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HEAT:010117Spherical shell r1=1 m, r2=2 m: equal resistances 1/(8π), Q=400π W, T=100(1 m/r) °C

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Heat Spherical Shell Series ResistanceHeat Radial Fourier Integration

Steady conduction and thermal resistanceHeat Transfer · Mixed review

HEAT:010118Generating solid cylinder R=1 m: surface flux 4 W/m², Ts=22 °C, Tcenter=23 °C

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Heat Cylinder Generation Surface FluxHeat Radial Poisson Centerline Rise

Steady conduction and thermal resistanceHeat Transfer · Mixed review

HEAT:010219Lump Cth=1000 J/K, hA=10 W/K: T=20+80 e^{-t/100}, time to 40 °C is 100 ln 4 s

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Heat Lumped Capacitance ExponentialHeat Lumped Time And Energy Lost

Fins and transient conductionHeat Transfer · Mixed review

HEAT:010220Semi-infinite step to 100 °C: η=1, T=100-80 erf 1, surface flux 80000/√π W/m²

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Heat Semi Infinite Erf SimilarityHeat Semi Infinite Surface Energy

Fins and transient conductionHeat Transfer · Mixed review

HEAT:010221Two C=1 lumps with H=G=1: θ1=5e^{-t}+5e^{-3t}, total excess energy 10e^{-t}

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Heat Two Lump Modal DecompositionHeat Two Lump Common Mode Energy

Fins and transient conductionHeat Transfer · Mixed review

HEAT:010322Fully developed laminar tube at constant q'': h=100, Tout=302 K, outlet wall 312 K

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Heat FD Laminar Constant Flux NusseltHeat Tube Energy Balance Wall Bulk

External and internal convectionHeat Transfer · Mixed review

HEAT:010323Constant wall 400 K internal flow: Tout=375 K, Q=750 W, LMTD=75/ln 4, UA=10 ln 4

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Heat Constant Wall Exponential MeanHeat Internal Flow Lmtd Closure

External and internal convectionHeat Transfer · Mixed review

HEAT:010424Infinite gray plates eps=1/2 and 1/4: network denominator 5 and q''=3 sigma 300^4

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Heat Gray Plate Radiosity NetworkHeat Black Limit Radiation Exchange

Thermal radiation and enclosure exchangeHeat Transfer · Mixed review

HEAT:010425One black shield between black 600/300 plates: Ts=300(17/2)^{1/4} and half the no-shield flux

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Heat Black Shield Fourth Power BalanceHeat Series Radiation Space Resistances

Thermal radiation and enclosure exchangeHeat Transfer · Mixed review

HEAT:010426Selective solar absorber: T=(4000/sigma)^{1/4}, hotter than gray by sqrt(2)

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Heat Selective Solar Energy BalanceHeat Gray Limit Fourth Root Ratio

Thermal radiation and enclosure exchangeHeat Transfer · Mixed review

HEAT:010527Parallel-flow exchanger with UA=ln 4: Cr=1/2, epsilon=7/12, Q=140/3 kW

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Heat Parallel Flow Ntu EffectivenessHeat Two Stream Outlet Balance

Heat exchangers and effectiveness methodsHeat Transfer · Mixed review

HEAT:010528Phase-change cold side at 20 C: NTU=1, epsilon=1-e^{-1}, UA LMTD closes

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Heat Phase Change CR Zero NtuHeat Lmtd UA Product Closure

Heat exchangers and effectiveness methodsHeat Transfer · Mixed review

HEAT:010529Clean U=1000 plus fouling R=0.001: U_f=500 and the required area doubles

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Heat Fouling Overall CoefficientHeat Fixed Duty Area Scaling

Heat exchangers and effectiveness methodsHeat Transfer · Mixed review

HEAT:010630Three interior FD nodes with unit source: solution (3/2, 2, 3/2) and flux sum 3

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Heat Second Difference Poisson SolveHeat Discrete Flux Source Balance

Coupled modes and numerical heat transferHeat Transfer · Mixed review

HEAT:010631FTCS on (0,100,0): Fo=1/2 oscillates nonnegatively; Fo=0.6 goes negative

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Heat Ftcs Three Node MarchHeat Fourier Number Stability Bound

Coupled modes and numerical heat transferHeat Transfer · Mixed review