Modeling Heat Loss during Self-Heating Composting Based on Combined Fluid Film Theory and Boundary Layer Concepts

Abstract

The overall heat-transfer coefficients ( U-values) developed during the self-heating composting of mixed vegetables and chicken manure were determined based on a combined fluid film theory and thermal boundary layer concept. The heat flow was modeled into four heat transfer components. The heat transfer mechanisms have been modeled as comprising two conductive heat fluxes across the compost matrix and compost reactor walls, one heat flux across the film of water condensing on the inner reactor surface and a convective heat flux due to free convection on the outside surface of the reactor walls. Individual film heat-transfer coefficients have been calculated using a series of dimensionless correlations grouping the outer reactor surface temperature, the Nusselt (Nu), Prandtl ( Pr), Grashof ( Gr) and Rayleigh ( Ra) numbers. Gr has varied between 5.11 × 10^6 and 3.71 × 10^9, Pr from 0.692 to 0.712, and Ra from 3.64 × 10^6 to 2.56 × 10^9. Four different equations have been used to evaluate the heat transfer coefficients characterizing the heat flow due to free convection. The maximum U-values have been found to vary between 0.368 and 0.387 W.m^-2·K^-1, and the minimum U-values have ranged from 0.255 to 0.288 W.m^-2·K^-1. A 4-parameter Weibull model was found to describe the variation of U-value with compost matrix temperature reliably with R^2 = 0.9999.