Analysis of Radiation Heat Transfer in Furnace P

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 Face 1 Face 5 n North • Classification: Ø Basic models and their determinants Ø Based on quadrature set Ø Complex geometry of the furnace Face 4 y w Face 3 η μ West x e z s ξ South Face 6 East Face 2 L W H

Basic models for RTE in gas radiation RTE Optically Thin Directional Averaging 2 -Flux 4 -Flux Multiflux DOM Self-absorbing Differential Approximation Moment Modified. Moment PN - Approx. Optically Thick Energy Hybrid Zone MCM Numerical (FD, FV) 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: Face 1 Ø All six boundaries are diffuse and gray Ø Absorbing, emitting, non scattering gray medium Face 5 n North Face 4 Ø Same absorption coefficient at all points y w Face 3 η μ West x e z s ξ South Ø Thermophysical properties e. g. density, specific heat, thermal conductivity and optical property like extinction coefficient are constant. Ø Absorption coefficient = emission coefficient Governing equation for participating media (RTE): Face 6 East W Face 2 L Co-ordinate system for cubic enclosure Where; S is line of sight distance in the direction of propagation of the radiant intensity I H

Direction cosine in 2 D geometry RTE with consideration of direction cosine Where Im 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 Flame cell Temperature inside the flame cell (Heat generation per unit volume)

Solution of RTE • The exact (analytical or numerical) solution of integrodifferential 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 eeff 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. RO 2 & r. H 2 O c 1 : 1. 0 for coal and 0. 5 for wood c 2 : 0. 1 for PC flame, 0. 03 for Stoker flame. mh : Concentration of ash particles dh : diameter of ash particles : 13 mm for PC & 20 mm for stoker.

Thermal Efficiency Factor, y • If clean water wall is a perfect black body all radiation falling on it will be absorbed. • Fouling (x)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