Laminar Natural Convection of Power-Law Fluids in a Square Enclosure With Differentially Heated Sidewalls Subjected to Constant Wall Heat Flux (original) (raw)
Related papers
2014
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 10 3 −10 5 and a Prandtl number range of 10−10 5 . 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 10−10 5 . It has been found that the Nu values for the CWHF configuration remain smaller than the corresponding values in the case of CWT boundary condition (bc) for shear-thinning fluids, whereas Nu in the CWHF configuration for large values of n remains greater than the corresponding values in the case of CWT bc (for identical values of the power-law exponent and nominal Rayleigh and Prandtl numbers). We find that the steady two-dimensional convection in this configuration is realized in a narrower parameter range in the CWT bc than in the CWHF bc. Underpinned by a scaling analysis, new correlations have been proposed for the mean Nusselt number Nu for both CWT and CWHF boundary conditions and these correlations are shown to capture the computational results satisfactorily for the entire range of power-law exponents and nominal Rayleigh and Prandtl numbers considered here.
Rayleigh–Bénard Power-Law Fluid Convection in Rectangular Enclosures
Journal of Thermophysics and Heat Transfer
Influences of aspect ratio (ratio of height to length) on laminar Rayleigh-Bénard convection of powerlaw fluids in rectangular enclosures have been numerically investigated for constant wall heat flux boundary condition for horizontal walls. The steady state simulations have been conducted for the range of aspect ratio 0.25 to 4, nominal Rayleigh number range 10 3 to 10 5 , power-law index 0.6 to 1.8 for a representative single value of nominal Prandtl number (10 3). It has been found that convective transport weakens with increasing aspect ratio and thermal conduction dominates thermal transport for tall enclosures. Moreover, the critical Rayleigh number for the onset of convection increases with increasing values of power-law index and aspect ratio. Thermal convection irrespective of the value of aspect ratio has been found to augment with increasing (decreasing) Rayleigh number (power-law index) due to strengthening of buoyancy force in comparison to viscous resistance with increasing Rayleigh number (shear-thinning behaviour with decreasing power-law index). The simulations reveal that flow patterns and mean Nusselt number are dependent on the initial condition, and it is possible to obtain different steady-state solutions for different initial conditions. The numerical findings have been explained with the help of scaling arguments and in turn have been utilised to propose a correlation for the mean Nusselt number.
Laminar Natural Convection of Newtonian and Non – Newtonian Fluids in a Square Enclosure
2008
In this investigation, steady two-dimensional natural convection heat transfer of Newtonian and non-Newtonian fluids inside square enclosure has been analyzed numerically for a wide range of the modified Rayleigh number of (10 3 ≤ Ra ≤ 10 5), with non-dimensional parameter(NE) of Prandtl-Eyring model ranging from (0 to 10), and modified Prandtl number in the range (Pr* =1,10, and 100). Two types of boundary conditions have been considered. The first,is when the side walls are heated at different uniform temperatures and the horizontal walls are insulated. The second, when the bottom wall is heated by applying a uniform heat flux while the other walls are at the constant cold temperature. Also, the non-Newtonian fluids under consideration were assumed to obey the Prandtl-Eyring model. The numerical results of the values of average Nusselt number have been confirmed by comparing them to similar known yeslts of previous works using the same boundary conditions. Good agreement was obtained. The results are presented in terms of isotherms and streamlines to show the behavior of the fluid flow and temperature fields. In addition, some graphics represent the relation between average Nusselt number and the parameters that are mentioned previously. The results show the effect of non-dimensional parameter (NE) on the velocity and temperature profiles. It also shows that the average Nusselt number is a strong function of modified Rayleigh number, modified Prandtl number, nondimensional parameter, and the boundary conditions. Four different correlations have been made to show the dependence of the average Nusselt number on the non-dimensional parameter, the modified Rayleigh and Prandtl numbers.
Journal of Non-Newtonian Fluid Mechanics, 2010
In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with differentially heated sidewalls have been carried out where the enclosures are considered to be completely filled with a yield stress fluid obeying the Bingham model. Yield stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 10 3 -10 6 and a Prandtl number (Pr) range of 0.1-100. It is found that the mean Nusselt number Nu increases with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, Nu values obtained for Bingham fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to weakening of convective transport. The mean Nusselt number Nu in the case of Bingham fluids is found to decrease with increasing Bingham number, and, for large values of Bingham number Bn, the value settles to unity (Nu = 1.0) as heat transfer takes place principally due to thermal conduction. The effects of Prandtl number have also been investigated in detail and physical explanations are provided for the observed behaviour. New correlations are proposed for the mean Nusselt number Nu for both Newtonian and Bingham fluids which are shown to satisfactorily capture the correct qualitative and quantitative behaviour of Nu in response to changes in Ra, Pr and Bn.
Heat Transfer Engineering, 2014
Two-dimensional steady-state simulations of laminar natural convection in rectangular enclosures with differentially heated side walls have been conducted for a range of different aspect ratios (height/length) for both constant wall temperature and constant heat flux boundary conditions. The rectangular enclosures are considered to be completely filled with a yield-stress fluid obeying the Bingham model. Yield-stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number in the range 10 4 -10 6 and the aspect ratio range 1/8 to 8 for a single nominal Prandtl number (= 500). It is found that the mean Nusselt number increases (decreases) with increasing values of Rayleigh (Bingham) number irrespective of the boundary condition. For the constant wall temperature boundary condition, the aspect ratio at which the maximum mean Nusselt number occurs is found to decrease with increasing Rayleigh number. In contrast, the value of mean Nusselt number increases monotonically with increasing aspect ratio in the case of the constant wall heat flux boundary condition. Detailed physical explanations are provided for these aspect ratio effects. New correlations are proposed for the mean Nusselt number in both the constant wall temperature and wall heat flux boundary conditions, which are shown to satisfactorily capture the simulation results.
Journal of Non-Newtonian Fluid Mechanics, 2011
In this study, two-dimensional steady-state simulations of laminar natural convection in rectangular enclosures with differentially heated side walls have been conducted for a range of different aspect ratios AR (=H/L where H is the enclosure height and L is the enclosure width). The rectangular enclosures are considered to be completely filled with a yield-stress fluid obeying the Bingham model. Yield stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 10 4 -10 6 and the aspect ratio range 1/8 to 8 for a single Prandtl number (Pr = 7). It is found that the mean Nusselt number Nu increases with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, Nu values obtained for Bingham fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to weakening of convective transport. The mean Nusselt number Nu in the case of Bingham fluids is found to decrease with increasing Bingham number, and, for large values of Bingham number Bn, the value of Nu settles to unity (i.e. Nu = 1.0) as heat transfer takes place principally due to thermal conduction. The effects of aspect ratio AR have also been investigated in detail and it has been found the effects of thermal convection (diffusion) strengthens (weakens) with increasing aspect ratio and vice versa, for a given set of nominal values of Rayleigh number Ra and Prandtl number Pr. It is found that the aspect ratio AR max at which the maximum mean Nusselt number Nu occurs is found to decrease with increasing Rayleigh number. However, the value of AR max is shown to increase with increasing Bingham number Bn for a given set of values of Ra and Pr. Detailed physical explanations are provided for the observed phenomena. New correlations are proposed for the mean Nusselt number Nu for Bingham fluids, which are shown to satisfactorily capture the correct qualitative and quantitative behaviour of Nu in response to changes in Ra, AR and Bn.
academicjournals.org
In this study, we have numerically considered mixed convection heat transfer in a square enclosure with cold left and right walls, insulated moving upper wall and hot fixed lower wall. The governing flows of two reliable articles were initially modeled and after validating calculations, the given flow of the study was solved by finite volume method. To examine the effects of different factors, such as Prandtl, Reynolds and Rayleigh numbers on heat transfer in a square enclosure, the laminar flow of Newtonian fluids was approximated and then laminar flow of non-Newtonian fluids, such as carboxy methyl cellulose (CMC) and carboxy poly methylene (Carbopol) water solutions were studied for different Richardson numbers. It was found from the results obtained in the present study that when Ri is less than 1, governing heat transfer inside the enclosure is forced convection for non-Newtonian fluids similar to Newtonian ones. When Ri increases, the effect of forced convection is reduced and natural convection heat transfer increases. It was also found that in constant Grashof numbers, if n decreases, the dimensionless temperature increases. Also, if n is constant, any increase in Grashof number causes a higher dimensionless temperature. It may be related to the fact that in similar conditions, any increase in forced convection, makes shear stresses more.
Natural convection of power law fluids in inclined cavities
International Journal of Thermal Sciences, 2012
Steady two-dimensional natural convection in rectangular two-dimensional cavities filled with non-Newtonian power law-Boussinesq fluids is numerically investigated. The conservation equations of mass, momentum and energy are solved using the finite volume method for varying inclination angles between 0 and 90 and two cavity height based Rayleigh numbers, Ra ¼ 10 4 and 10 5 , a Prandtl number of Pr ¼ 10 2 and three cavity aspect ratios of 1, 4 and 8. For the vertical inclination of 90 , computations were performed for two Rayleigh numbers Ra ¼ 10 4 and 10 5 and three Prandtl numbers of Pr ¼ 10 2 , 10 3 and 10 4 . In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side walls and the inclination angle is varied. A comprehensive comparison between the Newtonian and the non-Newtonian cases is presented based on the dependence of the average Nusselt number Nu on the angle of inclination together with the Rayleigh number, Prandtl number, power law index n and aspect ratio dependent flow configurations which undergo several exchange of stability as the angle of inclination ɸ is gradually increased from the horizontal resulting in a rather sudden drop in the heat transfer rate triggered by the last loss of stability and transition to a single cell configuration. A correlation relating Nu to the power law index n for vertically heated cavities for the range 10 4 Ra 10 5 and 10 2 Pr 10 4 and valid for aspect ratios 4 AR 8 is given.
International Journal of Heat and Mass Transfer, 2015
In this analysis the effects of aspect ratio AR (ratio of enclosure height: length) on steady-state natural convection of yield stress fluids obeying the Bingham model within rectangular enclosures has been investigated for 1/4 6 AR 6 4. A nominal Rayleigh number range 10 3 6 Ra 6 10 5 (Ra defined based on the height) for a single representative value of nominal Prandtl number (i.e. Pr = 500) in a configuration with differentially heated horizontal walls subjected to constant wall temperatures with heated bottom wall has been considered. It has been found that the convective transport strengthens with increasing nominal Rayleigh number Ra for both Newtonian and Bingham fluids but the mean Nusselt number Nu for Bingham fluids remains smaller than the value obtained for Newtonian fluids for a given set of values of nominal Ra and Pr due to augmented viscous resistance arising from yield stress in Bingham fluids. For Bingham fluids Nu decreases with increasing Bingham number Bn (non-dimensional yield stress) and thermal transport becomes essentially conduction-driven for large values of Bn. The relative contribution of convection to the overall thermal transport diminishes (strengthens) with increasing (decreasing) AR for a given set of values of Ra and Pr for both Newtonian and Bingham fluids. Thus, the thermal transport is principally conduction dominated for tall enclosures. A detailed scaling analysis has been carried out to explain the effects of AR. This scaling analysis, in turn, has been utilised to propose a correlation, which has been demonstrated to predict Nu obtained from simulation data for 1/4 6 AR 6 4, 10 3 6 Ra 6 10 5 and Pr = 500.