free convection: empirical correlations and… phase change ...whitty/chen3453/lecture 27...natural...
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Free Convection:Empirical Correlations
and…Phase Change Heat Transfer!
Chapters 9 and 10
CH EN 3453 – Heat Transfer
Reminders…
• Homework #9 due today
• Project Results & Discussion section due Wednesday– Turn in to basket in ChE office by 4:00 PM
• Midterm #2 Wednesday next week– Covers chapters 6,7,8,9,11– Review Tuesday afternoon (time TBD)
Natural (Free) Convection
• Heat transfer due to fluid motion induced by buoyancy forces
• Buoyancy forces typically caused by temperature differences
• However, temperature differences do not always cause buoyancy
Types of Free Convection
Plume Buoyant Jet Boundary Layer
Stable vs. Unstable Gradients
Development of Boundary Layer
Similarity Solution for Vertical Plate
Empirical Correlations• Similar to approach used previously for
forced convection– Correlation for Nusselt number Nu– Instead of Re, we use Ra– Careful which expression to use
• Fluid properties determined at film temp.
• Solve for h through Nusselt number
Tfilm = Ts + T∞( ) / 2
NuL =hLk
NuD =hDk
Flow over Vertical Plate
• Rayleigh Number:
• Laminar Flow (RaL < 109):
• All Conditions:
(9.25)
(9.27)
(9.26)
Example: Problem 9.8A square aluminum plate 5 mm thick and 200 mm on a side is heated while vertically suspended in quiescent air at 40°C. Determine the average heat transfer coefficient for the plate when its temperature is 15°C. (a) using results from the similarity solution to the boundary layer equations (b) using results from an empirical correlation
Ver$cal(Plates
Inclined(and(Horizontal(Plates
Inclined(and(Horizontal(Plates
Long(Horizontal(Cylinder
Long(Horizontal(Cylinder((cont.)
Spheres
In(the(limit(as(RaD(→(0(,(how(maycondi$ons(be(characterized?
Pr≳0.7 and RaD≲1011
Table(9.2(Page(583
Do(not(ignore(superscripts(in(
tables(from(the(text!
Free(Convec$on(within(parallel(Plate(
Empirical(Correla$ons:(Key(Tables
Enclosures
Phase(Change(Heat(Transfer:Boiling(and(Condensa$on
Chapter(10(in(seven(slides
Boiling(of(Methanol
Forced(Convec$on(with(Phase(Change
Condensa$on:(Physical(Mechanisms
Condensa$on(on(a(Ver$cal(Plate
Condensa$on(on(Radial(Systems
Condensa$on(in(Horizontal(Tubes