CONDENSATION. Prabal Talukdar. Associate Professor Department of Mechanical Engineering IIT Delhi

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1 CONDENSATION Praba Taukdar Associate Professor Department of Mechanica Engineering IIT Dehi E-mai:

2 Condensation When a vapor is exposed to a surface at a temperature beow T sat, condensation in the form of a iquid fim or individua dropets occurs on the surface. Condensation can aso occur on the free surface of a iquid or even in a gas other than soid surfaces P.Taukdar/Mech- 2

3 Fim vs. Dropwise In fim condensation, the surface is banketed by a iquid id fim of increasing i thickness, and this iquid wa between soid surface and the vapor serves as a resistance to heat transfer. In dropwise condensation, however, the dropets side down when they reach a certain size, cearing the surface and exposing it to vapor. There is no iquid fim in this case to resist heat transfer. As a resut, heat transfer rates are more than 10 times arger in dropwise condensation. P.Taukdar/Mech- 3

soid surface and the vapor serves as a resistance to heat transfer.

4 Fim Condensation on a Vertica Pate heat transfer in condensation aso depends on whether the condensate fow is aminar or turbuent Re D h DhV μ 4Ac 4 P fim thickness at the owest part of the fow P.Taukdar/Mech- Re D h V μ 4m & pμ 4

aminar or turbuent Re D h DhV μ 4Ac 4 P fim thickness at

5 Hydrauic Diameter Modified Latent Heat of Vaporization: h * fg h C (T T ) + C (T T fg p sat s pv v sat ) With these considerations, the rate of heat transfer can be expressed as * Q& condenser ha s(t s T sat ) m& h fg P.Taukdar/Mech- Re D μ h V 4m& pμ 5

considerations, the rate of heat transfer can be expressed as *

6 Re 4Q & pμ conden * h fg 4A s h(t pμ sat * h fg T ) s the properties of the iquid shoud be evauated at the fim temperature T f (T sat + T s )/2, which is approximatey the average temperature of the iquid Fow Regimes P.Taukdar/Mech- 6

7 Heat Transfer Correations for Fim Condensation P.Taukdar/Mech- Assumptions: 1. Both T s and T sat, are maintained constant and the temperature acrosstheiquid fim varies ineary. 2. Heat transfer across the iquid fim is by pure conduction. 3. The veocity of the vapor is ow (or zero) so that it exerts no drag on the condensate (no viscous shear on the iquid vapor interface). 4. The fow of the condensate is aminar and the properties of the iquid are constant. 5. The acceeration of the condensate ayer is negigibe. 7

Heat transfer across the iquid fim is by pure conduction. 3.

8 Then Newton s second aw of motion for the voume eement in the vertica x-direction can be written as Fx max 0 Weight Viscous shear force + Buoyancy Force g( y)(bdx) μ du (bdx) + dy v g( y)(bdx) Canceing the pate width b and soving for du/dy gives du g( v)( y) dy μ P.Taukdar/Mech- 8

Buoyancy Force g( y)(bdx) μ du (bdx) + dy v g( y)(bdx) Canceing the

9 Integrating from y 0 where u 0 (because of the nosip boundary condition) to y y where u u(y) gives u(y) g( μ v ) y 2 y 2 m& The mass fow rate of the condensate at a ocation x, where the boundary ayer thickness is, is determined from (x) u(y)da A y 0 u(y)bdy whose derivative with respect to x is gb ( 3μ v ) 3 dm& dx 2 This represents the gb ( v ) d rate of condensation of μ dx vapor over a vertica distance dx The rate of heat transfer from the vapor to the pate through the iquid fim is simpy equa to the heat reeased as the vapor is condensed and is expressed as Tsat Ts d Q& h dm& k (bdx) P.Taukdar/Mech- dm& dx fg kb T h fg sat T s 9

This represents the gb ( v ) d rate of condensation of μ dx vapor over a vertica distance dx The rate of heat transfer from the vapor to the pate through the

10 3 d μk(t g ( sat T )h v s ) fg dx Integrating from x 0 where 0 (the top of the pate) to x x where (x), the iquid fim thickness at any ocation x is determined to be (x) 4 μ k(tsat Ts )x g( v)hfg 1/ 4 q& The heat transfer rate from the vapor to the pate at a ocation x can be expressed as x h h x x P.Taukdar/Mech- (T sat k (x) T s ) k h(x) T sat T s g ( v )hfg k 4μ(Tsat Ts )x 1 L 4 h have h xdx hx L L / 4 10

heat transfer rate from the vapor to the pate at a ocation x can be expressed as x h h x x P.

11 Incuding the effects of the noninear temperature profie in the iquid fim and the cooing of the iquid beow the saturation temperature, the average h for a vertica pate of ength L is: * 3 1/ 4 g ( v)h fgk h vertica μ(tsat Ts )L 4 h vertica have h x 3 k k h x L L (L) (L) hx L W/m 2 C, 0 < Re < 30 4k 3h vertica 1/ 4 1/ 4 4μk(T sat Ts )x 4μk(T sat Ts ) x ( x) g( v)hfg ghfg m(x) & gb ( 3μ v ) 3 gb 3μ 3 << v Re 4m& pμ P.Taukdar/Mech g k 4g k h μ x L 3ν 3h vertica /

943 μ(tsat Ts )L 4 h vertica have h x 3 k k h x L L (L) (L) hx L W/m 2 C, 0 < Re < 30 4k 3h vertica 1/ 4 1/ 4 4μk(T sat

12 Then the heat transfer coefficient h vert in terms of Re becomes: A properties of the iquid are to be evauated at the fim temperature T f (T sat + T s )/2. The h fg and v are to be evauated at the saturation temperature T sat. P.Taukdar/Mech- 12

13 Wavy Laminar Fow The increase in heat transfer due to the wave effect is, on average, about 20 percent, but it can exceed 50 percent. The exact amount of enhancement depends on the Reynods number P.Taukdar/Mech- 13

14 Turbuent Fow At a Reynods number of about 1800, the condensate fow becomes turbuent. Severa empirica reations of varying degrees of compexity are proposed for the heat transfer coefficient for turbuent fow. P.Taukdar/Mech- Nondimensionaised h for vertica pates 14

Severa empirica reations of varying degrees of compexity are

15 Incined Pates This approximation gives satisfactory resuts especiay for θ 60. h 1/ 4 incined hvertica(cosθ) This equation is deveoped for aminar fow of condensate, but it can aso be used for wavy aminar fows as an approximation P.Taukdar/Mech- 15

16 Vertica Tube/Horizonta Tubes & Spheres Reations for vertica pates can aso be used to cacuate the average heat transfer coefficient for aminar fim condensation on the outer surfaces of vertica tubes provided that the tube diameter is arge reative to the thickness of the iquid fim Nusset s s anaysis of fim condensation on vertica pates can aso be extended to horizonta tubes and spheres Tube 0.729, Sphere A comparison of the heat transfer coefficient reations for a vertica tube of height L and a horizonta tube of diameter D yieds P.Taukdar/Mech- 16

iquid fim Nusset s s anaysis of fim condensation on vertica pates can aso be extended to horizonta tubes and spheres Tube 0.729, Sphere 0.

17 Setting h vertica h horizonta gives L (1.29) 4 D 2.77D, which impies that for a tube whose ength is 2.77 times its diameter, the average heat transfer coefficient for aminar fim condensation wi be the same whether the tube is positioned horizontay or verticay For L > 2.77D, the heat transfer coefficient wi be higher in the horizonta position That is the reason why the tubes are paced horizontay in a condenser P.Taukdar/Mech- 17

whether the tube is positioned horizontay or verticay For L > 2.

18 Effect of Vapor Veocity If the vapor fows downward d : increases the average veocity of the iquid and thus decrease the fim thickness. This, in turn, wi decrease the therma resistance of the iquid id fim and thus increase heat transfer Upward vapor fow has the opposite effects: thickens the iquid fim, and thus decreases heat transfer P.Taukdar/Mech- 18

This, in turn, wi decrease the therma resistance of the iquid id fim and thus increase

19 Fim Condensation inside Horizonta Tubes Most condensation processes encountered in refrigeration and airconditioning appications, however, invove condensation on the inner surfaces of horizonta or vertica tubes For ow vapor veocities: P.Taukdar/Mech- 19

appications, however, invove condensation on the inner surfaces

20 Dropwise Condensation heat transfer coefficients can be more than 10 times arger than fim condensation Dropwise condensation, characterized by countess dropets of varying diameters on the condensing surface instead of a continuous iquid fim, is one of the most effective mechanisms of heat transfer, and extremey arge heat transfer coefficients can be achieved with this mechanism P.Taukdar/Mech- 20

condensing surface instead of a continuous iquid fim, is one of the most effective mechanisms of

21 Heat Pipe A heat pipe is a simpe device with no moving parts that can transfer arge quantities of heat over fairy arge distances essentiay at a constant temperature without requiring any power input A heat pipe is basicay a seaed sender tube containing a wick structure ined on the inner surface and a sma amount of fuid such as water at the saturated state. P.Taukdar/Mech- 21

External Flow Correlations (Average, Isothermal Surface)

External Flow Correlations (Average, Isothermal Surface) Externa Fow orreation (Average, Ioterma urface Fat Pate orreation Fow ondition aminar urbuent were Average et mber 1/ 0.66 Re 0. 6 /5 0.07 Re A 1/ 0.6 60 A /5 1/ 0.07 Rex, c 0.66Rex, c Re x, c Re 10 8