Mixed Convection In Power-law Fluids Research Articles

Investigation of the mixed convection of power-law fluids between two horizontal concentric cylinders: Effect of various operating conditions

The purpose of this paper is to study numerically the mixed convection between two rotating circular cylinders under horizontal arrangement. The cylinders have a concentric position with a blockage ratio of d/D = 2.5. The annular space is completely filled with non-Newtonian power-law fluid. The surface of the inner cylinder is hot whereas the surface of the outer one is cold. Three cases are studied: in the first one, the inner cylinder has a constant rotational speed, while the outer cylinder is completely fixed; the second case: both cylinders are rotating in the same direction and at the same rotational speed; in the last case, both cylinders are rotating in opposite directions at a similar rotational speed. All studied cases are examined for various values of Reynolds number (Re = 1–10), Richardson number (Ri = 0–3), and power-law index (n = 0.6–1.6) at Prandtl number Pr = 50.

Mixed convection of power-law fluids in cylindrical enclosures with a cold rotating top cover and a stationary heated bottom wall

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 non-monotonic 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.

Laminar mixed convection of power-law fluids in cylindrical enclosures with heated rotating top wall

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 steady-state 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‾ increases as Re and Pr increase, whereas Nu‾ 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 Nu‾ with n differs depending on the values of Re and Ri. For instance, for small values of Reynolds number, Nu‾ 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‾ monotonically increases with increasing values of n for high Richardson number cases. However, in the case of high Reynolds number, Nu‾ 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‾ based on an elaborate scaling analysis. Finally, the numerical findings have been used to propose a correlation for Nu‾ for the ranges of Re,Pr,Ri,n considered here.

Mixed Convection in Power-Law Fluids from a Heated Semicircular Cylinder: Effect of Aiding Buoyancy

Laminar aiding-buoyancy mixed-convection heat transfer in power-law fluids from a heated semicircular cylinder with its flat base facing the oncoming flow was studied in this work. The coupled momentum and energy equations were solved numerically over the following ranges of conditions: Richardson number (0 ≤ Ri ≤ 2), Reynolds number (0.1 ≤ Re ≤ 25), Prandtl number (1 ≤ Pr ≤ 100), and power-law index (0.3 ≤ n ≤ 1.8). Extensive results on the velocity and temperature fields are presented and discussed in terms of the streamline and isotherm contours adjacent to the heated object. Similarly, the distribution of the pressure coefficient and the local Nusselt number along the surface of the semicircular cylinder are analyzed to delineate the influence of the relevant dimensionless parameters listed above. Next, the pressure and total drag coefficient and surface average values of the Nusselt number describe the momentum and heat transfer aspects at the gross macroscopic level. Both the pressure and total drag coefficient exhibit the expected dependence on Richardson number, Prandtl number, and Reynolds number. Similarly, the average Nusselt number bears a positive dependence on each Richardson number, Prandtl number, and Reynolds number. Broadly, under otherwise identical conditions, heat transfer is augmented in shear-thinning fluids (n < 1) whereas it is somewhat impeded in shear-thickening fluids (n > 1) with reference to that in Newtonian fluids. Finally, the present numerical results of the average Nusselt number (recast in terms of the Colburn j H factor) were correlated as functions of the modified Reynolds number, Prandtl number, and power-law index thereby enabling its prediction in a new application.

Mixed convection of power-law fluids along a vertical wedge with convective boundary condition in a porous medium

The mixed convection of power-law fluids along a wedge in a porous medium is investigated numerically using an implicit finite difference method. Robin boundary condition is applied at the wedge surface. To explore the effects of mixed convection, both forced and free convection dominated regimes are considered separately. Non-similarity solutions are obtained for the variable heat transfer coefficient. Local dimensionless skin friction and Nusselt number are presented in tabular and graphical forms for the selected values of wedge and convective parameters. The wedge angle geometry parameter r m, power index of pseudoplastic fluids n and mixed convection parameter ξ range from 0 to 1 in both regimes, whereas different values of convective parameter hc are considered for investigating the behavior of skin friction and heat transfer rates.

Non-Darcy mixed convection in power-law fluids along a non-isothermal horizontal surface in a porous medium

The non-similar non-Darcy mixed convection from a horizontal surface in a porous medium saturated with a power-law type non-Newtonian fluid has been studied. Non-similarity solutions have been obtained for the case of a variable surface temperature of the form T w( x)= T ∞± Ax λ , λ≠1/2. It has been found that for λ=1/2, self-similar solution exists. A single mixed convection parameter has been used which covers the entire regime of mixed convection from pure forced convection to pure free convection limits. Both these limiting flows admit self-similar solutions. The partial differential equations governing the non-similar flow and the ordinary differential equations governing the self-similar flow have been solved numerically. The buoyancy force and the wall temperature have significant influence on the heat transfer and the velocity at the wall. For a fixed buoyancy force, the heat transfer and the velocity at the wall decrease with increasing non-Newtonian parameter, non-Darcy parameter and Peclet number.

On fully-developed mixed convection and flow reversal of a power-law fluid in a vertical channel

The fully-developed mixed convection of power-law fluids is investigated for laminar flow in a parallel-plate vertical channel. The boundary condition of uniform and unequal temperatures prescribed at the channel walls is considered. The velocity field, the viscous stress field and the temperature field are obtained by solving analytically the momentum and energy balance equations as well as the stress-strain constitutive equation. An expression which allows the evaluation of the friction factors is presented. The condition for the occurrence of flow reversal is obtained.