The finite-volume method has been shown to effectively predict radiant exchange in geometrically simple enclosures where the medium is gray, absorbing, emitting, and scattering. Cartesian and circular cylindrical meshes have always been used. The present article shows that the method applies equally well to geometrically complex enclosures where nonorthogonal, boundary-fitted meshes are used. This development permits radiant heat transfer to be computed on the same mesh employed to solve the equations of fluid motion.

Computation of radiant heat transfer on a nonorthogonal mesh using the finite-volume method

Internal-combustion engine heat transfer

Radiative heat transfer in a three-dimensional participating medium was predicted using the discrete-ordinates method. The discrete-ordinates equations are formulated for an absorbing, anisotropically scattering, and re-emitting medium enclosed by gray walls. The solution strategy is discussed and the conditions for computational stability are presented. Several test enclosures are modeled. Results have been obtained for the S2, S4, S6, and S8 approximation s that correspond to 8, 24, 48, and 80 fluxes, respectively, and are compared with the exact-zone solution and the P3 differential approximation. Solutions are found for conditions that simulate absorbing media and isotropically and anisotropically scattering media. Solution accuracy and convergence are discussed for the various flux approximations. The S4, S6, and S8 solutions compare favorably with the other methods and can be used to predict radiant intensity, incident energy, and surface heat flux. A an bn B C E G / L n q r S x y z a /U,,£,TJ p a a © V Nomenclature = north-south areas, m2 = coefficients of a Legendre series = coefficients of a modified Legendre series = east-west areas, m2 = front-back areas, m2 = emissive power ( = aT4), W/m2 = incident energy, /4w/d6, W/m2 = radiant intensity, W/(m2 • Sr) = enclosure dimension, m = unit normal = heat flux, W/m2 = position vector, m = source term, W/m3 = volume of pth control volume, m3 = weight function in a direction - m (fractional area of a unit sphere) = coordinate, m = coordinate, m = coordinate, m — finite-difference weighting factor = extinction coefficient, a -f K,m~l = surface emittance = absorption coefficient, m"1 = ordinates p = cos0, £ = sin0 sin , TJ = sinG cos = outgoing direction of radiation = phase function = surface reflectance = scattering coefficient, m"1 = Boltzmann's constant, 5.669 X 1(T 8 W/(m2

Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method

Three-dimensional radiative heat transfer solutions by the discrete-ordinates method

The use of the Monte Carlo method in radiative heat transfer is reviewed. The review covers surface-surface, enclosure, and participating media problems. Discussio. is included of research on the fundamentals of the method and on applications to surface-surface interchange in enclosures, exchange between surfaces with roughness characteristics, determination of configuration factors, inverse design, transfer through packed beds and fiber layers, participating media, scattering, hybrid methods, spectrally dependent problems including media with line structure, effects of using parallel algorithms, practical applications, and extensions of the method. Conclusions are presented on needed future work and the place of Monte Carlo techniques in radiative heat transfer computations

The Monte Carlo Method in Radiative Heat Transfer

A new numerical solution method for the calculation of the thermal radiation transfer in combustors is described. It has been especially developed for incorporation in general combustor prediction procedures for the flow, and chemical reaction. It combines features and advantages of the zone, Monte Carlo, and flux model solution methods while avoiding their shortcomings. It is based on the solving of representatively directed beams of radiation within the enclosure between the known wall boundary conditions and on the subsequent computing of the radiation sources which arise within the finite difference control volumes of the flow procedure due to the passage of the beams. It is fast, exact applicable to complex geometries, and it retains in evidence the physics of the problem by avoiding complex mathematics.

N.G. Shah

Papers

A new radiation solution method for incorporation in general combustion prediction procedures