Natural Convection Of Power-law Fluids Research Articles

Mesoscopic CUDA 3D MRT-LBM Simulation of Natural Convection of Power-Law Fluids in a Differentially Heated Cubic Cavity with a Machine Learning Cross-Validation

Mesoscopic CUDA 3D MRT-LBM Simulation of Natural Convection of Power-Law Fluids in a Differentially Heated Cubic Cavity with a Machine Learning Cross-Validation

Natural convection of power-law fluid in a horizontal annulus between outer cylinder and inner flat tube

Natural convection of power-law fluid in a horizontal annulus between outer cylinder and inner flat tube

Numerical investigation of steady state laminar natural convection of power-law fluids in side-cooled trapezoidal enclosures heated from the bottom

Laminar, steady-state, natural convection of power-law fluids in 2-D trapezoidal enclosures with a heated bottom wall, adiabatic top wall and cooled inclined sidewalls has been analyzed for the first time based on numerical simulations for a range of different values of nominal Rayleigh number (i.e. ), power-law index (i.e. ), nominal Prandtl number (i.e. ) and sidewall inclination angle (i.e. ). It has been found that the mean Nusselt number increases with increasing nominal Rayleigh number (up to a 187% increase for and up to 2.3% increase for between and ) and decreasing power-law index (up to a 4.1% increase for and up to 193% increase for between and 1.8) due to the strengthening of advective transport. Moreover, an increase in the sidewall inclination angle leads to a decrease in (approximately 44% decrease for across values of and up to 33% decrease for across values of ) due to an increase in the area for heat loss from the cavity. It has been found that does not vary significantly with the values of considered in the current study. Furthermore, a new correlation for the mean Nusselt number in this configuration has been identified which provides adequate approximation of the corresponding values obtained from the simulations.

Lattice Boltzmann Modeling for Natural Convection in Power-Law Fluids Within a Partially Heated Square Enclosure

Abstract This paper reports the numerical investigations for steady-state natural convection in power-law fluids inside a square enclosure embedded with bottom discrete heaters. The lattice Boltzmann method (LBM) is employed to model the flow and heat transfer phenomenon at different combinations of power-law index, Rayleigh number, and heat source length for a constant Prandtl number. The buoyancy force is incorporated in the collision term of the LBM through Boussinesq approximation. Simulation outcomes are furnished using streamlines, temperature contours, velocity profiles, and variation of heat transfer on the nonadiabatic walls to probe natural convection phenomena. The results indicate that the temperature and the flow fields in the enclosure are symmetric about the vertical centerline. The detailed physical interpretations have been provided for the reported results. Further, the increase in the power-law index means a rise in viscosity and a decrease in thermal energy transport for other constant parameters. The outcomes also specify that the intensity of circulation and heat transfer enhances with the increase of Rayleigh number and size of the localized heater. Finally, though, a rise in the size of the confined heat source enhances the rate of total thermal transport, it does not change the trend of fluid flow and local heat transfer rate.

Natural Convection in Power-Law Fluids from a Pair of Two Attached Horizontal Cylinders

Laminar natural convection in unconfined power-law fluids from two attached horizontal cylinders has been investigated numerically to elucidate the non-Newtonian behavior of the fluid over a wide range of pertinent parameters: Grashof number (10 to 105), Prandtl number (0.71 to 100), and power-law index (0.2 to1.8). The heat transfer characteristics are elucidated in terms of isotherms, local Nusselt number distributions, and average Nusselt number values, whereas the flow characteristics are interpreted in terms of streamlines, local distribution of the pressure drag, and skin friction drag coefficients along with the total drag coefficient values. Under identical conditions, the average Nusselt number shows a positive dependence on both Grashof and Prandtl number, whereas it shows an adverse dependence on power-law index. Overall, shear-thickening fluid behavior impedes the convection heat transfer, whereas shear-thinning fluid behavior promotes it with reference to the Newtonian fluids. The heat transfer from an individual cylinder in attached condition has been degraded compared to the case of a single horizontal cylinder. Furthermore, the heat transfer rate of the top cylinder is reduced by 29%–41% relative to that of the bottom cylinder due to preheating of the thermal plume.

Laminar natural convection of power-law fluid in a differentially heated inclined square cavity

Laminar natural convection of power-law fluid in a differentially heated inclined square cavity

Natural Convection of Power-Law Fluids Inside an Internally Finned Horizontal Annulus

In the present study, laminar natural convection of power-law fluid confined between two horizontal concentric cylinders with two radial fins attached to the inner cylinder is studied. Governing equations are solved using the finite element method. The computations are carried out for various Rayleigh numbers, fin lengths, fin inclination angles and Prandtl numbers for both shear-thickening and shear-thinning fluids, and their effects on average equivalent thermal conductivity (keq) are investigated. The results indicate that as we move from shear-thinning fluids to shear-thickening fluids, isotherm’s density decreases near the cylinders and at the same time, the thermal boundary layer thickness near the cylinders and fins increases, which results in reduction of the heat transfer rate. Net convective heat transfer for the shear-thinning fluids decreases as fin length ratio Lf increases. Also, it is shown that for shear-thickening fluids, fins orientation does not have significant effects on keq, similar to Newtonian fluids. But for shear-thinning non-Newtonian fluids, an increase in keq can be observed for fins inclination angle larger than about 50°.

Thermosolutal hydromagnetic convection of power law fluids in an enclosure with periodic active zones

A finite volume technique based double diffusive natural convection of power-law fluid in an enclosure has been studied numerically in the presence of magnetic field due to different physical parameters such as Rayleigh number (Ra), Lewis number (Le), Hartmann number (Ha) and Prandtl number (Pr). The flow is generated by the combined mechanism of a time periodic thermal and solutal gradient acts along the vertical walls. The combined buoyancy effect due to thermal and species diffusion plays a key role on the flow characterisation. The study dealt with the effect of pertinent parameters on fluid flow, heat and mass transfer in case of a laminar flow regime. The apparent power law indices and magnetic field strengths are varied using the non-Newtonian power law forms. The relevant results are presented in terms of streamlines, isotherms, isoconcentrations, average Nusselt number, Sherwood number and total entropy generation with the variation of power law index (n) from 0.2 to 1.8, Ra from 104 to 105,Ha from 0 to 20, Pr from 1 to 5 and buoyancy ratio (N) from -1 to 1. The entropy generation and Bejan number are determined to analyze the thermodynamic optimization of the conjugate double diffusive convection. It is observed that the average Nusselt and Sherwood number shows linear variation with the increase of amplitudes of the imposed sinusoidal temperature and concentration gradient and the fluctuation is found to be trivial. Also the results indicate that the power law index variation influences largely the rate of heat and mass transfer and average entropy generation. The magnetic field strength increases the strength of the fluid flow and also strongly supported by the increased values of n. It is found that with the decrement of flow behavior index n the buoyancy effect and the hydrodynamic behavior of the fluid is getting increased.

Natural convection of power-law fluids under wall vibrations: A lattice Boltzmann study

ABSTRACTThe natural convection of non-Newtonian power-law fluids in a rectangular cavity in the presence of wall vibrations has been investigated by the lattice Boltzmann method. The longitudinal and transverse vibrations are applied to the horizontal walls of the cavity separately, and the two vertical walls are set as high and low temperatures, respectively. The velocity fields and temperature distributions of power-law fluids are visualized with respect to the streamlines and isotherm contours. The heat transfer characteristics are interpreted in terms of averaged Nusselt number () near the surface of heated wall. The effects of power-law index n in the range of 0.5–1.2 on momentum transport and heat transfer are investigated for Rayleigh number (Ra) in the range of 103–105 and Prandtl number (Pr) of 10. near the hot wall is increased significantly with the fluid exponent increase at high Ra, but it is smaller than that without wall vibrations. Moreover, wall vibrations show slight and even no influence on of power-law fluids at low Ra. The maximum velocity components of shear-thinning fluids are both decreased under wall vibrations with increasing n, but it is unchanged in shear-thickening fluids. The velocity components along the central lines of the cavity are decreased significantly for power-law fluids under wall vibrations. It is concluded that wall vibrations influence the streamlines, isotherm contours, and heat transfer characteristics of power-law fluids significantly at high Ra (∼105). In addition, it has been found that the heat transfer rate is decreased as both aspect ratio and Pr increase.

A thermal non-equilibrium model for 3D double diffusive convection of power-law fluids with chemical reaction in the porous medium

The article reports a numerical study of the double-diffusive natural convection of power-law fluids in a porous cubic cavity with chemical reaction under the local thermal non-equilibrium (LTNE) state and submitted to horizontal temperature and concentration gradients. The complete governing equations, in which the generalized non-Darcy model is employed as momentum equation and a two-temperature model that represents temperature fields of the fluid and solid phases separately is used for energy equation, are solved by the compact high order finite volume method. Special attentions are given to detecting the effects of the porosity modified conductivity ratio (γ), the inter-phase heat transfer coefficient (H), the chemical reaction parameter (λ), the Dufour parameter (Du), the Soret parameter (Sr) and the Lewis number (Le) on the fluid flow as well as on rates of heat and mass transfer. Our simulations show that the heat transfer rate of solid increases, while the heat transfer rate of fluid and mass transfer rate keep constants, as the LTNE parameters (i.e., γ and H) increase. For any relatively large value of γ and H, the almost thermal equilibrium state is achieved due to the similar thermal distribution of fluid and solid phases. On the contrary, the chemical reaction parameter has significant influence on mass transfer than on heat transfer under the LTNE conditions. In addition, the heat and mass transfer enhance with the increment of the Soret and Dufour parameters. Augmentation of Lewis number enhances mass transfer but reduces heat transfer. Apart from that, our numerical tests show the flow field is influenced appreciably by the presence of the power-law index (n), Darcy number (Da) and porous thermal Rayleigh number (Ra).

Natural Convection in Power-Law Fluids in a Square Enclosure from Two Differentially Heated Horizontal Cylinders

ABSTRACTLaminar natural convection has been numerically investigated from two differentially heated horizontal cylinders in a square enclosure filled with power-law fluids. Two basic configurations, namely, vertical- and diagonal-alignment of the cylinders at various locations have been considered. The coupled continuity, momentum and energy equations have been solved numerically to elucidate the effect of the Grashof number (102–104), Prandtl number (0.7–100) and power-law index (0.2–2) for a range of symmetric and asymmetric locations of the cylinders. The velocity and temperature fields are visualized in terms of streamlines, isothermal contours and plots of the local and average Nusselt number for different positions of the cylinders. The occurrence of the power-law index in the definitions of the Grashof and Prandtl numbers accentuates the interplay between the viscous, inertial and buoyancy forces thereby leading to nonlinearity in the observed trends. The presence of the dead zones coupled with the dominance of conduction under certain conditions strongly influences the overall heat transfer. All else being equal, it is possible to improve heat transfer for asymmetric positioning of the cylinders, especially at high values of the Prandtl number and Grashof number in shear-thinning fluids. A predictive correlation has been developed thereby enabling the estimation of the heat transfer coefficient in a new application in terms of the geometric and kinematic parameters.

Influences of aspect ratio on natural convection of power-law fluids in cylindrical annular space with differentially heated vertical walls

Natural convection of power-law fluids in cylindrical annular spaces has not been analysed in detail in spite of its industrial importance in food and chemical processing, solar collectors and cooling of electronics. Therefore, laminar natural convection of power-law fluids in rectangular cross-sectional cylindrical annular spaces with differentially heated vertical walls subjected to the both constant wall temperature (CWT), and constant wall heat flux (CWHF) boundary conditions has been investigated in this study. Two-dimensional axisymmetric steady-state numerical simulations have been conducted for a range of values of normalized internal radius 0.125⩽ri/L⩽16 (where ri internal cylinder radius, L is the difference between outer and inner cylinder radius), aspect ratio 0.125⩽AR⩽8 (AR=H/L, where H is the enclosure height), power-law index (i.e. 0.6⩽n⩽1.8) and nominal Rayleigh number (i.e. Ra=103-106) for a single value of nominal Prandtl number: Pr=103. It is found that the mean Nusselt number based on the inner periphery of the annular space Nu‾i increases with an increase in Ra due to the strengthening of buoyancy forces. By contrast, Nu‾i increases with a decrease in n due to the weakening of viscous resistance. The mean Nusselt number Nu‾i decreases with an increase in ri/L before approaching the mean Nusselt number for a rectangular enclosure in the limit of ri/L→∞. By contrast Nu‾i normalized by the corresponding Nusselt number for pure conduction (i.e. Nu‾i/Nucond) increases with an increase in ri/L. The contribution of convection to overall thermal transport strength increases with an increase in ri/L, since the Nusselt number for pure conductive transport Nucond decreases with an increase in ri/L for cylindrical annular spaces. Additionally, it has been found that Nu‾i exhibits a non-monotonic variation with an increase in AR for same set of values of Ra,Pr,ri/L for shear thinning (n<1), Newtonian (n=1) and shear thickening (n>1) fluids in the CWT configuration, while Nu‾i increases monotonically with an increase in AR in the CWHF configuration irrespective of the value of n. The completion between the strengthening of thermal convection and the weakening of conductive thermal transport with an increase in AR is responsible for the non-monotonic AR dependence of Nu‾i in the CWT boundary condition. A scaling analysis is utilised to explain the influences of normalized radius, aspect ratio, nominal Rayleigh and Prandtl numbers, power-law index on Nu‾i for natural convection of power-law fluids within rectangular cross-sectional cylindrical annular spaces. Finally, new correlations have been proposed for Nu‾i for both CWT and CWHF boundary conditions, which have been shown to provide satisfactorily predictions of Nu‾i for the range of the parameters considered in this analysis.

Effects of aspect ratio on laminar Rayleigh–Bénard convection of power-law fluids in rectangular enclosures: A numerical investigation

The effects of aspect ratio AR (ratio of enclosure height to length) on Rayleigh–Bénard convection of inelastic non-Newtonian fluids obeying the power-law model of viscosity within rectangular enclosures have been numerically analysed where the horizontal walls are subjected to constant wall temperatures with the bottom wall at higher temperature. Simulations have been undertaken for the range of aspect ratio 0.25⩽AR⩽4, nominal Rayleigh number range 103⩽Ra⩽105 (Ra defined based on the enclosure height) for a single representative value of nominal Prandtl number (Pr=103). It is found that convection weakens with increasing aspect ratio and the heat transfer takes place purely due to thermal conduction for tall enclosures (i.e. AR>2) for all values of Ra and n considered here. Additionally, the flow pattern for AR⩽2 has been found to be dependent not only on Ra and n but also on the choice of initial condition used for the simulation. Although viscous resistance weakens with decreasing power-law exponent for a given set of values of Ra, AR and Pr, the mean Nusselt number Nu‾ does not exhibit a monotonic increase with decreasing n for AR⩽2 because of the change in flow pattern (i.e. number of convection rolls/cells) within the enclosure. Accordingly, it has been found that the flow pattern and the mean Nusselt number Nu‾ are dependent on initial conditions and it is possible to obtain different steady-state solutions for different initial conditions. Furthermore, it is possible to obtain a steady solution for shear-thinning (i.e. n<1) fluids only for some initial conditions, whereas other initial conditions may yield unsteady flow patterns. The key simulation results have been explained based on scaling arguments and the scaling relations have been utilised to identify different regimes of natural convection of power-law fluids accounting for aspect ratio effects.

FDLBM simulation of entropy generation in double diffusive natural convection of power-law fluids in an enclosure with Soret and Dufour effects

In this paper, double-diffusive natural convection with Soret and Dufour effects in a square cavity filled with non-Newtonian power-law fluid has been simulated by Finite Difference Lattice Boltzmann Method (FDLBM) while entropy generations through fluid friction, heat transfer, and mass transfer are analyzed. This study has been conducted for certain pertinent parameters of Rayleigh number (Ra=104 and 105), power-law index (n=0.6–1.4), Lewis number (Le=2.5 and 5), Dufour parameter (Df=0–1), Soret parameter (Sr=0–1) and the buoyancy ratio (N=−1,0.1,1). Results indicate that the augmentation of the power-law index causes heat and mass transfer to drop. Entropy generation due to fluid friction, heat and mass transfer rises with increase in Rayleigh number. Augmentation of Lewis number enhances entropy generation due to mass transfer. At N=0.1 and 1, growth of power-law index causes different types of entropy generation to drop. The rise of buoyancy ratio from N=−1 to 1 augments the total irreversibility. The Dufour parameter provokes heat and mass transfer to rise while results in the enhancement of the total irreversibility. The Soret parameter augments mass transfer, but it does not affect heat transfer and total entropy generation considerably.

Mesoscopic simulation of magnetic field effect on natural convection of power-law fluids in a partially heated cavity

In this paper, effect of a magnetic field on natural convection of non-Newtonian power-law fluids in a partially heated cavity, has been analyzed by using the Finite-Difference Lattice Boltzmann Method (FDLBM). This study has been conducted for certain pertinent parameters of Rayleigh number (Ra=104 and 105), Hartmann number (Ha=0–60), power-law index (n=0.5–1.5), and length of heated section (H/L=0.25, 0.5, and 0.75), as the magnetic field is applied horizontally. Results indicate that the augmentation of the power-law index in the absence of the magnetic field causes heat transfer to drop. Generally, the magnetic field decreases heat transfer in different power-law indexes. The increment of the magnetic field power declines the effect of the power-law index on heat transfer. The magnetic field for various Hartmann numbers at Ra=104; has different effects on heat transfer with the enhancement of power-law index. At Ra=105 and for Ha=0 to 30, heat transfer falls with rise of the power-law index as the effect is weakened by increase in Hartmann number significantly. The influence of power-law index on heat transfer augments with increase in the size of the heated section.

Boundary Condition Effects on Laminar Natural Convection of Power-Law Fluids in a Square Enclosure Heated from below with Differentially Heated Horizontal Walls

Two-dimensional steady-state laminar natural convection of power-law fluids in square enclosures with differentially heated horizontal walls (heated from below) subjected to constant wall temperature (CWT) and constant wall heat flux (CHWF) boundary conditions has been analyzed in detail based on computational simulations and a detailed scaling analysis. The effects of power-law exponent n ranging from 0.6 to 1.8 on the thermal transport have been investigated for nominal values of Rayleigh number in the range 103–105 and a Prandtl number range of 10–105. It is found that the mean Nusselt number Nu increases with increasing (decreasing) values of Rayleigh number (power-law exponent) for both CWT and CWHF configurations because of the strengthening of convective transport. In contrast, the mean Nusselt number Nu remains insensitive to changes in Prandtl number Pr in the range 10–105. It has been found that the Nu values for the CWHF configuration remain smaller than the corresponding values in the case ...

Laminar natural convection of power-law fluids in a square enclosure submitted from below to a uniform heat flux density

Two-dimensional steady-state simulations of laminar natural convection of non-Newtonian power-law fluids in square enclosures heated through the lower horizontal wall have been carried out for constant wall heat flux boundary conditions. The effects of power-law index n on heat and momentum transport have been analysed for nominal values of Rayleigh number (Ra) in the range 103–105 and a Prandtl number (Pr) range of 10–106. It has been demonstrated that the mean Nusselt number Nu¯ increases with increasing values of Rayleigh number for both Newtonian and power-law fluids. Moreover, Nu¯ values obtained for power fluids with n<1 (n>1) are greater (smaller) than that obtained in the case of Newtonian fluids with the same nominal Rayleigh number Ra due to strengthening (weakening) of convective transport. The effects of convection strengthen with increasing Ra for a given set of values of Pr and n, which is reflected in the increasing trend of Nu¯ with increasing Ra. By contrast, the Prandtl number is shown to have marginal influence on Nu¯. In addition a detailed comparison has been undertaken between these new results for the case of heating from below with existing results for the sidewall heating case. It has been found that Nu¯ in the differentially heated horizontal wall configuration assumes smaller values than in the differentially heated vertical wall configuration for a given set of values of n and Prandtl number in shear-thinning fluids (i.e. n<1) for high values of Ra, whereas Nu¯ values remain comparable for both differentially heated vertical and horizontal wall configurations for the Newtonian (i.e. n=1) and shear-thickening fluids (i.e. n>1). However for small values of Rayleigh number, Nu¯ attains greater values in the differentially heated horizontal wall configuration for Newtonian (n=1.0) and shear-thinning (n<1) fluids. In contrast, Nu¯ assumes higher values in the differentially heated vertical sidewall configuration for shear-thickening fluids(n>1) for small values of Ra. Detailed physical explanations have been provided for the observed Ra, Pr and n dependences of Nu¯. A new correlation has been proposed for Nu¯ for natural convection of power-law fluids in square enclosures heated from below subjected to constant heat fluxes. The new correlation is shown to satisfactorily capture both the qualitative and quantitative behaviour of Nu¯ in response to the changes in Ra, Pr and n obtained from simulation data.

Natural convection in power-law fluids from two square cylinders in tandem arrangement at moderate Grashof numbers

In this work, free convective flow and heat transfer in power-law fluids from two heated square cylinders in tandem arrangement is studied. The governing differential equations have been solved numerically over wide ranges of Grashof number, 10 ≤ Gr ≤ 1,000, Prandtl number, 0.71 ≤ Pr ≤ 50 and power-law index, 0.4 ≤ n ≤ 1.8. In order to elucidate the extent of inter-cylinder interaction, the non-dimensional inter-cylinder spacing, L/d is varied in the range, 2 ≤ L/d ≤ 6. The results are interpreted in terms of streamline and isotherm contours in the proximity of two cylinders to gain physical insights into the nature of flow. At the next level, the distribution of the local Nusselt number along the surface of the cylinders is presented. At the minimum inter-cylinder spacing due to the intense interference, the downstream cylinder contributes much less to the overall heat transfer whereas it experiences much higher hydrodynamic drag than the upstream cylinder. Broadly, the local and average Nusselt number for both cylinders show a positive dependence on both Grashof and Prandtl numbers. Also, all else being equal, shear-thinning fluid behaviour promotes the rate of heat transfer and shear-thickening fluid behaviour impedes it. Finally, the present numerical results have been correlated by using simple forms of equations thereby enabling the estimation of Nusselt number in a new application.

Laminar natural convection of non-Newtonian power-law fluids between concentric circular cylinders

The two-dimensional steady-state natural convection of power-law fluids is studied numerically between two concentric horizontal cylinders with different constant temperatures. The governing equations are discretized using finite volume technique based on second order upwind and are solved using the SIMPLE algorithm. The effects of Rayleigh number (103≤Ra≤105) and Prandtl number (10≤Pr≤103) on the dimensionless velocity and temperature are investigated for both pseudoplastic and dilatant fluids. Also the mean Nusselt number for various values of governing parameters is obtained and discussed. The results indicate that with increasing the power-law index from 0.6 to 1.4, the mean Nusselt number decreases. In the best case among the range of parameters considered here the heat transfer rate for pseudo-plastic fluid (n=0.6) is 170% higher than the Newtonian one and for dilatant fluid (n=1.4) the heat transfer rate is 43% lower than the Newtonian fluid. So the pseudoplastic and dilatant fluids are more efficient than Newtonian fluids for cooling and insulating purposes, respectively. It is shown that as the Rayleigh number increases the cooling effect of pseudoplastic fluid and the insulating effect of dilatant fluid become more pronounced.

Natural convection of power-law fluid between two-square eccentric duct annuli

The present paper numerically studies two-dimensional steady-state natural convection of non-Newtonian power-law fluid between two eccentric horizontal square ducts with constant temperature. The inner and outer ducts are assumed to be held at hot and cold temperatures, respectively. The conservation equations of mass, momentum and energy are dicretized using finite volume technique based on second order upwind and finally SIMPLE algorithm is utilized to solve the resultant system of equations. The effects of power-law index (0.6⩽n⩽1.4), Rayleigh number (103⩽Ra⩽106), aspect ratio (0.25⩽AR⩽0.75), eccentricity (-0.2⩽e⩽+0.2) and Prandtl number (10⩽Pr⩽103) on heat and fluid flows are investigated. Also the Nusselt number for various values of governing parameters is obtained and discussed. The results indicate that with increasing the power-law index n from 0.6 to 1.4 the mean Nusselt number that indicates heat transfer rate decreases. It is shown that there is a minimum situation for the Nusselt number versus the eccentricity dependent on the other parameters. Also it is found that varying the Prandtl number almost does not affect heat transfer characteristics except for some cases.