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Free convection about a vertical cylinder in a porous medium subject to constant wII tempemmre or conxtant wall heat flux is considered. The influence of uniform bteml m a flux on the boundary4ayer transport ic studied. Numerrerrcal results for heat transfer along the boundary and tempemtwe profiles are presented for various wlues of the pammeter w which is a measure of the effect of injection or withdiowl of fluid as compared to the combined transverse eurvahre and bteml mass f i x effects.

Combined conductive and radiative heat transfer through a gray, absorbing, emitting, and scattering medium with internal heat generation in a finite cylindrical enclosure is analyzed. The radiative transport equation is solved by the discrete ordinates method using the DOT-IV transport code, which is coupled to a compatible control-volume-based finite-difference code for the temperature field calculations. The coupled radiative transfer and the energy equations are solved by an iterative procedure. The effects of the conduction-radiation parameter, scattering, optical thickness, and wall emissivity on the medium temperatures and surface heat fluxes are discussed. Nomenclature a = aspect (half-height-to-radius) ratio, H/R I = dimensionless radiation intensity, i/4oT 4 w k = thermal conductivity N = conduction-radiation parameter, kp/4dT 3 w Q R = dimensionless radiative heat flux, q R /oT* w Q T = dimensionless total heat flux, q T /oT 4 w r -position vector T w = wall temperature U = dimensionless internal heat generation, up P = extinction coefficient, K 4-o e =wall emissivity 6 = dimensionless temperature, T/T W K = absorption coefficient o = scattering coefficient a = Stefan-Boltzmann constant r = optical distance, PS, s = r or z T R ,T H = optical depths in the r-, ^-direction, PR, PH fl = direction vector co = single scattering albedo, a/P V T = dimensionless gradient operator, P~l V

Combined natural convection and radiation in an asymmetrically heated square enclosure is studied numerically with both adiabatic and perfectly conducting end walls. The momentum and energy equations are solved by a control volume based finite difference algorithm which is coupled with the discrete ordinates method for radiative heat transfer calculations. The changes in the flow patterns and temperature distributions due to the presence of radiation in an enclosure with conducting end walls are compared with those for the case of an enclosure with adiabatic end walls, and significant differences are noted. The flow field is stronger, and the heat input along the hot wall and the end walls are greater for the conducting end wall case. The effects of optical thickness, scattering and wall emissivity on the flow and temperature fields and heat transfer rates are analysed.

write a program (or proceed by hand calculation) to generate the array g. Running the commercial program with/and g as separate load cases would then give the strains to be used as input to an additional small, user written program for calculating the force Ff (and F«) of Eq. (5).Referencê allagher, R.H., Finite Element Analysis Fundamentals, Prentice-Hall, Englewood Cliffs, N.J., 1975, pp. 310-311. dimensional cylindrical and spherical geometries. To this effect, a linear phase function is used. Modest and Azad 3 showed that a slightly modified form of the linear model, used together with the differential P l approximation, yields quite accurate results in planar geometry. AnalysisConsider the equation of transfer ft.V/=o/,,-(a! + a)/+ -f /(IT) •/>(!),IT)dw-' 4TT J4* (1) Nomenclature B= emissive power, irl b I -radiation intensity I b = blackbody intensity t = direction cosine n = radius ratio, r 2 //*/ P = phase function Q = a constant r = dimensionless radial direction (a + a)r' r' = radial direction X = position vector a.= absorption coefficient j8 = polar angle e = emissivity X = scattering albedo, a/(a + a) % =cos0 a = scattering coefficient T = optical thickness, r 2 -r 1 -azimuthal angle w = solid angle 0 = unit direction vector Subscripts 1,2 = inner and outer boundary, respectively