Heat Transfer Models

The HeatTransferModels namespace provides various model functions relevant to heat transfer.

Cylindrical Thermal Conductance

The function cylindricalThermalConductance computes the thermal conductance across a cylindrical medium using a steady thermal resistance analysis (Incropera et al., 2002):

H=krˉln(ro/ri),\mathcal{H} = \frac{k}{\bar{r} \ln(r_o / r_i)} \,,(1)

where

  • rir_i is the inner surface radius,

  • ror_o is the outer surface radius,

  • rˉ\bar{r} is the arithmetic mean radius, and

  • kk is the medium thermal conductivity.

Cylindrical Gap Conduction Heat Flux

The function cylindricalGapConductionHeatFlux computes the heat flux qq at a point across a cylindrical gap due to conduction, using the thermal conductance given in Cylindrical Thermal Conductance:

q=H(TiTo),q = \mathcal{H} (T_i - T_o) \,,

where

  • TiT_i is the inner surface temperature,

  • ToT_o is the outer surface temperature, and

  • H\mathcal{H} is computed from Eq. (1).

Note that the convention here is that a positive heat flux corresponds to heat moving from the inner surface to the outer surface.

Cylindrical Gap Radiation Heat Flux

The function cylindricalGapRadiationHeatFlux computes heat flux qq at a point across a cylindrical gap due to radiation, assuming opaque, gray, diffuse surfaces with infinitely long, concentric cylinders (Incropera et al., 2002):

q=σ(Ti4To4)R,q = \frac{\sigma (T_i^4 - T_o^4)}{\mathcal{R}} \,,R=1ϵi+riro(1ϵoϵo),\mathcal{R} = \frac{1}{\epsilon_i} + \frac{r_i}{r_o} \left( \frac{1 - \epsilon_o}{\epsilon_o} \right) \,,

where σ\sigma is the Stefan-Boltzmann constant.

Note that the convention here is that a positive heat flux corresponds to heat moving from the inner surface to the outer surface.

References

  1. Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine, and others. Fundamentals of Heat and Mass Transfer. Wiley New York, sixth edition, 2002.[BibTeX]