A point to be noted is that the present model used the conduction heat transfer obtained independently based on the theory of conduction through contact spots, whereas the contribution of the convective heat transfer mode was determined separately under a unique experimental condition which decouples the convection mode from the conduction mode.Therefore, this model offers an independent estimate of the total heat transfer (Nut) which shows agreement with the experimental data reported in the literature. Nomenclature a, radius of sphere, m Ape, surface area of spheres, m2 As', area of bed per sphere j=4a2 (at i = 1) and 2o2/V3 (at i -2¡, m2 Arm, modified Archimedes number, (2a)3gpf(ps -Pf)/µ2 Bi, Biot modulus, hf"-a/ks, dimensionless Cp, specific heat, J/kg K Dt, tube diameter, m e, thermal emissivity, dimensionless E, Young's modulus, N/m2 G, mass velocity, kg/m2 s h, heat transfer coefficient, J/m2 s K Jht, Colburn J factor, (ht/cpGf)Pr2/3, dimensionless k, thermal conductivity, J/m s K K\ correction factor (=1 (at i = 1) and 1/V6 (at i = 2)), dimensionless Nut, total Nusselt number, ht-2a/kf, dimensionless P, pressure on contact spots \ = (W / 2) / (ttD2 / 4)\, N/m2 Pn, Legendre polynomial of order n, dimensionless Pr, Prandtl number, cpp¡/k r0, radius of contact spot between spheres in bed, m Rcd, resistance to heat conduction, s K/J t, temperature (of solids); T = ttf, K AT, temperature drop per layer of spheres, K T, average temperature driving force JAP.eTdA / /AP-«dA, K x0, defined as cos 0, |=r0/a = |0.75/P[(1 -v2)/E][P As'/a2]i1''3, dimensionless Greek Letters p, density; kg/m3 Pi, viscosity, N s/m2 v, Poisson's ratio, dimensionless Subscripts cd, pertaining to conduction e, effective f, of fluid fp, fluid-particle or convective r, radiative red, radiative/conductive s, of solid t, total Literature Cited