Condensation inclined plate

The above analysis of condensation on a vertical plate can be easily extended to condensation on an inclined plate. Consider a plate inclined at an angle, 0, with respect to the gravity vector as shown in Fig. 11.10. 

Control volume used in setting up force balance for a condensed film on an inclined plate. 

Equation l,p-22 was developed for vertical plates, but it can also be used for laminar fififi eondensation on the upper surfaces of plates that are inclined by an angle S.ifrom the vertical, by replacing g in that equation by g cos (Fig, 10-27). This approximatiot) gives satisfactory results especially for d 60 . Note that the condensation heat transfer coefficients on vertical and inclined plates are related to each other by... 

Laminar film condensation on vertical or inclined plates, and on the inside or outside of a vertical tube. 

This formula is valid for flat plates and cylindrical tubes of diameter larger than around 1/8 inch. In both cases the inclination angle should be lower than 90°. Additionally, Pr > 0,5 and [c (Ts - To) / ifc] < 1. A better approximation can be obtained when the condensate viscosity is calculated at [7o + 0,31 (Ts - 7 0)]. 

A 30-cm high by 150-cm wide plate is maintained at 5°C and is inclined at 45° from the vertical. Calculate the rate of condensation, the heat transfer rate, and the maximum film thickness when the plate is exposed to stagnant saturated water vapor at 20°C. Do die calculation both with and without the effect of film subcooling. What is the value of the Jakob number for this problem ... 

B Calculate the heat flux associated with condensation on inclined and horizontal plates, vertical and hoiizonlal cylinders or spheres, and tube bundles,... 

Equations for vertical plates can also be used for laminar film condensation on Ihc upper surfaces of the plates that are inclined by an angle 0 from llie vertical, by replacing g in that equation by g cos 9. Vertical plate equations can also be used to calculate the average heat transfer coefl icieni for laminar film condensation on the outer surfaces of vertical tubes provided that the tube diameter is large relative to the thickness of the liquid film. 

Shigechi et al. [112] conducted a boundary layer analysis of this problem and included momentum and convection effects in the condensate film. They obtained different solutions using as a boundary condition various inclination angles of the liquid-vapor interface at the plate edge. Their maximum average Nusselt number was found to agree well with Eq. 14.98. Chiou et al. [214] included surface tension in their model and showed that heat transfer decreases in relation to Eq. 14.98 as the surface tension of the condensate increases. 

The surface area of the kaolinite and the produced sample are obtained using nitrogen adsorption/desorption at 77 K (Fig.3). The lUPAC hysteresis analysis for both samples show types H4 and H3, respectively, as a result of capillary condensation in mesoporous structure. The hysteresis loop for kaolinite sample shows vertically inclined parallel branches at a pressure close to saturation. This is attributed to the existence of narrow slit-like pores. Those pores have opened more with hydroxide treatment and yielded a product with aggregates of plate-like pores (Fig. 4). The total pore volume of 0.0339 cmVg is obtained in comparison with the 0.016476 cmVg for the original kaolinite. The Single point surfaee area of the produced sample obtained at a relative pressure of 0.3 is 6.85 mVg. 

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