Unsteady regimes of hydrodynamics and heat transfer at production of high-temperature silicate melts

Unsteady Natural Convection with Temperature-Dependent Viscosity in a Square Cavity Filled with a Porous Medium

“…Optimum value of the relaxation parameter was chosen on the basis of computing experiments. The time step used here was chosen to be τ = 10 −3 , which was also used in papers by Aleshkova and Sheremet (2010), Bondareva et al (2013), Sheremet (2010Sheremet ( , 2012. The accuracy of the numerical code developed by the authors was checked by preparing the benchmark solutions for natural convection with temperature-dependent viscosity in a square cavity filled with a pure fluid (see Hyun and Lee 1988).…”

“…The partial differential equations (5)- (7) with corresponding initial and boundary conditions (9) were solved by finite difference method (see Aleshkova and Sheremet 2010;Bondareva et al 2013;Sheremet 2010Sheremet , 2012 using the uniform grid. For the approximation of the convective terms, we used the difference scheme of the second order, and for the approximation of the diffusion terms, we used the central differences.…”

“…The governing equations of convective heat transfer in dimensionless variables stream function -vorticity become (see Aleshkova and Sheremet 2010;Bondareva et al 2013):…”

“…The study of convective flow and heat transfer of fluids with temperature-dependent properties is of considerable interest in the modern fluid systems of practical importance (see Alim et al 2014;Bondareva et al 2013;Hirayama and Takaki 1993;Hyun and Lee 1988;Jiji 2006;Juarez et al 2011;Martynenko and Khramtsov 2005;Parveen and Alim 2011;Sivasankaran and Ho 2008;Umavathi and Ojjela 2015). It is well known that in the case of the moderate temperature differences, an influence of the temperature-dependent fluid properties in cavities on the fluid structure and heat transfer becomes more essential.…”

“…They found that the velocity and temperature profiles are distorted in the case of the influence of the temperature-dependent properties. Bondareva et al (2013) have analyzed numerically and experimentally unsteady fluid flow and heat transfer of high-temperature silicate melt of temperature-dependent viscosity and heat capacity inside the melting furnace. Mathematical model formulated in the dimensionless stream function, vorticity and temperature has been carried out on the basis of finite difference schemes of the second order.…”