Why do these conditions yield smaller heat transfer rates than those for a hot upper surface or cold lower surface? (9.32)

Problem: Solar Receiver Problem 9.33: Convection and radiation losses from the surface of a central solar receiver. KNOWN:Dimensions and emissivity of cylindrical solar receiver. Incident solar flux. Temperature of ambient air. FIND:(a) Heat loss and collection efficiency for a prescribed receiver temperature, (b) Effect of receiver temperature on heat losses and collector efficiency. = h L / k

Problem: Solar Receiver (cont.) PROPERTIES:Table A-4, air (Tf= 550 K): k= 0.0439 W/m⋅K, ν= 45.6 ×10-6m2/s, α= 66.7 ×10-6m2/s, Pr= 0.683, β= 1.82 ×10-3K-1. ANALYSIS:(a) The total heat loss is ()4radconvssssqqqAThATTεσ∞=+=+−With RaL= gβ(Ts- T∞)L3/να= 9.8 m/s2(1.82 ×10-3K-1) 500K (12m)3/(45.6 ×66.7 ×10-12m4/s2) = 5.07 ×1012, the Churchill and Chu correlation, Eq. 9.26, yields (){}21/6228/279/160.3870.0439W/m K0.8250.82542.46.83W/mK12m10.492 /LRakhLPr⋅=+=+=+"#$$$$⋅%&$$'()*$$+,-.Hence, with As= πDL= 264 m2()()4282422264m0.25.6710W/mK800K264m6.83W/mK 500Kq−=×××⋅+×⋅656radconv1.23 10 W9.01 10 W2.13 10 Wqqq=+=×+×=×

Cylinders The Long Horizontal Cylinder • Boundary Layer Development and Variation of the Local Nusselt Number for a Hot Cylinder: ()21/6128/279/160.3870.601010.559 /DDDRaNuRaPr!"##=+<$%&'##+()*+(9.34) Spheres • The Average Nusselt Number: ()1/44/99/160.589210.469 /DDRaNuPr=+!"+#$(9.35)

Boiling Chapter 10 Sections 10.1 through 10.5

Distillation: Convert sea water to fresh water?Why does water vapor enter small condenser tube?

Steam has 2,613kW Thermodynamic analysis

Heat transfer rate [W] = 357 kW In condenser (max) 2,613kW

Vapor Compression Distillation System Compressor work = mdot (h2-h1) 50 kW 2614 kW Lose 357 kW Lose 2,256 kW 2564 kW Assume

General Considerations General Considerations • Agitation of the liquid by vapor bubbles is one mechanism that provides for large convection coefficients and hence large heat fluxes at low-to-moderate surface-to-fluid temperature differences. • Special form of Newton’s law of cooling: ()satΔsseqh TThT!!=−=Air at 1 atm Heater Boiling Water @ 100oC Is water at the saturation temperature? Excess temperature Saturation temperature

Boiling Curve The Boiling Curve Saturated pool boiling case: "Little vapor formation. "Liquid motion is due principally to single-phase natural convection. • Free Convection Boiling ()Δ5 CeT<o• Onset of Nucleate Boiling - ()ONBΔ5 CeT≈oWater at 1 atm Excess Temperature

General Considerations (cont.) • Special Cases "Pool Boiling: Liquid motion is due to natural convection and bubble-induced mixing."Saturated Boiling: Liquid temperature is slightly higher than saturation temperature. "Forced Convection Boiling: Fluid motion is induced by external means, as well as by bubble-induced mixing. "Subcooled Boiling: Liquid temperature is less than saturation temperature.