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The purpose of this paper is to fundamentally develop a mathematical model for predicting the particle size distribution (PSD) in fluidized beds because their hydrodynamics depend on the PSD and its evolution during operation. To predict the gradual PSD change in a fluidized bed by using the population balance method (PBM), the kinetic parameter for agglomerate formation should be known and this parameter, in this work, is determined by the results of computational fluid dynamic–discrete element method (CFD-DEM) simulation.

Momentum and energy conservation equations and soft-sphere DEM are used to simulate the agglomeration phenomenon at high temperature in a two-dimensional air-polyethylene fluidized bed in bubbling regime. The Navier–Stokes equations for motion of gas are solved by the SIMPLE algorithm. Newton’s second law of motion is applied to describe the motion of individual particles. Collision between particles is detected by the no-binary search algorithm.

A correlation is proposed for estimating the kinetic parameter for agglomerate formation based on collision frequency, collision efficiency and inlet gas temperature. Based on the corrected kinetic parameter, the PBM is able to predict the PSD evolution in the fluidized bed in a fairly good agreement with the results of the CFD-DEM.

The results of the agglomeration process cannot be compared quantitatively with experimental results. Because three-dimensional fluidized bed mostly contains millions of particles and simulating them takes a long computing time in DEM. As far as temperature is a dominant parameter in the agglomeration process, effects of inlet gas temperature are examined on the kinetic parameter. On the other hand, wider and deeper insights in which the effect of other parameters, such as velocity and so on will be studied, is one of the goals in the authors’ next works to compensate for the shortcomings in this work.

This study helps to understand the effect of the inlet gas temperature during the agglomeration process on the kinetic parameter and provides fundamental information in dealing with kinetic parameter to attain PSD in fluidized bed by the PBM.

This study aims to propose a practical, virtue-centric model of leadership based on Islamic principles. The structure of the Islamic leadership construct is validated through confirmatory factor analysis. Its relationship with performance and organizational commitment is examined and the mediating role of organizational commitment is assessed.

Islamic leadership model is tested using confirmatory factor analysis with data collected from employees working in the services sector in Turkey. Relationships between Islamic leadership, organizational commitment and performance are examined through a path analysis.

The factor analysis results presented a good fit for the proposed Islamic leadership model, which consists of wisdom, religiosity, justice and kindness dimensions. Regarding path analysis, findings indicated a positive relationship between Islamic leadership and job performance. Moreover, organizational commitment partially mediated the relationship between Islamic leadership and job performance.

Previous studies on Islamic leadership contain a very little number of empirical models. This study proposes a valuable empirical model of Islamic leadership consisting of moral values, spirituality, ethics and wisdom. In addition, the proposed model is supported with empirical pieces of evidence. Evidence of the partial mediating role of organizational commitment between Islamic leadership and job performance is also revealed by the study.