Numerical modeling of the natural convection of a non-Newtonian fluid in a closed cavity

Abstract

In this paper, a time-dependent natural convective heat transfer in a closed square cavity filled with non-Newtonian fluid was considered in the presence of an isothermal energy source located on the lower wall of the region under consideration. The vertical boundaries were kept at constant low temperature, while the horizontal walls were completely insulated. The behavior of a non-Newtonian fluid was described by the Ostwald de Ville power law. The process under study was described by transient partial differential equations using dimensionless non-primitive variables "stream function-vorticity-temperature". This method allows excluding the pressure field from the number of unknown parameters, while the non-dimensionalization allows generalizing the obtained results to a variety of physical formulations. The considered mathematical model with the corresponding boundary conditions was solved on the basis of the finite difference method. The algebraic equation for the stream function was solved by the method of successive lower relaxation. Discrete analogs of the vorticity equation and energy equation were solved by the Thomas algorithm. The developed numerical algorithm was tested in detail on a class of model problems and good agreement with other authors was achieved. Also during the study, the mesh sensitivity analysis was performed that allows choosing the optimal mesh. As a result of numerical simulation of unsteady natural convection of a non-Newtonian power-law fluid in a closed square cavity with a local isothermal energy source, the influence of governing parameters was analyzed including the impact of the Rayleigh number in the range 10 4-10 6 , power-law index n = 0.6-1.4, and also the position of the heating element on the flow structure and heat transfer performance inside the cavity. The analysis was carried out on the basis of the obtained distributions of streamlines and isotherms in the cavity, as well as on the basis of the dependences of the average Nusselt number. As a result, it was established that pseudoplastic fluids (n < 1) intensify heat removal from the heater surface. The increase in the Rayleigh number and the central location of the heating element also correspond to the effective cooling of the heat source.

Optimal wall natural convection for a non-Newtonian fluid with heat generation/absorption and magnetic field in a quarter-oval inclined cavity

“…But in non-Newtonian fluids, the amount of fluid viscosity depends on the force applied to that fluid. In Newtonian fluids, the relationship between stress and strain rate is linear, but in non-Newtonian fluids, this relationship is nonlinear, and in this range of fluids, the duration of stress plays an important role in the resulting shear stress [26][27][28].…”

“…Also, the effect of applying a magnetic field on the rate of heat transfer was greater for Hartmann numbers less than 30. Loenko et al [27] investigated heat transfer of non-Newtonian and Newtonian fluids in a square chamber with a heat-generating barrier. The results showed that increasing the fluid power-law fluid index led to reducing the fluid velocity and a faster stationary mode was achieved.…”

Coupling LES with soot model for the study of soot volume fraction in a turbulent diffusion jet flames at various Reynolds number configurations

“…Although many studies have been performed to consider computational techniques for different models for different approaches, it is essential to improve the past research on computational methods (Mahian et al , 2019; Dogonchi et al , 2018; Izadi et al , 2018; Sheremet et al , 2018; Sheremet et al , 2017; Ellahi et al , 2016; Pop et al , 2016; Dinarvand et al , 2016; Bondareva et al , 2015; Dinarvand et al , 2015; Izadi et al , 2020; Miroshnichenko et al , 2020; Bondareva et al , 2020; Loenko and Sheremet, 2020; Sheremet et al , 2019; Astanina et al , 2019; Gibanov and Sheremet, 2019; Miroshnichenko et al , 2018; Sheremet et al , 2018; Bondareva et al , 2018; Chamkha et al , 2020; Mehryan et al , 2020; Krishna et al , 2020; Mansoury et al , 2020; Sadeghi et al , 2020; Dogonchi et al , 2020; Ghalambaz et al , 2020; Ishak et al , 2020; Rejvani et al , 2019; Alsabery et al , 2019; Mehryan et al , 2019; Hoseinzadeh et al , 2019; Taamneh et al , 2019; Raza et al , 2019). The overall strategy considered in this study was to couple the LES with the BMH soot model through a non-premixed flamelet combustion model for the study of soot evolution process in a diffusion flame for three different configurations at an average stain rate of 4,100 (s −1 ) to understand soot dynamics study such as SVF and the various stages of soot formation such as soot nucleation rate, coagulation rate, soot surface oxidation rate and soot surface growth rate.…”