Heat transfer coefficient

Definition

The heat transfer coefficient, h (SI units: W·m⁻²·K⁻¹), quantifies the rate of heat transfer between a surface and an adjoining medium per unit area per unit temperature difference. In its most common use for convection at a fluid–solid boundary, it appears in Newton’s law of cooling:

q″ = h (T_surface − T_fluid),

where q″ is heat flux. For a surface of area A, the total heat rate is Q̇ = h A (T_surface − T_fluid). The coefficient can be defined locally, h(x,y), or as an area-averaged value.

Although most often associated with convection, engineers also use “effective” heat transfer coefficients to represent:

Solid–solid interfaces (thermal contact conductance, h_c), which capture microscopic contact, interstitial gaps, and any thermal interface materials.
Radiative exchange, by linearizing the Stefan–Boltzmann law around a mean temperature as an equivalent h_rad.
Multilayer systems via the overall heat transfer coefficient U, which combines series resistances of convection and conduction: 1/U = 1/h_i + Σ(L/k) + 1/h_o (+ fouling terms).

What h depends on

The heat transfer coefficient is not a material constant; it depends on operating conditions and geometry. Key influences include:

Fluid properties: thermal conductivity k, viscosity μ, density ρ, specific heat c_p, and their temperature dependence; non-Newtonian behavior when relevant.
Flow regime and features: natural vs forced convection; laminar, transitional, or turbulent flow; boundary-layer development; separation and reattachment; crossflow over banks of tubes; impinging jets; internal (ducts, pipes) vs external flow.
Geometry and length scales: characteristic length, curvature, finning, confinement, surface orientation (important in natural convection), and porosity for porous media.
Surface condition: roughness, cleanliness, coatings, wettability, contact pressure (for h_c), and the presence of thermal interface materials; fouling or scaling that adds resistance over time.
Phase change: boiling and condensation dramatically alter h and introduce regime-dependence (e.g., nucleate vs film boiling; dropwise vs film condensation).
Radiation: if treated as an “effective” h, emissivity and mean temperature strongly affect the value.

Typical application areas

Heat exchangers: design and rating of condensers, evaporators, radiators, oil coolers, economizers, and recuperators.
Flow in passages: internal convection in pipes, channels, cooling plates, microchannels, and manifolds.
Electronics and power devices: heat sinks, cold plates, immersion cooling, and enclosure cooling.
Manufacturing and materials processing: quenching, casting solidification, injection molding, autoclave/oven curing, consolidation and bonding, hot stamping, and tool–workpiece/interface heat transfer.
Built environment and HVAC: internal/external surface coefficients, building envelopes (with U-values), radiant panels, and occupant comfort modeling.
External aerothermal problems: convection on vehicles, aircraft, wind turbine blades, buildings, and pipelines exposed to wind.
Energy and process industries: boilers, condensers, reactors, fuel cells, electrolyzers, and solar thermal receivers.

Related terms and dimensionless groups

Convective heat transfer coefficient (emphasizes fluid convection).
Film coefficient or surface coefficient (common synonyms).
Thermal contact conductance h_c (solid–solid interfaces).
Overall heat transfer coefficient U (thermal transmittance or U-value in buildings).
Thermal conductivity k (material property for conduction; distinct from h).
Thermal resistance R (inverse of conductance; used to combine layers and interfaces).
Nusselt number: Nu = h L / k (dimensionless measure of convective heat transfer).
Reynolds (Re) and Prandtl (Pr) numbers (govern forced convection).
Grashof (Gr) and Rayleigh (Ra) numbers (govern natural convection).
Biot number: Bi = h L_c / k_s (compares surface convection to internal conduction; Bi ≲ 0.1 supports lumped-capacitance analysis).

Typical magnitudes (very approximate; depend strongly on details)

Natural convection in air: 2–25 W·m⁻²·K⁻¹.
Forced convection in air (external flow, typical velocities): 20–200 W·m⁻²·K⁻¹; impinging jets can be higher.
Forced convection in water/glycol: 500–10,000 W·m⁻²·K⁻¹ (internal turbulent flows often in the 1,000–5,000 range).
Phase change: condensation or nucleate boiling commonly 5,000–100,000 W·m⁻²·K⁻¹, depending on regime and fluid.
For comparison, overall heat transfer coefficients U: gas–gas exchangers ~10–50; gas–liquid ~50–300; liquid–liquid ~300–2,000 W·m⁻²·K⁻¹.

How h is obtained in practice

Correlations and dimensionless analysis: Compute Re, Pr (and Gr/Ra for natural convection); select a correlation appropriate to geometry and regime (e.g., Dittus–Boelter, Sieder–Tate, Gnielinski for internal flow; Churchill–Bernstein or Hilpert for external flow; various impinging-jet and cylinder-in-crossflow relations). For phase change, use boiling or condensation correlations suited to the regime and fluid.
Computational methods: CFD and conjugate heat transfer simulations can predict local h distributions when validated turbulence and multiphase models are used.
Experiments and system identification:
- Direct measurement using known heat input and measured temperatures to infer h.
- Transient methods (lumped or inverse heat conduction), infrared thermography with inverse modeling, and transient calorimetry.
- Heat exchanger “Wilson plot” techniques to separate film coefficients from wall resistance and fouling.
- Thermal contact conductance measured with standardized setups (e.g., guarded hot plate or steady/transient contact resistance rigs) under specified pressure, roughness, and TIM conditions.

Advantages

Provides a compact, engineering-level description of complex interfacial transport, enabling simple relationships like Q̇ = h A ΔT or Q̇ = U A ΔT for design, sizing, and control.
Scales across fluids, geometries, and operating conditions via dimensionless groups, facilitating extrapolation and similarity analysis.
Easily incorporated into system models and reduced-order simulations.

Limitations and common pitfalls

Not a property of a material or surface alone; it is highly case-specific and may vary spatially and temporally. Using a single scalar h can mask important nonuniformities (e.g., near leading edges, stagnation points, or flow recirculation zones).
Transitional and turbulent regimes, property variations with temperature, and surface changes (fouling, roughening, wetting) introduce significant uncertainty.
Many “effective” h values implicitly include other mechanisms (e.g., radiation or added interfacial resistance). Be explicit about what is included.
Correlations have domains of validity; applying them outside their intended ranges (Re, Pr, Ra, geometry, boundary conditions) can produce large errors.
Internal conduction in the solid can dominate or interact with surface convection (use Biot number to assess). Assuming uniform surface temperature or constant h may be inappropriate if Bi is not small.
In two-phase heat transfer, regime transitions (e.g., onset of nucleate boiling, critical heat flux, film boiling) can cause abrupt changes in h; single correlations rarely span all regimes.

Practical tips

Clarify whether h is local or area-averaged, and whether it excludes or includes radiation and fouling.
Specify the reference fluid temperature (bulk, free-stream, or film temperature) used to define ΔT.
For multilayer systems, prefer the overall coefficient U to avoid ambiguity about how resistances are combined.
Where possible, validate computed or correlated h with targeted measurements under representative operating conditions.