Falling film flow of a viscoelastic fluid along a wall

Abstract

In this paper, we study the heat transfer in the fully developed flow of a viscoelastic fluid, a slag layer, down a vertical wall. A new constitutive relation for the stress tensor of this fluid is proposed, where the viscosity depends on the volume fraction, temperature, and shear rate. For the heat flux vector, we assume the Fourier's law of conduction with a constant thermal conductivity. The model is also capable of exhibiting normal stress effects. The governing equations are non-dimensionalized and numerically solved to study the effects of various dimensionless parameters on the velocity, temperature, and volume fraction. The effect of the exponent in the Reynolds viscosity model is also discussed. The different cases of shear-thinning and shear-thickening, cooling and heating, are compared and discussed. The results indicate that the viscous dissipation and radiation (at the free surface) cause the temperature to be higher inside the flow domain.

Stability for the Kelvin–Voigt variable order equations backward in time

“…Under condition (A), the theorem is proved by appealing to (17) and (19). Under conditions (B) of the theorem we employ the arithmetic-geometric mean inequality on the last term in (10) to arrive at an inequality of form (16) but where now…”

“…Among such non‐Newtonian fluids are viscoelastic fluids which typically display history‐dependent behaviour. Analyses of fading memory fluids or general viscoelastic fluids may be found in, for example, previous works 1–11 . The subject of this article is a particular class of fading memory fluids attached to the names of Kelvin and of Voigt, see, for example, previous studies 12–17 .…”

“…Analyses of fading memory fluids or general viscoelastic fluids may be found in, for example, previous works. [1][2][3][4][5][6][7][8][9][10][11] The subject of this article is a particular class of fading memory fluids attached to the names of Kelvin and of Voigt, see, for example, previous studies. [12][13][14][15][16][17] We are especially interested in the class of Kelvin -Voigt fluids succinctly described and analysed particularly in the Russian literature; see Karazeeva et al, 18 Oskolkov, 19,20 Oskolkov and Shadiev, 21 and Sviridyuk and Sukachevaand.…”

Effects of Shear Dependent Viscosity and Variable Thermal Conductivity on the Flow and Heat Transfer in a Slurry

“…In this paper we use the constitutive model given in [37] and advocated by Miao et al [38,39], where:…”

“…To apply the integral condition given by Equation (38), the volume fraction values are integrated using the composite Simpson's rule:…”