Phase 1: Heat Transfer Foundations
Introduction to Heat Transfer
What moves heat, and how fast? This chapter introduces the three mechanisms, using a 3D printer nozzle as the unifying example where all three operate at once.
- Conduction, convection, and radiation
- Fourier's law, Newton's law of cooling, Stefan-Boltzmann law
- Heat flux vs. total heat flow
- Shell balance derivation (on demand)
Steady-State Conduction and Thermal Resistance
Heat flowing through a polymer wall behaves like current through a resistor. This chapter builds that analogy into a systematic tool for multilayer systems.
- Thermal resistance networks
- Multilayer slabs, cylinders, and spheres
- Thermal conductivity of polymers
- Shell balance as the primary derivation method
The General Heat Conduction Equation
A single equation governs temperature in any solid. This chapter derives it from first principles and shows how boundary conditions turn it into a solvable problem.
- Derivation from energy conservation
- Cartesian, cylindrical, and spherical forms
- Boundary condition types
- Steady state vs. transient limiting cases
1-D Steady-State Conduction: Cylinders, Spheres, and Fins
Pipe walls, hollow spheres, and extended surfaces each require their own resistance formula. The critical radius of insulation is one of the most counterintuitive results in engineering heat transfer.
- Cylindrical and spherical thermal resistance
- Critical radius of insulation
- Fin efficiency and the fin equation
- Why polymer fins are nearly useless
Phase 2: Polymer Processing Applications
Heat Transfer in Polymer Extrusion
An extruder barrel heats polymer from solid pellets to melt. Cooling dies solidify it into the final shape. Both processes are solved heat transfer problems.
- Overall heat transfer coefficient U
- Series resistances: melt, wall, coolant
- Melt energy balance and throughput
- Post-die cooling and crystallinity
Heat Transfer in Injection Molding
Cycle time in injection molding is dominated by cooling. Understanding the transient heat transfer in a mold directly determines process economics.
- Heat content of the shot
- Overall U for mold cooling
- Cooling time: scales as sΒ²/α
- Thermal diffusivity comparison
Thermal Characterisation of Polymers
DSC, TGA, and TMA each measure a different thermal property. This chapter connects those measurements to the transport parameters used in calculations.
- Thermal diffusivity Ξ± = k/(Οcβ)
- DSC: crystallinity, Tg, melting enthalpy
- TGA: filler content and decomposition
- TMA: linear thermal expansion coefficient
Midterm Examination β Chapters 1β7
Midterm Exam Practice
Ten conceptual questions and ten calculation problems covering heat transfer foundations and polymer processing. Answer key included. Print and distribute to students as a take-home review before the exam.
Covers: Ch. 1β7 β conduction, resistance networks, heat conduction equation, 1-D steady state, extrusion, injection molding, thermal characterisation. Timed for administration after Mardi Gras break.
Midterm Exam
Same scope as the practice exam, different numbers. No answer key. Designed to be printed and administered in class. Password prevents accidental student access to the digital file.
Covers: Ch. 1β7. Recommended timing: week 7β8, shortly after Mardi Gras break, before LSU midterm grade deadline.
Phase 3: Transient Conduction and Convection
Transient Conduction
Temperature changes with time in every real process. The lumped capacitance method gives quick estimates; exact series solutions give precision when you need it.
- Biot number and lumped capacitance
- Thermal time constant τ
- Fourier number and exponential cooling
- Cooling curves for printed polymer parts
Forced Convection
When a fan blows air over a hot surface, heat transfer intensifies. This chapter develops the boundary layer picture and the Nusselt correlations that quantify it.
- Velocity and thermal boundary layers
- Reynolds, Prandtl, and Nusselt numbers
- Flat plate and Dittus-Boelter correlations
- Cooling fans and mold channels
Natural Convection
No fan required. Density differences in heated fluid drive circulation on their own. This is the mechanism behind hot polymer melt pools and unheated furnace walls.
- Buoyancy and the Grashof number
- Vertical plate and horizontal surface correlations
- Churchill–Chu correlation for all Ra
- Melt pool circulation in polymer reactors
Phase 4: Mass Transfer
Molecular Diffusion
Concentration gradients drive diffusion the same way temperature gradients drive heat. Fick's law is the exact analogue of Fourier's law, and the parallels run remarkably deep.
- Fick's first and second laws
- Diffusivity and its physical meaning
- Steady-state diffusion through a slab
- Stokes-Einstein equation
Diffusion in Polymers
Solvent uptake, gas permeability, and anomalous swelling are all diffusion problems. Free-volume theory and the Arrhenius model explain why D in a polymer matrix varies so dramatically with temperature and structure.
- Free volume theory of diffusion
- Fickian and Case II (anomalous) solvent uptake
- Arrhenius temperature dependence
- Effect of crystallinity on barrier performance
Convective Mass Transfer
When fluid flows past a surface, concentration gradients are swept into boundary layers just as temperature gradients are. The Sherwood number is the mass-transfer Nusselt number: same correlations, same logic.
- Film theory and mass transfer coefficients
- Sherwood and Schmidt numbers
- Sh correlations for pipes and flat plates
- Concentration polarization in reverse osmosis
Membrane Transport and Separation
A membrane is a selective barrier. The solution-diffusion model, partition coefficients, and the Robeson upper bound predict which polymers make the best membranes and why no material can have both unlimited permeability and unlimited selectivity.
- Solution-diffusion model: P = D × S
- Selectivity and the Robeson upper bound
- Partition coefficients
- Osmotic pressure and reverse osmosis
Phase 5: Advanced Topics
Coupled Heat and Mass Transfer
Drying, reactive processing, and membrane distillation involve heat and mass moving together. This chapter builds the coupled framework from the individual tools developed across the course.
- Lewis number and the heat-mass analogy
- Drying of polymer films and coatings
- Reactive extrusion with solvent removal
- Membrane distillation
Polymer Nanopore Translocation
A polymer chain threading through a nanometer-scale pore is a capstone problem: diffusion, Joule heating, electrostatics, and polymer dynamics operating simultaneously. The physics that makes DNA sequencing possible.
- Entropic and enthalpic barriers to translocation
- Joule heating in nanopore membranes
- Polymer dynamics under confinement
- DNA and synthetic polymer sequencing
Final Examination β Chapters 1β16
Final Exam Practice
Ten conceptual questions and ten calculation problems covering the full course, weighted toward mass transfer and coupled phenomena from the second half. Answer key included. Print and distribute as a review.
Covers: Ch. 1β16 β full course, heat and mass transfer, membrane separations, and advanced topics.
Final Exam
Same scope as the practice exam, different numbers. No answer key. Designed to be printed and administered. Password prevents accidental student access to the digital file.
Covers: Ch. 1β16 β full course. Recommended duration: 2 hours.