Prof. Nico Hotz

ME 150 – Heat and Mass Transfer

1

Review Convection

Chap. 18: Review Convection

Midterm II Review:

Exam on Wednesday, November 16, 11:40am, Teer 203 Topics: Convection (forced external/internal, natural, phase change, heat exchangers)

Prof. Nico Hotz

ME 150 – Heat and Mass Transfer

2

Material covered in Incorpera (in class):

Chap. 18: Review Convection

•  Introduction to convection –  Ch. 6 (except mass convection) (Chapter 12)

•  External convection –  Ch. 7.1-7.5 (Chapter 13)

•  Internal convection –  Ch. 8.1-8.5; 8.6 (browse) (Chapter 14)

•  Free convection –  Ch. 9.1-9.5; 9.6-9.9 (browse) (Chapter 15)

•  Boiling and condensation –  Ch. 10.1-10.3; 10.6 (Chapter 16)

•  Heat exchanger –  Ch. 11.1-11.4 (Chapter 17)

Prof. Nico Hotz

ME 150 – Heat and Mass Transfer

3

Closed Book Section:

•  Physics of convection –  Velocity and thermal boundary layers –  Role of laminar and turbulent flows –  External convection boundary layer over flat plate –  Internal convection boundary layer in circular pipes –  Free convection boundary layer on a vertical plate –  Modes of pool boiling –  Parallel and counter flow heat exchangers

•  Non-dimensional parameters –  Re, Pr, Nu, Ra, Gr, NTU

•  Derivations –  Heuristic derivation of boundary layer thickness for forced and

free convection –  Thermal analysis for internal flow with const q” or Ts and

particularly LMTD and NTU

Chap. 18: Review Convection

Prof. Nico Hotz

ME 150 – Heat and Mass Transfer

4

Open Book Section:

•  Open BLID, Notes, Homework –  Distributed HW solutions and solution manuals are not permitted

•  Follow the standard methodology –  Pay attention to units and orders of magnitude –  Otherwise, wrong answer = zero

•  Draw a schematic (if there is not one) and identify heat transfer processes

•  List key assumptions simplifying the problem

•  Complete the analysis before substituting values and carry units in the calculation

Chap. 18: Review Convection

Prof. Nico Hotz

ME 150 – Heat and Mass Transfer

5

(1) Identify the flow geometry (configuration, wetted area, etc.)

(2) Specify the appropriate reference temperature and determine the flow properties (density, viscosity, etc) at that temperature. Appropriate reference temperature: often the free-stream temperature. Some correlations use other reference temperatures, e.g. film temperature.

(3) Calculate the Reynolds or Rayleigh number using the appropriate reference dimension (length for plates / wings, diameter for spheres, cylinders, etc.)

(4) Decide whether you want an average heat transfer coefficient (often the case) or a local heat transfer.

(5) Select the appropriate correlation (often: Nusselt correlations)

Methodology for Application Problem

Chap. 18: Review Convection

Prof. Nico Hotz

ME 150 – Heat and Mass Transfer

6

-  Forced convection / Natural convection -  External flow / Internal flow -  Laminar flow / Turbulent flow -  Different geometries and configurations -  Local and average Nusselt number / heat transfer -  Different correlations for different material properties -  …

Explain and justify these distinctions in your solutions!

You have to distinguish between:

Chap. 18: Review Convection

Prof. Nico Hotz

ME 150 – Heat and Mass Transfer

7

Log Mean Temperature Difference for Heat Exchangers

The LMTD Method is used to design heat exchangers for known inlet and outlet temperatures of the fluids and a known configuration of the heat exchanger.

1) Determine known or specified inlet and outlet temperatures. 2) Calculate LMTD using formula for the given heat exchanger configuration (parallel, counter, cross flow). 3) Calculate total heat transfer from inlet and outlet temperatures and fluid properties. 4) Calculate overall thermal resistance using q and LMTD. 5) Calculate geometry from overall thermal resistance and heat transfer coefficients.

Possible Procedure to Design Heat Exchanger:

Chap. 18: Review Convection

Prof. Nico Hotz

ME 150 – Heat and Mass Transfer

8

( )12

12

ln TTTTTTAUq lmlm ΔΔ

Δ−Δ=Δ→Δ⋅⋅=

1: x = 0, inlet for cold and hot 2: x = L, outlet for cold and hot

icihi TTTT ,,1 −=Δ=Δ

ocoho TTTT ,,2 −=Δ=Δ

1: x = 0, hot inlet and cold outlet 2: x = L, cold inlet and hot outlet

ocihch TTTTT ,,1,1,1 −=−=Δ

icohch TTTTT ,,2,2,2 −=−=Δ

Parallel flow heat exchanger Counter flow heat exchanger

LMTD Method:

Chap. 18: Review Convection

Prof. Nico Hotz

ME 150 – Heat and Mass Transfer

9

NTU-effectiveness Method for Heat Exchangers

The NTU Method is used to evaluate heat exchangers for known inlet temperatures of the fluids and a known geometry of the heat exchanger (outlet temperatures unknown).

1) Calculate overall thermal resistance from known geometry. 2) Calculate NTU from overall thermal resistance. 3) Calculate effectiveness from NTU. 4) Calculate total heat transfer q from effectiveness and inlet temperatures. 5) Calculate outlet temperatures from known inlet temperatures and total heat transfer q.

Possible Procedure to Analyze Heat Exchanger:

Chap. 18: Review Convection

Prof. Nico Hotz

ME 150 – Heat and Mass Transfer

10

Parallel flow heat exchanger Counter flow heat exchanger

NTU Method:

( ) ( )icihp TTcmqq ,,max min −⋅⋅⋅=⋅= εε

( )( )

( )( )⎟

⎟⎠

⎞⎜⎜⎝

⎛

⋅

⋅+

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅

⋅+⋅−−

=

p

p

p

p

cmcm

cmcm

maxmin

1

maxmin

1NTUexp1

ε

( )( )

( )( )

( )( ) ⎥

⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅

⋅−⋅−⋅

⋅

⋅−

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅

⋅−⋅−−

=

p

p

p

p

p

p

cmcm

cmcm

cmcm

maxmin

1NTUexpmaxmin

1

maxmin

1NTUexp1

ε

( )pcmAU⋅

⋅=

minNTU

Chap. 18: Review Convection

Prof. Nico Hotz

ME 150 – Heat and Mass Transfer

11