Heat & Mass Transfer
From transcript: 20ME620 Heat & Mass Transfer (C) · 20ME67L Heat & Mass Transfer Lab (B)
Cheat sheet
Formulas
Fourier: q = −k A dT/dx ; R_cond = L/(kA)
Convection: q = h A (Ts−T∞) ; R_conv = 1/(hA)
Radiation (gray body net approx): q = ε σ A (Ts⁴ − Tsur⁴) ; σ=5.67e−8
Plane wall overall U: 1/U = Σ R_i ; q = U A ΔT
Critical radius insulation cylinder: r_cr = k_ins / h
Lumped: Bi = h Lc / k ≪ 0.1 ; (T−T∞)/(Ti−T∞)=e^{−h A t/(ρ V c)}
Heisler/transient charts when not lumped — Fo, Bi parameters
Nu = h L / k_f = f(Re, Pr) ; Pr = ν/α ; Gr for natural convection
Flat plate laminar average Nu ~ 0.664 Re^{1/2} Pr^{1/3} (local 0.332…)
LMTD: ΔT_lm = (ΔTa−ΔTb)/ln(ΔTa/ΔTb) ; q = U A F ΔT_lm (F correction)
ε-NTU: ε = f(NTU, Cr) ; NTU = U A / C_min ; Cr = C_min/C_max
Boiling/condensation: regimes; h much larger than single-phase often
Mass: analogous Nu↔Sh, Pr↔Sc ; N̈A = h_m Δρ or k_G Δp
Fin efficiency η_f ; overall surface efficiency with fins
Conduction (Fourier): q = −k A dT/dx
Plane wall: Q = kA(T1−T2)/L
Lumped transient: (T−T∞)/(Ti−T∞) = exp(−hAt/(ρVc))
Biot: Bi = hL/k (lumped OK if Bi ≪ 0.1)
Newton cooling: q = h A (Ts − T∞)
Radiation: q = ε σ A (T^4 − Tsurr^4) ; σ = 5.67e−8
Heat exchanger LMTD: Q = U A ΔT_lm
NTU effectiveness: ε = f(NTU, Cr)
Definitions
- Conductivity k
- Ability to conduct heat — metals high, insulators low
- Convection coefficient h
- Surface heat transfer intensity — flow & geometry dependent
- Biot Bi
- Internal conduction resistance / boundary convection resistance
- Fourier Fo
- Dimensionless time α t / L²
- Nusselt Nu
- Dimensionless h — enhanced over pure conduction
- Prandtl Pr
- Momentum diffusivity / thermal diffusivity
- Blackbody
- Perfect emitter/absorber; ε=1; Wien, Stefan–Boltzmann
- View factor Fij
- Fraction of radiation leaving i intercepted by j
- LMTD
- Log mean temperature difference for exchangers
- NTU
- Number of transfer units — exchanger size measure
- Thermal resistance
- R = L/(kA) or 1/(hA) — series/parallel networks
- Sherwood / Schmidt
- Mass-transfer analogs of Nu / Pr
Topic-wise short notes
Conduction & convection
- 1D steady: plane, cylinder, sphere resistance networks.
- Contact resistance at interfaces often non-negligible.
- Extended surfaces (fins): optimize length/thickness/material.
- Forced vs free convection — which ΔT and velocity drive h.
- Turbulators/roughness raise h and ΔP — tradeoff.
Exchangers & mass transfer
- Parallel vs counterflow: counterflow higher effectiveness.
- Shell-and-tube, plate, crossflow — pick by duty/pressure/cleaning.
- ε-NTU preferred when outlet temps unknown.
- Psychrometric processes: sensible/latent; cooling & dehumidification.
- Diffusion Fick’s law; convective mass transfer Sh correlations.
Conduction & lumped systems
- Validity Bi≪0.1; else spatial gradients — use Heisler or 1-term series.
- Multi-lump networks for electronics cooling intuition.
Convection, radiation, exchangers
- Shields between surfaces cut radiation net heat.
- Solar absorptivity vs IR emissivity for coatings (selective surfaces).
Radiation essentials
- σ T⁴ blackbody; real surfaces ε, α, ρ, τ with α+ρ+τ=1.
- Kirchhoff: α=ε at equilibrium for given λ/T band approximations.
- View factors reciprocity Ai Fij = Aj Fji; enclosure rules.
- Radiation shields in series drastically cut net q.
Heat exchanger practical
- F correction <1 for multipass/crossflow vs pure counterflow LMTD.
- Fouling Rd adds 1/(UA) — design margin & cleaning schedule.
- Pressure drop vs heat transfer — pump power tradeoff.
Exam traps & quick notes
- Identify mechanism first: conduction / convection / radiation / phase change.
- Extended surfaces (fins): efficiency & effectiveness.
- Solar EPC: module heating, derating — convection + radiation balance.
- Series resistances add; parallel conductances add.
- Critical radius: adding insulation can increase heat loss until r_cr.
- Natural convection: Ra = Gr Pr ; orientation matters.
- Radiation dominates at high T or in vacuum.
- Fouling factors add resistance in real exchangers.
- Analogy: heat ↔ mass transfer correlations often interchangeable form.
Comprehensive notes
Conduction & convection
2D conduction numerics intro; forced/natural correlations (Dittus–Boelter, Churchill–Chu).
Exchangers & mass transfer
Parallel/counterflow LMTD correction; shell-and-tube; condensation/boiling regimes; diffusion basics.
External: Heat exchanger effectiveness (NTU) ↗
Conduction & lumped systems
Fourier law; thermal resistance networks; critical radius of insulation. Lumped capacitance if Bi≪0.1. Heisler charts for transient when not lumped.
External: NPTEL ↗ Engineering Toolbox ↗
Convection, radiation, exchangers
Nu=f(Re,Pr) correlations. Natural vs forced. Radiation shields. LMTD and ε-NTU for heat exchangers; fouling factors in practice.
External: NPTEL ↗ Engineering Toolbox ↗
Interview Q&A for this subject
Q: When is lumped capacitance valid?
A: Biot Bi=hL/k ≪ 0.1 — internal conduction resistance negligible vs surface convection.
External: ASQ / quality ↗ MIT OCW ↗