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