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    The effects of bottom wall heating on mixed convection of yield stress fluids in cylindrical enclosures with a rotating end wall
    (Pergamon-Elsevier Science Ltd, 2018) Turan, Osman; Chakraborty, Nilanjan
    Steady-state laminar mixed convection of Bingham fluids in cylindrical enclosures with a rotating top cover has been numerically analysed for the configuration where the bottom cover is kept at a higher temperature than the rotating top cover. The numerical investigations have been carried out based on steady-state axisymmetric incompressible flow simulations for a range of different values Reynolds, Richardson, and Prandtl number given by 500 <= Re 3000, 0 <= Ri <= 1 and 10 <= Pr <= 500 respectively. The aspect ratio (i.e. height: radius = AR = H/R) of the cylindrical container is considered to be unity (i.e. AR = H/R = 1). The mean Nusselt number (Nu) over bar has been found to decrease sharply with increasing Bn owing to flow resistance arising from yield stress, but subsequently (Nu) over bar asymptotically approaches a value of unity, which is indicative of a conduction-driven transport. In addition, the mean Nusselt number (Nu) over bar has been found to increase with increasing Reynolds number due to the strengthening of advective transport. However, the mean Nusselt number (Nu) over bar exhibits a non-monotonic trend (i.e. increases with increasing Ri for small values of Richardson number before showing a weak decreasing trend) with increasing Ri for Newtonian fluid (i.e. Bn = 0), whereas (Nu) over bar increases with increasing Ri for small values of Richardson number before becoming a weak function of Ri for Bingham fluids. A step change in the mean Nusselt number has also been observed with an increase in Richardson number for some Bingham number values due to a change in flow pattern. The influences of Prandtl, Reynolds, Richardson, and Bingham numbers on the mean Nusselt number have been explained in detail based on both physical and scaling arguments. The simulation data and scaling relations have been utilised to propose a correlation for the mean Nusselt number, which has been shown to capture the numerical findings satisfactorily for the parameter range considered here. 2018 Elsevier Ltd. All rights reserved.
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    Effects of wall heating on laminar mixed convection in a cylindrical enclosure with a rotating end wall
    (Elsevier France-Editions Scientifiques Medicales Elsevier, 2018) Turan, Osman; Yigit, Sahin; Chakraborty, Nilanjan
    Steady-state laminar mixed convection in a cylindrical enclosure has been numerically analysed for different values of Reynolds, Richardson and Prandtl numbers given by 500 <= Re <= 3000, 0 <= Ri <= 1 and 10 <= Pr <= 500 respectively. The aspect ratio (i.e. height: radius = AR = H/R) of the cylindrical container is considered to be unity (ie. AR = H/R = 1). The bottom and top covers of the cylindrical enclosure are kept at different temperatures (T-C < T-H), while the cylindrical surface is taken to be adiabatic. The simulations for rotating top and bottom cover configurations yield the same numerical values of the mean Nusselt number (Nu) over bar when the thermal boundary conditions are kept unaltered. For this reason, only rotating top hot wall (ie. C1 configuration) and rotating top cold wall (ie. C2 configuration) have been considered for this analysis. The mean Nusselt number (Nu) over bar has been found to assume higher values in the C2 configuration than in the Cl configuration. Moreover, it has been found that the variation of the mean Nusselt number with Richardson number in the C2 configuration is qualitatively different from that in the C1 configuration. The simulation data has been used to propose a correlation for (Nu) over bar for the range of Re, Ri and Pr considered here for both Cl and C2 configurations. In addition to this, a regime diagram has been proposed for the C2 configuration in order to demarcate different flow regimes.
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    Free convection of power-law fluids in enclosures with partially heating from bottom and symmetrical cooling from sides
    (Pergamon-Elsevier Science Ltd, 2019) Yigit, Sahin; Battu, Madhusudhan; Turan, Osman; Chakraborty, Nilanjan
    Steady-state laminar free convection of power-law fluids in a square enclosure with partial heating from below and symmetrical cooling from sides has been investigated based on numerical simulations. The partially heating is conducted by a centrally heated heat source on the bottom wall for different values of normalised heat source length IA (ranging from 0.2 to 0.8); power-law index n (from 0.6 to 1.8); nominal Rayleigh number (Ra) (from 10(3) to 10(6)) and nominal Prandtl number Pr (from 10 to 10(3)). An increase in the power-law index n leads to weakening of thermal advection owing to the augmentation of viscous resistance. This is reflected as an increment in the mean Nusselt number (Nu) over bar with decreasing value of n. Additionally, (Nu) over bar increases with an increase in Ra and IA for shear thinning (i.e. n < 1), Newtonian (i.e. n = 1) and shear thickening (i.e. n > 1) fluids. The observed influences of Ra, Pr, n and 1/L on (Nu) over bar have been explained by physical and scaling arguments and parameterized by a correlation for the mean Nusselt number. (C) 2019 Elsevier Ltd. All rights reserved.
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    Laminar mixed convection of power-law fluids in cylindrical enclosures with heated rotating top wall
    (Pergamon-Elsevier Science Ltd, 2018) Turan, Osman; Yigit, Sahin; Liang, Ruibin; Chakraborty, Nilanjan
    Laminar mixed convection of inelastic non-Newtonian fluids obeying a power law model in a cylindrical enclosure with a heated rotating top cover has been investigated numerically in this study. The steadystate axisymmetric simulations have been carried out for a range of different nominal Reynolds, Prandtl, Richardson numbers (i.e. 500 <= Re <= 2000; 10 <= Pr <= 500 and 0 <= Ri <= 1) and power-law index (i.e. 0.6 <= n <= 1.8) for an aspect ratio (height/radius) of unity (i.e. AR = 1.0). It has been found that mean Nusselt number (Nu) over bar increases as Re and Pr increase, whereas (Nu) over bar decreases with increasing values of Ri for shear-thinning (i.e. n < 1), Newtonian (i.e. n = 1) and shear-thickening (i.e. n > 1) fluids. It has also been observed that the variation of Ni with n differs depending on the values of Re and Ri. For instance, for small values of Reynolds number, (Nu) over bar exhibits a non-monotonic trend (i.e. increases before reaching a maximum followed by a decreasing trend) with increasing n for small values of Richardson number, whereas (Nu) over bar monotonically increases with increasing values of n for high Richardson number cases. However, in the case of high Reynolds number, (Nu) over bar increases with n before reaching a maximum value which is followed by a decreasing trend for all values of Ri considered here. Detailed physical explanations are provided for the influences of Re, Pr, Ri, and n on (Nu) over bar based on an elaborate scaling analysis. Finally, the numerical findings have been used to propose a correlation for (Nu) over bar for the ranges of Re, Pr, Ri, n considered here. (C) 2018 Elsevier Ltd. All rights reserved.
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    Mixed convection of power-law fluids in cylindrical enclosures with a cold rotating top cover and a stationary heated bottom wall
    (Elsevier, 2020) Turan, Osman; Yigit, Sahin; Chakraborty, Nilanjan
    Steady-state laminar mixed convection in cylinders with a rotating top cold cover and a heated bottom has been numerically analysed for inelastic shear-thinning/shear-thickening fluids by applying power-law model of viscosity. In this analysis, axisymmetric incompressible flow simulations have been conducted for a range of different values of Reynolds, Richardson, Prandtl numbers (i.e. 500 <= Re <= 2000; 0 <= Ri <= 1.0; 10 <= Pr <= 1000) and power-law index (i.e. 0.6 n 1.8) for an aspect ratio (height/radius) of unity (i.e. AR = 1.0). The thermal convective transport has been found to strengthen with increasing Re and Pr, which in turn gives rise to an increase in the mean Nusselt number Nu. By contrast, an increase in Ri leads to a mild increase in Nu for small Richardson number values but Nu becomes insensitive to the changes in Ri for large Richardson numbers within the range of 0 <= Ri <= 1.0 for all values of n considered here. The mean Nusselt number Nu exhibits a nonmonotonic trend (i.e. increases before reaching a maximum followed by a decreasing trend) with the variation of n. The influences of Ra, Pr and Ri on the mean Nusselt number Nu have been explained in terms of scaling arguments. The scaling relations along with the numerical findings have been utilised to propose a correlation for the mean Nusselt number for the configuration and the parameter range considered here.