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An abstract of the article "Bayesian estimation of posterior means of heritability for weight at week 8 in Iranian indigenous chickens," by R. Lotfi and colleagues are presented.

The population balance equation considers the change of the bubble size and the bubble number density due to coalescence and break-up in bubbly flows. Although a number of theoretical models exist for coalescence and break-up rates, nearly no experimental data for the validation of these models exist for turbulent flow with high void fraction. To overcome this lack, vertical air–water pipe flows were examined. A comprehensive validation of the population balance equation is based on the knowledge of the development of the number density distribution function and of the liquid flow turbulence along the pipe flow. The experimental and analytical procedure to obtain these parameters is presented. The void fraction, interfacial area density and mean bubble volume were calculated as statistical moments of the number density distribution function. For its measurement a combination of single and double fibre optical probes was used that allowed measurement in high void fraction flows. X-hotfilm probes were used to measure the liquid flow turbulence level of the two-phase flow. The flow inlet condition was influenced with the aid of turbulence grids. The results show that the number of coalescence and break-up events depend strongly on the number of bubbles per unit volume and the on bubble volume that differ even for the same gas and liquid superficial velocities. From the axial development of the number density distribution function coalescence and break-up events could be identified within certain bubble volume ranges and the source terms of the population balance equation could be quantified. In a first step the data were used to check two existing theoretical models with respect to coalescence and break-up rates. [Copyright &y& Elsevier]