Natural convection of power law fluids in inclined cavities (original) (raw)
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Conference: ASME IMECE 2009 : American Society of Mechanical Engineers International Mechanical Engineering Congress & Exposition 2009, Lake Buena Vista, Florida, USA, Nov 13-19, 2009, Volume 9: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B and C, Paper No. IMECE2009-12748; pp. 141-145, 2009
ABSTRACT: Steady two-dimensional natural convection in rectangular cavities has been investigated numerically. The conservation equations of mass, momentum and energy under the assumption of a Newtonian Boussinesq fluid have been solved using the finite volume technique embedded in the Fluent code for a Newtonian (water) and three non Newtonian carbopol fluids. The highly accurate Quick differential scheme was used for discretization. The computations were performed for one Rayleigh number, based on cavity height, of 105 and a Prandtl number of 10 and 700, 6,000 and 1.2×104 for the Newtonian and the three non-Newtonian fluids respectively. 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. The simulations have been carried out for one aspect ratio of 6. Comparison between the Newtonian and the non-Newtonian cases is conducted based on the behaviour of the average Nusselt number with angle of inclination. Both Newtonian and non-Newtonian fluids exhibit similar behavior with a sudden drop around an angle of 50° associated with flow mode transition from multi-cell to single-cell mode.
Conference: ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting, Montreal, Québec, Canada; Volume: 1, Symposia – Parts A, B, and C: p. 1411-1420; Paper No. FEDSM-ICNMM2010-30243; ISBN: 978-0-7918-4948-4 | eISBN: 978-0-7918-3880-8, 2010
ABSTRACT: 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 = 104 and 105 , a Prandtl number of Pr = 102 and two cavity aspect ratios of 1, 4. For the vertical inclination of 90°, computations were performed for two Rayleigh numbers Ra = 104 and 105 and three Prandtl numbers of Pr = 102 , 103 and 104 . 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 O̸ 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. Despite significant differences in the heat transfer rate and flow configurations both Newtonian and non-Newtonian fluids of the power law type exhibit qualitatively similar behavior.
Heat Transfer of Non-Newtonian Dilatant Power Law Fluids in Square and Rectangular Cavities
Journal of Applied Fluid Mechanics 4(3):37-42, 2011
ABSTRACT: Steady two-dimensional natural convection in fluid filled cavities is numerically investigated for the case of non- Newtonian shear thickening power law liquids. The conservation equations of mass, momentum and energy under the assumption of a Newtonian Boussinesq fluid have been solved using the finite volume method for Newtonian and non-Newtonian fluids. The computations were performed for a Rayleigh number, based on cavity height, of 10(exponent 5) and a Prandtl number of 100. 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. The simulations have been carried out for aspect ratios of 1 and 4. Comparison between the Newtonian and the non-Newtonian cases is conducted based on the dependence of the average Nusselt number on angle of inclination. It is shown that despite significant variation in heat transfer rate both Newtonian and non-Newtonian fluids exhibit similar behavior with the transition from multi-cell flow structure to a single-cell regime.
Energies 12(11):2149, 2019
Development of modern technology in microelectronics and power engineering necessitates the creation of effective cooling systems. This is made possible by the use of the special fins technology within the cavity or special heat transfer liquids in order to intensify the heat removal from the heat-generating elements. The present work is devoted to the mathematical modeling of thermogravitational convection of a non-Newtonian fluid in a closed square cavity with a local source of internal volumetric heat generation. The behavior of the fluid is described by the Ostwald-de Waele power law model. The defining Navier-Stokes equations written using the dimensionless stream function, vorticity and temperature are solved using the finite difference method. The effects of the Rayleigh number, power-law index, and thermal conductivity ratio on heat transfer and the flow structure are studied. The obtained results are presented in the form of isolines of the stream function and temperature, as well as the dependences of the average Nusselt number and average temperature on the governing parameters.
Journal of Heat Transfer, 2012
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 10 3 -10 5 and a Prandtl number (Pr) range of 10-10 6 . 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.
Double Diffusive Convection in an Inclined Rectangular Cavity
IJMTT, January, 2018
The natural convection which is caused by combined effect of temperature buoyancy and concentration buoyancy is studied analytically in an inclined tall rectangular cavity with uniform heat flux and mass flux along the vertical sides. The analytical part is true to the boundary layer regime where the heat transfer and mass transfer rates are governed by convection. An Oseen-linearized solution is for tall rectangular cavity filled with the combination characterized by Lewis number Le which is equal to one and arbitrary buoyancy ratios. The influence of the angle of inclination for different Rayleigh number Ra, on velocity and temperature distributions is determined. It is found that Nusselt number Nu and Sherwood number Sh increases the angle of inclination, passes through an apex and then begins to fall down. The effect of inclination on Nu and Sh is more identified as the Ra is increased. The apex of the Nu and Sh occurs at a lesser inclination angle when Ra is raised. The effect of Le is recorded by a similarity solution valid for Le beyond one in heat transfer driven flow, and for Le less than one in mass transfer driven flow.
IOP Conference Series: Materials Science and Engineering, 2019
Effects of cavity aspect ratios and cavity inclination angles to natural convection in a rectangular cavity are numerically investigated. Investigation is performed at the Rayleigh number (Ra) equal to 104, the cavity aspect ratios from 1 to 50 and the cavity inclination angles from 0 to 180°. Consequently, Heat transfer enhancement or decreasing due to the effects is exposed. In addition, streamline contours in the rectangular cavity are illustrated. Multi-cellular flow figuring on the appropriate conditions is exhibited. A new correlation of the average Nusselt number, the cavity aspect ratio and the cavity inclination angle is formulated at Ra equal to 104.
Laminar natural convection in inclined rectangular cavities with a localized heat source
Alexandria Engineering Journal, 2013
The paper investigates numerically laminar natural convection in inclined rectangular cavities with a localized heat source. A mathematical model was constructed where the conservation equations governing the mass, momentum, and thermal energy together with their boundary conditions were solved. The calculation grid used in the solution is investigated to determine the best grid spacing, the required number of iterations, and other parameters which affect the accuracy of the generated solutions. The numerical method and computer program were tested for the case of pure conduction to assure validity and accuracy of the numerical method. The numerical investigation used air as the fluid and covered Rayleigh numbers based on scale length, s/A ranging from 10 2 to 10 6 , aspect ratio from 0.5 to 5, position ratio from 0.25 to 0.75, heater size ratio from 0.25 to 1, and the tilt angle measured from horizontal was varied from 0 to 180°. The results are presented graphically in the form of streamline and isotherm contour plots. The heat transfer characteristics, velocity profiles, local and average Nusselt numbers were also presented. A correlation was developed which represents the present numerical heat transfer results with an average deviation of less than 11.5%.
Natural convection in tilted rectangular cavities due to bidirectional temperature gradient
International Journal of Heat and Technology, 2017
The study by the CFD for a 3D natural convection in a tilted rectangular cavity filled by silicone oil at high Prandtl number has been compared to experimental results. A constant vertical temperature gradient has been performed by subjecting the horizontal walls to temperature Th and Tc; respectively. Other walls are adiabatic except the left small sidewall is differentially heating with temperature TA creating the horizontal temperature gradient. Different values of the lateral heating and the tilt with respect to the horizontal plane are imposed. The results draw dynamic maps. The influence of two factors (TA and ) on the flow pattern and on the convective heat transfer are analysed and discussed. The simulation flow pattern results are close to those obtained experimentally for treated cases with a minimum discrepancy between the both. A spectral analysis is done to show the fluctuations seen on the natural convective flow after the stability caused by the lateral heating and tilted angle; which based on the visualization of the amplitude as a function to the frequency. The results also show a significant impact on the flow fields and the heat transfer performance is improved.