Heat Transfer
Script
Norberto Lemcoff
Mon 8/11 – 8:05- 9:30 AM
Introduction to the Course
Review of the Relationship between Heat Transfer and Thermodynamics (Rate Form)
Heat, Work, Internal Energy, Enthalpy, Entropy, Specific Heats
Irreversible Heat Flow between two reservoirs
Heat Transfer Mechanisms - Introduction
Heat Conduction: Heat Flux; Fourier Law; Heat Equation
Heat Convection: Newton’s Law of Cooling; Energy Balance Equation; Biot Number
Heat Radiation: Electromagnetic Radiation, Black Body; Stefan-Boltzmann’s law; Heat Exchange,
View Factor
Mon 8/11 – 9:30-10:00 AM Break
Mon 8/11 – 10:00 – 11:25 AM
Video: Ansys-Fluent Tutorial 10-10:15 AM
Heat Diffusion Equation
Thermal Conductivity of Common Materials
Control Volume in a Heat Flow Field
Example: Steady State Setting of a Concrete Floor - Step by Step Solution
Example: Steady State Conduction in a Cylindrical Hollow Pipe - Step by Step Solution
Example: Convective Boundary Condition – Steady State Heat Flow through the Wall of a Hollow
Cylinder - Step by Step Solution
Concept of Driving Force and Thermal Resistance for Heat Transport Rate Q (W)
Overall Heat Transfer Coefficient
Example: Steady State Heat Conduction through a Composite Wall
Example: Steady State Heat Conduction through a Furnace Wall
Mon 8/11 – 11:30 AM - 1:00 PM Lunch Break
Mon 8/11 – 1:00 – 2:00 PM
Heat Exchanger Design
Types of Heat Exchanger: Parallel, Counter and Cross Flow
Logarithmic Mean Temperature Difference (LMTD)
Heat Exchanger Effectiveness
Overall Heat Transfer Coefficient
Heat Exchange Area
Total Heat Capacity of Cold and Hot Fluids (mass flow rate times specific heat)
Examples of Heat Exchanger Calculations.
Use of the LMTD The epsilon-NTU method
Mon 8/11 – 2:00 – 2:30 PM Break
Mon 8/11 – 2:30 – 4:20 PM
Example 3.5 Text
COMSOL Tutorial on Shell and Tube Heat Exchangers 3-3:15 PM
Exercise 4.4 - Exercises List – Heat Exchanger Average Heat Transfer Coefficients
Exercise 3.6 - Exercises List – Insulation Thickness for a Furnace Wall
Tues 8/12 – 8:00- 9:30 AM
Conduction Heat Transfer
The Heat Diffusion Equation
Need for Initial Condition and Boundary Conditions
Boundary Conditions: Dirichlet, Neumann, Robin
Steady State Heat Conduction with Internal Heat Generation in One Dimension in Cartesian Coordinates
Transient Heat Conduction with Internal Heat Generation under Uniform Temperature (Lumped
Parameter Model – Make the internal Heat Generation Equal to the Convective Loss)
Transient Heat Conduction without Internal Heat Generation in One Dimension in Cartesian Coordinates
(Separation of Variables)
Steady State Heat Conduction with Internal Heat Generation in Two Dimensions in Cartesian
Coordinates (Separation of Variables)
Example: Flat Slab cooled from its sides heated with a sinusoidal T profile along upper edgeo
Comments about Fin Design
Heat Conduction in a Fin
Tues 8/12 – 9:30 – 10:00 AM Break
Tues 8/12 – 10:00- 11:30 AM
Analysis of steady state heat transfer in a long fin of circular cross section
Extreme case of the very long fin
Fin efficiency and Fin Design
Example: Design of a fin attached to a pipe carrying hot water
Transient Heat Conduction: Cooling of a Hot Solid or Heating of a Cold Solid (Dirichlet BC)
Separation of Variables
Boundary Conditions (Characteristic functions)
Initial Condition
Transient Heat Conduction: Cooling of a Hot Solid or Heating of a Cold Solid (Neumann BC)
Heisler Charts
Tues 8/12 – 11:30 AM – 1:00 PM Lunch Break
Tues 8/12 – 1:00- 2:00 PM
Example: Using Heisler charts to investigate the cooling of apples
Example: Transient Heat Conduction to a Semi-Infinite Region
Dirichlet BC
Neumann BC
Robin BC
Example: How long can a finger be over a 800 Celsius flame without burning?
Tues 8/12 – 2:00 – 2:30 PM Break
Tues 8/12 – 2:35- 4:25 PM
Finite Element Modeling of Heat Conduction using COMSOL – Demos
Transient Heat Conduction in a Short Cylinder (COMSOL Library)
Showing the effect of changing Material Properties
Changing BCs on horizontal boundaries to simulate Infinite Cylinder
Post-processing Results
Example: Conduction in a composite solid
Example: Quenching of a Steel Billet – Analytical calculation and COMSOL comparison
Wed 8/13 – 8:00- 9:30 AM
Convection Heat Transfer
Flow near solid surfaces: Boundary Layer
Laminar to Turbulent Flow Transitions for Fluid Flow over a Flat Plate
Flow Boundary Layer Thickness and Thermal Boundary Layer Thickness
The Momentum Conservation Equation for the flow around a Boundary Layer
Formulation in terms of dimensionless variables (Blasius) f f’’ + 2 f’’’ = 0
Skin Friction Coefficient; Local Skin Friction (or Skin Drag) Coefficient; Overall Skin Friction Coefficient
The Energy Equation in the Presence of Fluid Flow
Heat Transfer Coefficient for flow near a wall: h = q/(Tw-Tinf)
Energy Balance Equation with Convective Term
Reduction for 2D steady convective heat transfer without heat sources
The Prandtl number (viscous transport/conductive transport)
Nusselt-Reynold-Prandtl correlation for laminar flow over a constant temperature flat plate
The Peclet Number (=Re*Pr) (inertial transport/conductive transport)
Average Heat Transfer Coefficient h_av = 0.664 (Re)^1/2 Pr^1/3 (k/L) (also Eq 6.58 Text)
Example 6-5: Air Flow over a Flat Plate
Wed 8/13 – 9:30 – 10:00 AM Break
Wed 8/13 – 10:00- 11:30 AM
Continuing with discussion of heat transfer for non-isothermal flow over a plate
The Reynolds analogy Cf = 2 h Pr^2/3 /rho Cp u_inf
The Stanton Number: St = (Cf/2)/Pr^2/3 = h/rho Cp u_inf (heat flux to fluid/heat flux capacity of fluid)
Example 6-7.
Turbulent Boundary Layers
Average and Fluctuating Components of Velocity in a Turbulent Flow Field
Turbulence shear stresses
Total time averaged shear stress
Eddy diffusivity for Momentum (epsilon_m)
Mixing Length l ~ k y where k = von Karman constant
The viscous sublayer ( nu > epsilon_m) u_ave ~ y
The log layer (epsilon_m > nu) u_ave ~ ln y
Skin friction coefficient in turbulent flow Cf
Eddy Diffusivity for Momentum (Bousinesq) and modification of Fourier’s law for heat flux in
turbulent flow (Eddy Diffusivity for Heat) -> Turbulent Prandtl Number
Reynolds-Colburn analogy
Stanton Number for turbulent flow
Nusselt Number for turbulent flow
Example 6-9 text:
Wed 8/13 – 11:30 AM – 1:00 PM Lunch Break
Wed 8/13 – 1:00- 2:00 PM
Heat Transfer in Laminar Flow in Pipes
Entrance Length for Velocity and for Temperature
Concept of Mixing Cup Temperature
Local Nu for fully developed flow = 4.364 = Nu_D
Thermal Entrance Region
The Graetz number Gz_x = Re Pr (D/x)  Plot Nu vs 2/Gz (Asymptotic at large x)
Turbulent Entry Lengths (Velocity and Temperature)
Example 7-1, p. 352 text
Plot of Friction Factor vs Reynolds Number (Text p. 361)
Wed 8/13 – 2:00 – 2:30 PM Break
Wed 8/13 – 2:30- 4:30 PM
Finite Element Modeling of Heat Convection using COMSOL – Demos
Steady Temperature field in a fluid region without and with flow
Example 7-1 p. 352 text
Example: Hot Wire Anemometer – A HWA is 0.01 in diam, 0.5 in long, is exposed to air at 70 F flowing at
100 ft/s. How much current must flow through the wire to keep its surface temperature constant at 600
F?
Qualitative Description of the Various Patterns of Flow normal to a Cylinder as a function of the
Reynolds number. Flow Separation; Vortex Shedding; Von Karman Vortex Street.
Strouhal Number vs Reynolds Number plot
Churchill-Bernstein correlation for Nu in flow around cylinders
Example 7-7, p. 381 text
Thurs 8/14 – 8:00- 9:30 AM
Conjugate/Multiphase Heat Transfer
Natural Convection and Film Condensation
Governing Equations: Momentum w/Pressure gradient due to rho g (far fluid or vapor)
8:15-8:40 Sympodium malfunction
Correlations for Natural Convection Nu = f(Ra, Pr)
Grashof Number (buoyancy force/viscous force)
Rayleigh Number Ra = Gr Pr
Estimation of the heat transfer coefficient h for natural convection on a vertical surface
Squire-Eckert equation for Nu for natural convection on a vertical plate
Natural Convection Correlations for horizontal isothermal cylinders
Film Condensation
The Jakob Number (sensible energy.latent energy)
Thurs 8/14 – 9:30 – 10:00 AM Break
Thurs 8/14 – 10:00- 11:30 AM
Heat and Mass Flow in a Condensing Film
Thickness of the condensing film
Plot Nu vs Ja
Sadasivan-Lienhard correction
Example 8-6
Boiling Phenomena
Nukiyama’s experiment: Boiling arounf an immersed heated wire -> Boiling Hysterisis Loop
Modes of Pool Boinling
Natural Convection Boiling
Nucleate Boiling (Isolated Bubbles -> Slugs and Columns
Transition Boiling
Film Boiling
Peak Heat Flux and Burnout Point
Example 9-1, p. 469 text
Taylor-Helmholtz instability of the vapor film next to a heated surface surrounded by liquid
Example 9-3, p. 479
Estimation of qmax on an infinite horizontal plate (Zuber 1959)
Example 9-5, p. 482 text
Thurs 8/14 – 11:30 AM – 1:00 PM Lunch Break
Thurs 8/14 – 1:00- 2:00 PM
Boiling - contd.
Correlations for prediction of the maximum (peak) heat flux in pool boining (Table 9-3, p. 486 text)
Film Boiling
Correlations for Nu (Lienhard)
Minimum Heat Flux (Zuber 1959)
Transition Boiling (Berenson 1960)
Forced Convection Boiling in Tubes (Fig. 9-18, p. 499 text)
Concept of Quality x (Vapor Fraction ; =0, liquid; =1 vapor)
The Convection Number
The Boiling Number ( = heat flux/mass flux x latent heat)
Example 9-9, p. 504
Two-Phase Flow in Horizontal Tubes
The Froude Number
Dropwise Condensation
Heat Pipes
Thurs 8/14 – 2:00 – 2:30 PM Break
Thurs 8/14 – 2:30- 4:30 PM
Videos and Demo 2:30-3:45 PM
Video - AltaSim – Simulating Quenching of a short cylinder using COMSOL
COMSOL Demo - Model Library - Melting of Ice (phase_change.mph)
Video – Predicting Boiling Heat Transfer in IC Engine using ANSYS
Exercise: Heat Loss from Heat Water Pipes
Fri 8/15 – 8:00- 9:30 AM
Radiation Heat Transfer
Radiation Exchange between two solid surfaces at different temperatures
Temperature, Areas, Shape, Orientation, Properties, Other surfaces, Medium between
View Factor: Fraction of radiation emitted by surface 1 that reaches surface 2 (F12)
Transfer Factors
Emittance: Monochromatic and Total
Diffuse and Specular Emittance and Reflection
Intensity of Radiation
Kirchoff’s Law
The Gray Body Approximation
View Factors for Simple Configurations of Radiating Surfaces
Parallel infinite surfaces; Perpendicular Surfaces (one of size 1, the other infinite)
View Factor Reciprocity
Fri 8/15 – 9:30 – 10:00 AM Break
Fri 8/15 – 10:00- 11:30 AM
Example 10.1 , p. 541 text – Radiation from a molten metal jet through a slit in a radiation shield
General Integral Expressions for the Calculation of View Factors for arbitrary surfaces
Example 10.3 , p. 549 text – Disc Heater with Radiation Shield
Evaluating View Factors from Tables
Example 10.4 , p. 550 text –
Concepts of Irradiance (H) and Radiosity (B)
Fri 8/15 – 11:30 AM – 1:00 PM Lunch Break
Fri 8/15 – 1:00- 2:00 PM
Example 10.4 , p. 550 text – Clarification
Multi-surface Enclosure Problems
Example 10.10 – p. 563 text – Radiation HT in a duct with triangular cross section
Gaseous Radiation
Monochromatic Absorption, Scattering, Extinction Coefficients
Beer’s Law
Heat Transfer from Gases to Walls
Fri 8/15 – 2:00 – 2:30 PM Break
Fri 8/15 – 2:30- 4:30 PM
Demo: Radiation Heat Transfer Example – COMSOL
Video – Webinar – Solar Thermal Energy Engineering – Prof. Lemcoff
Exercise: Radiation Inside a Cubical Furnace with walls at different temperatures – Evaluation of Heat
Transfer between the two horizontal Surfaces and between the lower horizontal surface and a vertical
surface.