Numerical study of laminar mixed convection heat transfer of power-law non-Newtonian fluids in square enclosures by finite volume method (original) (raw)
Related papers
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.
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.
Influences of side wall angle on heat transfer of power-law fluids in trapezoidal enclosures
2016
In recent years, there is an important increase in technological applications of non-Newtonian fluids (NNF). NNFs are preferred over Newtonian fluids (NF) because of their superior hydrodynamic and thermal properties. NNFs are particularly used as damping fluid in shock absorbers, raw material for making of armors in defense industry and insulator in thermal systems. The use of NNF has become widespread in thermal systems in order to prevent over-heating problem which affects the efficiency. This study presents a numerical analysis for the natural convection in a two dimensional trapezoidal (isosceles trapezoid) enclosure filled with powerlaw NNF. The effects of various parameters are investigated on heat transfer on the bottom wall by developing a two dimensional model of such a cell. The bottom edge of the trapezoidal enclosure is considered as hot, top edge as cold while the side walls are considered as adiabatic. The considered parameters are power-law index (n) and Rayleigh num...
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.
Study of Natural Convection Heat Transfer in a Closed Wall with Thermal Conditions
Lecture Notes in Mechanical Engineering, 2021
In this study, conjugate natural convection in a square cavity filled with fluids under steady-state condition is numerically investigated with the finite element method. The left side wall is considered as hot wall, and the right wall is considered to be cold. The top and bottom walls are assumed to be adiabatic. Different boundary conditions are introduced on the walls, and a thorough investigation is done in the present study. Numerical simulations have been done for different parameters of Grashof number (10 3-10 7) and Prandtl number. The graph of Nusselt number versus Grashof number and Nusselt number versus Prandtl number is plotted. It is observed that the buoyant forces developed in the cavity due to thermally induced density gradients vary as the value of acceleration due to gravity (g) differs, due to the change in temperature and stream function. Keywords Conjugate natural convection heat transfer Á Square cavity Nomenclature AR aspect ratio (H/L) g acceleration due to gravity (m s −2) H height of square cavity (m) K thermal conductivity (W m −1 K −1) L length of the square cavity (m)
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.
The Canadian Journal of Chemical Engineering, 1963
In the present study, an experimental investigation of heat transfer and fluid flow characteristics of buoyancy-driven flow in horizontal and inclined annuli bounded by concentric tubes has been carried out. The annulus inner surface is maintained at high temperature by applying heat flux to the inner tube while the annulus outer surface is maintained at low temperature by circulating cooling water at high mass flow rate around the outer tube. The experiments were carried out at a wide range of Rayleigh number (5 · 10 4 \ Ra \ 5 · 10 5 ) for different annulus gap widths (L/D o = 0.23, 0.3, and 0.37) and different inclination of the annulus (a = 0°, 30°and 60°). The results showed that: (1) increasing the annulus gap width strongly increases the heat transfer rate, (2) the heat transfer rate slightly decreases with increasing the inclination of the annulus from the horizontal, and increasing Ra increases the heat transfer rate for any L/D o and at any inclination. Correlations of the heat transfer enhancement due to buoyancy driven flow in an annulus has been developed in terms of Ra, L/D o and a. The prediction of the correlation has been compared with the present and previous data and fair agreement was found.
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.
International Journal of Engineering Research and Technology (IJERT), 2014
https://www.ijert.org/analysis-of-mixed-convection-flow-characteristics-in-square-cavity-with-uniformly-heated-bottom-wall-by-finite-volume-method https://www.ijert.org/research/analysis-of-mixed-convection-flow-characteristics-in-square-cavity-with-uniformly-heated-bottom-wall-by-finite-volume-method-IJERTV3IS100099.pdf Mixed convection from a uniform heat source on the bottom of a square cavity is studied numerically. Two-dimensional forms of non-dimensional Navier-Stokes equations are solved by using control volume based finite volume technique. Three typical values of the Reynolds numbers are chosen as Re = 1, 10, and 100 and steady, laminar results are obtained in the values of Richardson number as Ri = 0, 1 and 10 and the values of Prandtl numbers as Pr = 0.1, 0.71, 1 and 10. The parametric studies for a wide range of governing parameters show consistent performance of the present numerical approach to obtain as stream functions and temperature profiles. Heat transfer rates at the heated walls are presented based on the value of Re and Pr. The computational results indicate that the heat transfer is strongly affected by Reynolds number and Richardson number. In the present investigation, bottom wall is uniformly heated while the two vertical walls are maintained at constant cold temperature and the top wall is well insulated. A complete study on the effect of Ri shows that the strength of circulation increases with the increase in the value of Ri irrespective of Re and Pr. As the value of Ri increases, there occurs a transition from conduction to convection dominated flow at Ri =1. A detailed analysis of flow pattern shows that the natural or forced convection is based on both the parameters Ri and Pr.
2014
Mixed convection heat transfer to air inside an enclosure is investigated experimentally. The bottom wall of the enclosure is maintained at higher temperature than that of the top wall which keeps in oscillation motion, whereas the left and right walls are well insulated. The differential temperature of the bottom and top walls changed several times in order to accurately characterize the temperature distribution over a considerable range of Richardson number. Adjustable aspect ratio box was built as a test rig to determine the effects of Richardson number and aspect ratio on the flow behavior of the air inside the enclosure. The flow fields and the average Nusselt number profiles were presented in this work. The results show that, at a constant value of the Richardson number, average Nusselt number (Nuav.) increases with aspect ratio. Furthermore, as Richardson number decreases, the time period decreases with constant values of aspect ratio.