Natural Convection of Non-Newtonian Power-Law Fluid in a Square Cavity with a Heat-Generating Element

Abstract

Development of modern technology in microelectronics and power engineering necessitates the creation of effective cooling systems. This is made possible by the use of the special fins technology within the cavity or special heat transfer liquids in order to intensify the heat removal from the heat-generating elements. The present work is devoted to the mathematical modeling of thermogravitational convection of a non-Newtonian fluid in a closed square cavity with a local source of internal volumetric heat generation. The behavior of the fluid is described by the Ostwald-de Waele power law model. The defining Navier–Stokes equations written using the dimensionless stream function, vorticity and temperature are solved using the finite difference method. The effects of the Rayleigh number, power-law index, and thermal conductivity ratio on heat transfer and the flow structure are studied. The obtained results are presented in the form of isolines of the stream function and temperature, as well as the dependences of the average Nusselt number and average temperature on the governing parameters.

Influence of the chamber inclination angle and heat-generating element location on thermal convection of power-law medium in a chamber

“…The time-dependent partial differential equations in the Boussinesq approximation, describing the process under study, in the primitive variables “velocity – pressure” are (Loenko et al , 2019, Hatami and Jing, 2017): …”

“…By introducing the stream function and vorticity and dimensionless quantities (Astanina et al , 2019; Loenko et al , 2019, Hatami et al , 2017), we obtain the following differential problem: …”

Convective heat transfer of power-law fluid in a cavity with a heat source of time-dependent volumetric heat generation

“…Сформулированная краевая задача для дифференциальных уравнений в частных производных (2.3)-(2.6) с соответствующими начальными и граничными условиями решена методом конечных разностей [13,14] Разработанный метод решения был протестирован на ряде модельных задач свободноконвективного теплопереноса. Детальное описание тестовых задач представлено в работах [14,15].…”

Study of the Flow and Heat Transfer of a Viscoelastic Fluid Using Hybrid Neural Network-Particle Swarm Optimization (Hnnpso)

“…Many researchers have studied the flow and heat transfer phenomena over open surfaces and channels. For instance, the MHD flows [12,13,14], flow over flat surfaces [15], natural and mixed convection flow and heat transfer [16][17][18], flow over a cylinder [19], and entropy generation [20] have been studied in past years. The non-Newtonian fluids are important in industrial applications as the behavior of many practical fluids cannot be described using the Newtonian model of fluids.…”