ME 150 – Heat and Mass Transfer
Chap. 18: Review Convection
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
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ME 150 – Heat and Mass Transfer
Chap. 18: Review Convection
Material covered in Incorpera (in class): • Introduction to convection – Ch. 6 (except mass convection) • External convection – Ch. 7.1-7.5 • Internal convection – Ch. 8.1-8.5; 8.6 (browse) • Free convection – Ch. 9.1-9.5; 9.6-9.9 (browse) • Boiling and condensation – Ch. 10.1-10.3; 10.6 • Heat exchanger – Ch. 11.1-11.4
Prof. Nico Hotz
(Chapter 12) (Chapter 13) (Chapter 14) (Chapter 15) (Chapter 16) (Chapter 17)
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ME 150 – Heat and Mass Transfer
Chap. 18: Review Convection
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 Prof. Nico Hotz
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ME 150 – Heat and Mass Transfer
Chap. 18: Review Convection
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
Prof. Nico Hotz
4
ME 150 – Heat and Mass Transfer
Chap. 18: Review Convection
Methodology for Application Problem (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)
Prof. Nico Hotz
5
ME 150 – Heat and Mass Transfer
Chap. 18: Review Convection
You have to distinguish between: - - - - - - -
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!
Prof. Nico Hotz
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ME 150 – Heat and Mass Transfer
Chap. 18: Review Convection
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. Possible Procedure to Design 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.
Prof. Nico Hotz
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ME 150 – Heat and Mass Transfer
Chap. 18: Review Convection
LMTD Method:
q = U ⋅ A ⋅ ΔTlm
→
ΔTlm =
ΔT2 − ΔT1 ln(ΔT2 ΔT1 )
Parallel flow heat exchanger
Counter flow heat exchanger
1: x = 0, inlet for cold and hot 2: x = L, outlet for cold and hot
1: x = 0, hot inlet and cold outlet 2: x = L, cold inlet and hot outlet
ΔT1 = ΔTi = Th ,i − Tc ,i
ΔT1 = Th ,1 − Tc ,1 = Th ,i − Tc ,o
ΔT2 = ΔTo = Th ,o − Tc ,o
ΔT2 = Th , 2 − Tc , 2 = Th ,o − Tc ,i
Prof. Nico Hotz
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ME 150 – Heat and Mass Transfer
Chap. 18: Review Convection
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). Possible Procedure to Analyze Heat Exchanger: 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.
Prof. Nico Hotz
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ME 150 – Heat and Mass Transfer
Chap. 18: Review Convection
NTU Method: q = ε ⋅ qmax = ε ⋅ min (m ⋅ c p )⋅ (Th,i − Tc ,i )
NTU =
U⋅A min(m ⋅ c p )
Parallel flow heat exchanger ⎡ ⎛ min(m ⋅ c p ) ⎞⎤ ⎟ 1 − exp⎢− NTU ⋅ ⎜1 + ⎜ max (m ⋅ c ) ⎟⎥ p ⎠ ⎥ ⎢⎣ ⎝ ⎦ ε= ⎛ min(m ⋅ c p ) ⎞ ⎜1 + ⎟ ⎜ max (m ⋅ c ) ⎟ p ⎠ ⎝
Counter flow heat exchanger ⎡ ⎛ min(m ⋅ c p ) ⎞⎤ ⎟ 1 − exp⎢− NTU ⋅ ⎜1 − ⎜ max (m ⋅ c ) ⎟⎥ p ⎠ ⎦ ⎥ ⎝ ⎣⎢ ε= ⎡ ⎛ min(m ⋅ c p ) ⎞⎤ min(m ⋅ c p ) ⎟ 1− ⋅ exp⎢− NTU ⋅ ⎜1 − ⎜ max (m ⋅ c ) ⎟⎥ max (m ⋅ c p ) p ⎠⎥ ⎢⎣ ⎝ ⎦
Prof. Nico Hotz
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ME 150 – Heat and Mass Transfer
Prof. Nico Hotz
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