Encyclopaedia Index


BY : Dr S V Zhubrin, CHAM Ltd

DATE : October, 2000

FOR : Validation case for V3.3.1.


An IMMERSOL application is presented aimed at the validation of the method for the situation when the thermal radiation is dominant.


A radiant heater panel consists of a row of cylindrical electrical heating elements 1 cm in diameter, 150 cm long, spaced at a 3 cm pitch, and backed by a well insulated wall. The panel has dimensions 30x150 cm and is located 30 cm above a workpiece floor, which is also 30x150 cm. The heater elements are rated at 5 kW each. The emittances of the elements and back wall are 0.9 and 0.8, respectively; the workpiece floor and side walls are assumed black at 300K.

The task is to calculate the operating temperatures of the heater elements.


Conservation equations

The independent variables of the problem are the two components of cartesian coordinate system, namely X and Y.

The main dependent (solved for) variables are:

Model of radiative transfer

The IMMERSOL model is used to simulate the distribution of T3 and TEM1 within the space filled with transparent air. From the temperature fields the radiant heat fluxes, QRX and QRY, W/m^2, are calculated and used as the heat sources in iterative manner.

Properties and auxiliary relations

The gas physical properties are taken constant as for air at 20C with no absorption and scattering.

Boundary conditions

All walls are made from aluminium with emittances and temperatures as given.

Existing solution

The problem has been taken from the textbook by A.F. Mills "Heat Transfer" R.D. IRWIN Inc, 1992 p.518, where approximate solution is obtained by way of single-node method used in engineering practice.

The heater temperature represented by a single node value was computed to be 1311K.


The plots show the distribution of temperature and X-, Y-direction radiant heat fluxes within the enclosure.

The operating element temperatures are in the range of 841-1114K: the lower temperatures are for the elements in the vicinity of the cold side walls, as expected.

Pictures are as follows :


All model settings have been made in VR-Editor of PHOENICS 3.3.1.

The relevant Q1 file can be inspected by clicking here.