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Particle-laden jet flows can be observed in many industrial applications. In this investigation, the horizontal motion of particle laden jets is simulated using the Eulerian–Lagrangian framework. The two-way coupling is applied to the model to simulate the interaction between discrete and continuum phase. In order to track the continuum phase, a passive scalar equation is added to the solver. Eddy Life Time (ELT) is employed as a dispersion model. The influences of different non-dimensional parameters, such as Stokes number, Jet Reynolds number and mass loading ratio on the flow characteristics, are studied. The results of the simulations are verified with the available experimental data. It is revealed that more gravitational force is exerted on the jet as a result of the increase in mass loading, which deflects it more. Moreover, with an increase in the Reynolds number, the speed of the jet rises, and consequently, the gravitational force becomes less capable of deviating the jet. In addition, it is observed that by increasing the Stokes number, the particles leave the jet at higher speed, which causes a lower deviation of the jet.

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There are two primary laws including the first and second laws of thermodynamics that should be used to assess a process. Generally, only the first law of thermodynamics is investigated in numerical solutions, so it is possible to exist some numerical results that do not satisfy the second law of thermodynamics because of numerical errors. To achieve reliable numerical outcomes, it is better to apply two indexes of HEAT BALANCE ERROR and VIRTUAL ENTROPY GENERATION, which come from the second law of thermodynamics. In other words, an approach to develop computational fluid dynamics investigations is to take second law of thermodynamics into consideration. In this study, two different models including counterflow double-pipe heat exchanger and single-pipe with constant wall temperature are simulated in various cases with different efficiencies and temperature ratios. It is found that 46 cases of total 523 double-pipe models and 24 cases of total 402 simulations of single-pipe models had unacceptable results regarding to two mentioned criteria. The results revealed that it is less likely to gain unreliable results in smaller efficiency and lower inlet temperature for double-pipe heat exchanger and single-pipe respectively. K E Y W O R D S entropy generation, heat balance error, heat exchanger, second law of thermodynamics, virtual entropy generation Heat Transfer-Asian Res. 2019;48:1933-1945.wileyonlinelibrary.com/journal/htj