Encyclopaedia Index

### TITLE : RADIANT TRANSFER IN A FURNACE

BY : Dr S V Zhubrin, CHAM Ltd

DATE : October, 2000

FOR : Validation case for V3.3.1.

### INTRODUCTION

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

### THE STATEMENT OF THE PROBLEM

A long furnace used for stress relieving and annealing is 3mx3m in cross section, with side walls and roof at 1700K and 1400K, respectively. All the surfaces are gray, diffuse and have an emittance of 0.5.

The task is to calculate radiant heat flux to the work floor.

### Conservation equations

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

The main dependent (solved for) variables are:

• Temperature of the medium, TEM1 and

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, QRZ and QRX, 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.516, where the solution is obtained by way of radiosity-shape-factor method widely used in engineering practice.

The value of radiant heat flux across the work floor as computed from the system of three algebraic equations for radiosities is -159.0 kW/m^2.

### THE RESULTS

The plots show the distribution of temperature and Z-direction radiant heat flux within the furnace enclosure.

The simulated heat fluxes across the work floor agree very well with existing solution.

Pictures are as follows :

### THE IMPLEMENTATION

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

The relevant Q1 file can be inspected by clicking here.