Analysis of Radiation Heat Transfer in Furnace P M V Subbarao Professor Mechanical Engineering Department Test for Cooling Capacity of Furnace Surface….

Complexity of Gas-Wall Radiation Process

Governing equation in a gas radiation For gas radiation governing differential equation is known as Radiative Transfer Equation (RTE) The RTE for an absorbing, emitting, gray medium is Classification:  Basic models and their determinants  Based on quadrature set  Complex geometry of the furnace Face 5 Face 4 Face 1 Face 2 x y z L W Face 6 Face 3 South North East West H w n e s μ η ξ

Basic models for RTE in gas radiation 2-Flux 4-Flux Multiflux DOM Moment Modified- Moment P N - Approx. Zone MCM Numerical (FD, FV) RTE Optically ThinSelf-absorbingOptically Thick Directional AveragingDifferential Approximation EnergyHybrid DTM Ray Tracing Radiation Element

Radiation inside furnace Types of radiation: Surface and volumetric radiation Characterization of participating media: usually, the radiant energy is scattered, absorbed and emitted by tiny suspended particles or gases like CO 2 and water vapor, such media are called participating media. Gas radiation involved Absorption: attenuation of intensity  absorption coefficient  Emission: augmentation of intensity  emission coefficient Scattering  scattering coefficient  Radiant heat transfer occur from the source (Flame) to sink (water walls) in a furnace

Gas radiation-Governing equation Assumptions:  All six boundaries are diffuse and gray  Absorbing, emitting, non scattering gray medium  Same absorption coefficient at all points  Thermophysical properties e.g. density, specific heat, thermal conductivity and optical property like extinction coefficient are constant.  Absorption coefficient = emission coefficient Face 5 Face 4 Face 1 Face 2 x y z L W Face 6 Face 3 South North East West H w n e s μ η ξ Co-ordinate system for cubic enclosure Governing equation for participating media (RTE): Where; S is line of sight distance in the direction of propagation of the radiant intensity I

Direction cosine in 2D geometry RTE with consideration of direction cosine Where I m radiation intensity

Boundary condition At x = 0; At x = L;

DOM with heat generation Incident irradiation at the center of each cell containing only gas (Heat generation per unit volume) Temperature inside the flame cell Flame cell

Solution of RTE The exact (analytical or numerical) solution of integro- differential radiative transfer equation (RTE) is generally a formidable task. Although there have been a few attempts to formulate RTE for non-isothermal rectangular enclosures. Explicit solutions are only available for simplified situations such as black walls and constant properties etc. There is growing interest in approximate solutions for furnace design and analysis. The exact solutions even for these simplest systems are used to serve as benchmarks against which the accuracy of approximate solutions is tested.

Radiation heat transferred to furnace wall Radiation heat transfer Where  eff is the emissivity of flame and water wall system. Emissivity of PC flame S : Effective thickness of radiant (flame) layer. V is the volume of the gas and A is the enclosing surface area

K is the coefficient of radiant absorption Volume fraction of RO 2 & H 2 O : r RO2 & r H2O c 1 : 1.0 for coal and 0.5 for wood c 2 : 0.1 for PC flame, 0.03 for Stoker flame.  h : Concentration of ash particles d h : diameter of ash particles : 13  m for PC & 20  m for stoker.

Thermal Efficiency Factor,  If clean water wall is a perfect black body all radiation falling on it will be absorbed. Fouling (  leads to drop in emissivity of the wall. Water walls consists of tubes which generate an angular coefficient, x. Angular coefficient varies with the location of water wall. Thermal efficiency factor is defined as the fraction of incident radiation absorbed by the tubes: The average thermal efficiency factor is calculated as