Expert-level heat transfer covering conduction, convection, radiation, heat exchangers, fins, transient heat transfer, and computational heat transfer.
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Fourier law: q = negative k A dT over dx, heat flows down temperature gradient. Thermal resistance: R = L over kA for flat wall, ln(r2 over r1) over 2 pi k L for cylinder. Composite walls: resistances in series and parallel, total R determines heat flux. Fins: extended surfaces increase heat transfer area, fin efficiency eta_f. Biot number: Bi = hL over k, ratio of convection to conduction resistance.
Newton cooling law: q = h A delta T, h is convection coefficient. Nusselt number: Nu = hL over k, dimensionless convection coefficient. Forced external: flat plate Nu correlations, cylinder in cross flow. Forced internal: Dittus-Boelter for turbulent pipe flow, Sieder-Tate with viscosity correction. Natural convection: buoyancy driven, Rayleigh number Ra = Gr times Pr.
Stefan-Boltzmann: q = epsilon sigma A T4, radiation from surface at T. View factor: F_12 is fraction of radiation from 1 intercepted by 2. View factor reciprocity: A1 F12 = A2 F21. Radiation network: analogous to electrical resistance for enclosures. Gray body: emissivity constant with wavelength, simplifies radiation calculations.
LMTD method: Q = UA times LMTD, log mean temperature difference. Effectiveness-NTU: useful when outlet temperatures unknown. Parallel flow vs counterflow: counterflow achieves closer temperature approach. Fouling: additional thermal resistance from deposits, reduces performance over time.
| Pitfall | Fix |
|---|---|
| Lumped capacitance when Bi greater than 0.1 | Use spatial analysis or numerical method |
| Wrong correlation for flow regime | Check Re and geometry match correlation assumptions |
| Ignoring radiation at high temperature | Radiation scales as T4, dominates above 500 C |
| LMTD undefined for equal inlet-outlet temperatures | Use effectiveness-NTU method instead |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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