Encyclopaedia Index
### 2. Radiative-heat-transfer models in PHOENICS

PHOENICS is supplied with five models of radiation, namely:-

- The composite-flux model of Schuster and Hamaker, as formulated by Spalding [1980]; this
is also known as the six-flux model;
- The composite-radiosity model of Spalding [1994]; this is similar to the P-1
spherical-harmonic model ( Ozisik [1973]).
- The Rosseland [1936] diffusion model, which in PHOENICS is derived from the radiosity
model.
- The IMMERSOL model, which is a more complete version of (b).
- The surface-to-surface radiation model.

### Preliminary notes on each

Models a, b, c and d use the "radiative-conductivity" concept, whereas model
e allows fully for angular effects.

Of these, only d can also handle conjugate heat transfer (i.e. heat conduction within
large immersed solids) and two-phase flow (i.e. additional suspended solids within the
flowing medium).

Model a is restricted to Cartesian and cylindrical-polar grids, whereas models b, c and
d are applicable to BFC grids also.

The PHOENICS implementation of all models is restricted to "gray" radiation, *i.e.* to that in which the influence of wave-length can be neglected.

Models d and e can handle radiation between solids separated by non-absorbing media,
whereas the others cannot. Model e is, in principle, the more accurate; model d is the more
economical.

### Structure of this Encyclopaedia article

Because of its novelty and wide applicability, model d (IMMERSOL) is presented first,
in section 3.

Sections 4, 5 and 6 are devoted to the older models a, b and c. Model d is the only one
to combine universal applicability with economic practicability for complex geometries.

Model e is not described in this article; but information about it can be found in the
lecture entitled
"Surface to Surface Radiation" in the Lectures on PHOENICS
section of POLIS.

### A remark about other models of radiative heat transfer

Other models of radiation are known, for example:-

- statistical (Monte Carlo),
- zonal,
- discrete-transfer,
- discrete-ordinates,

and
- multi-flux.

PHOENICS implementations of the discrete-transfer and discrete- ordinates methods have
been reported by Kjaldman [1993] and Muller et al [1994], respectively.

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