Experimental examination of heat transfer in disperse media at low Reynolds numbers

Abstract

Because of the extensive application of plants with a fixed bed of particles in chemical technology and other areas of industry, it is important to know the relationships governing the heat transfer between the particles of the bed and the heat carrier moving through the bed. The experimental data on interphase heat transfer both in disperse and packed media differ to the largest extent in the region of low Reynolds numbers [1][2][3].One of the reasons for these differences is the fact that in processing the results of the measurements of the heat conductivities of the phases were neglected or incorrectly taken into account.In the present work, the interphase coefficients of heat transfer are determined from the variation of the temperature of the air flow at the exit from the bed of the particles which is the response to the stepped variation of the flow temperature at the entry into the bed. Heat transfer is described by a linear system of equations taking into account the longitudinal heat conductivities of the individual phaseswith the initial conditions at @ = 0, t s = tag = tg = O, and the boundary conditions: at entryOl s d~g where y~ = YslXm.= Xg/~ m are the dimensionless effective coefficients of longitudinal heat conductivity ~ respectively the solid phase and the heat carrier; X m is the coefficient of molecular heat conductivity of the heat carrier; ts, tg, tag are the dimensionless mean temperatures of respectively the particles of the solid phase, the heat carrier, and the interface; x = X/d is the dimensionless longitudinal coordinate; Nu v = ~vd2/%m is the Nusselt criterion calculated from the bulk heat-transfer coefficient a v = uSv; a is the surface heat-transfer coefficient; S v is the area of the surface of particles in the unit volume of the charge; 8 = ~T is dimensionless time; ~ = Xm/[(l --S)CsPsd=)]; T is the time; ~ is the porosity; Ca, Ps are respectively specific heat capacity and density of the particles; Pe = RePr = c~p~Ud/v is the Peclet number; Re = pgUd/~ is the Reynolds criterion; Pr = CgV/X m is the Pran~t~ criterion; c~,0g,~ are respectively the specific heat capacity at constant pressure, density, and dynamic viscosity of the heat carrier; U is the rate of filtration calculated from the total cross section of the charge; B = ~Cgp~/ [(l --r is the ratio of the volume heat capacities of the phases; d is the equivalen~ diameter of the particles.In most cases, the family of the equations (i), (2) is solved using the insufficiently justified assumption on the isothermal nature of the solid phase particles, i.e., at t s = tag.In the present work, the ratio of the mean particle temperature t s to the surface temperature particles tag was determined by solving the unidimensiona! heat conductivity equations with respect to particles I a t otp ~. otp

Review of the experimental research on the thermal‐hydraulic characteristics in the pebble bed nuclear reactor core and fusion breeder blankets

“…The original D‐C model ignores the thermal conduction through the pebbles, causing the obtained convective heat transfer data less reliable at low Reynolds numbers 68‐70 . This disadvantage can be solved by introducing large axial effective dispersion coefficient into the original D‐C model 63,68,70 . Abdelhafeez et al 69 introduced a shot pulse of heat to the cold air before it entered the pebble bed test section.…”

“…Wall effects were neglected in some experiments where the parameters such as the porosity and superficial velocity were obtained in average over the whole test section 63,69,76,77 . For those with the pebble bed‐to‐pebble‐diameter ratio large enough, the results were acceptable due to the negligible impact on the flow resistance and convective heat transfer characteristics in the pebble bed 51,52,69,70,76,83,84 . Wall effects can also be eliminated by the proper design in the near wall zone.…”

“…Some experiments adopting non‐steady methods based on Schumann models or D‐C models, or transient single‐blow technique ignores the axial distribution of the convective heat transfer coefficient and caused uncertainties in the experimental results 53,66,69,70,76,77 . To eliminate the entrance effects, test sections with internal heat generation put several layers of unheated pebbles at the inlet to ensure the fluid to be hydrodynamically developed before entering the heated section 3,67 …”