximum heat flux:- The heat flux at point a is called the critical or maximum heat flux. For water critical heat flux exceeds 1 MW/m2.

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Nucleate boiling is the most desirable boiling regime in practice because high heat transfer rates can be achieved in this regime with relatively small values of ∆Texcess.

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Peak heat flux:-

The peak heat flux for Nucleate boiling is indicated as point a in fig (9.3). Zuber has developed an analytical expression for the peak heat flux in nucleate boiling by considering the stability requirements of the interface between the vapor film and liquid. This relation is

qmax = hfg ρν [ ]1/4 (1+ ) ½ …………………………….(9.37)

Heat Transfer Correlation in Pool boiling:-

Nucleate Boiling:Rohse now correlated experimental data for nucleate pool boiling,

Csf[ { }]0.33

Or,[ ]3= { }

Or, , q= µlhfg[ ]1/2[ ]3---------------------(9.33)

Where,q = heat flux, w/m2

µl = liquid viscosity, kg/m.shfg = enthalpy of vaporization, J/kgg = gravitational acceleration, m/secρl = Density of saturated liquid, kg/m3

ρν = Density of saturated vapor, kg/m3

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σ = Surface tension of liquid vapor interface, N/mCpl = Specific heat of the saturated liquid, J/kg.KΔTexcess= Temperature excess = Tw-Tsat, KPrl = Prandtl Number of saturated liquid s = Experimental constant that depend on the fluid.

= 1.0 for water, 1.7 for other liquids. Cst=experimental constants depend on Scarface –liquid combination, table (9.2)-HolmanFluid properties of equation (9.33) are to be evaluated at Tsat . The rate of heat transfer in during nucleate boiling is essentially independent of the geometry and orientation of the heated

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surface. þ↑ hfg↓ q↑.

If P is increased hfg decreased and q will be increased

# Water is to boiled at atmospheric pressure in a mechanically polished stainless steel pan placed on top of a heating unit .The inner surface of the bottom of the pan is maintained at 108℃.If the diameter of the bottom of the pan is 30 cm , determine (a) the rate of heat transfer to the water and (b) the rate of evaporation of water.Solution:Tsat=100℃(Corresponding to 1 atm)Tw108℃For Tsat=100℃σ =58.8mN/m (Table 9.1.Holman)=0.0588 N/mΡl=957.9 kg/m3, ρv=.6 kg/m3 (Steam stable)Prl=1.75 , hfg =2257 kj/kg (Table -9)μ l =2.82×10-4kg/m.sCpl =4217 j/kg.kCsf =0.0132 Table (9.2) HolmanFor water mechanically polished stainless steel

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S=1.0 For water

Equation (9.33)

q = 2.82 -4 2257 1000[ ]1/2 [ ]3

=68912.9 w/m2

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Rate of heat transfer,

Q = qA =68912.9 π/4 ( )2 watt

= 4871.2 watt

Rate of evaporation of water

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m= = = 2.16 10-3 kg/sec

Problem: Water in a tank is to be boiled at sea level by 1 cm diameter nickel plated heating element (csf =0.013) equipped with electrical resistance wires inside . determine the maxm heat flux that can be attained in the nucleate boiling regime & the surface temp r

of the heater surface in that case .

Solution : Tsat = 1000c

α = 0.0588 N/m Table (9.1), Holman

ρl = 957.9 kg / m3 table (A-9), holman s = 1

cpl = 4217 j/kg.k csf =0.013

hfg = k j/kg

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prl = 1.75

μl =2.82 10-4 kg / m.s

ρv = 0 .6 kg/m3 (steam table)

equition (9.37)

qmax = 2257 1000 0.6 [ ]1/4 (1+ ) ½

=1109352.1 w/m2

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From equition (9.33)

Ggg q = μl hfg [ ]1/2 [ ]3

Or, ( 1/2 ( )3 = ( Tw- Tsat )3

Or, Tw = ( )1/3 ( )1/6 ( ) + Tsat

= ( )1/3 ( )1/6 ( ) +100

= 119.90C

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Film boiling heat transfer:

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Bromley suggests heat transfer coefficient s in the stable film boiling region on a horizontal tube:

h = hb ( )1/3 +hr …………………. (9.42)

Where hb = 0.62 [ ]1/4 ………………(9.41)

(Considering only conduction)

d = Tube diameter

hr = ……………………………………………… (9.43)

Where = Stefan – Boltzmann constant

= Emissivity of the surface

Vapor properties at Tf =

µl , ρl , hfg at Tsat

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Holman: 9.3: Q/A or q

9.4: Q

9.5:

Ozisik: 10.5: q and m, [10.34] Holman 9.33 equation

10.6: [10.34] equation

10.7: [10.34] equation

10.8: [10.34] and [10.35] ozisik, Holman [9.33, 9.37]

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***THE END***

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