Natural Convection of non-Newtonian Shear-Thinning Fluid Flow inside a Skewed Cavity (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.
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.
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.
Study of mixed convection flow of power‐law fluids in a skewed lid‐driven cavity
Heat Transfer
This study conducts a numerical simulation of mixed (combined) convective non‐Newtonian fluid flow inside a two‐dimensional cavity (skewed) having a moving lid. The upper and bottom extremities of the cavity with different temperatures and two insulated side walls cause natural convection. Moreover, the forced convection is maintained by the motion of the lid with constant velocity. The governing equations are nondimensionalized with appropriate transformations and then transformed into curvilinear coordinates. A finite volume numerical procedure with a collocated grid arrangement is used to solve these equations. Comparisons with previously reported results are carried out, which shows an excellent agreement. Non‐Newtonian behaviors such as pseudo‐plastic (shear‐thinning) and dilatant (shear‐thickening) are considered using the power‐law model, and thus the power‐law index is chosen accordingly. A wide range of the governing dimensionless parameters which affect the mixed convectio...
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.
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.
In the present study, natural convection problem has been solved in a cavity having three flat walls and the right vertical wall consisting of one undulation and three undulations. The two vertical and bottom walls are cold walls maintained at a fixed temperature whereas the top wall is heated with spatially varying temperature distribution. Air has been taken as the working fluid with Pr =0.71. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear coordinates. A wide range of Rayleigh number (10 3 to 10 6) has been chosen for this study. For small Ra, the heat transfer was dominated by conduction across the fluid layers. With increase of Ra, the process began to be dominated by convection. In the presence of undulation the peak point of the heat rejection (negative local Nusselt number) in the right wall increases by 5.54% than left wall for Ra = 10 4. The three undulations case had maximum heat transfer to the uppermost undulation compared to that of the one undulation case.
Numerical Simulation of Non-Newtonian Power-Law Fluid Flow in a Lid-Driven Skewed Cavity
Non-Newtonian power-law, 2019
Non-Newtonian laminar fluid flow in a lid-driven skewed cavity has been studied numerically using power-law viscosity model. The governing two-dimensional unsteady incompressible Navier-Stokes equations were initially non-dimensionalized using appropriate transformation , and then the dimensionless form is transformed to generalized curvilinear coordinates to simulate complex geometry. The transformed equations are discretized using finite volume method with the collocated grid arrangement. The code is first validated against the existing benchmark results for two-dimensional lid-driven square cavity problem considering both Newtonian and non-Newtonian fluids. The validation has also been carried out for a lid-driven skewed cavity in the case of a Newtonian fluid. Then the code is applied to the skewed cavity problem involving non-Newtonian fluid flow which can be described by the power-law viscosity model. Moreover, grid independence test has been performed for a skewed cavity for different values of power-law index. In the present case, the skewness of the geometry has been changed by changing the skew angle for both shear-thinning and shear-thickening fluids. The consequent numerical results are presented in terms of the velocity as well as streamlines for the different values of the power-law index n = 0.5, 1 and 1.5, Reynolds number Re = 100, 200, 300 and 500 as well as for the different angles of the skewed cavity (α = 15 • to 165 •). Keywords Curvilinear coordinates · Non-orthogonal grid · Non-Newtonian fluid flow · Skewed cavity · Power-law model · Finite volume method List of Symbols A i j Cofactors of the Jacobian matrix D Non-dimensional fluid viscosity J Jacobian matrix B Md. Mamun Molla
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.
Mathematics, 2022
Flow of a liquid in an enclosure with heat transfer has drawn special focus of researchers due to the abundant thermal engineering applications. So, the aim of present communication is to explore thermal characteristics of natural convective power-law liquid flow in a square enclosure rooted with a T-shaped fin. The formulation of the problem is executed in the form of partial differential expressions by incorporating the rheological relation of the power-law fluid. The lower wall of the enclosure along with the fin is uniformly heated and vertical walls are prescribed with cold temperature. For effective heat transfer within the cavity the upper boundary is considered thermally insulated. A finite element based commercial software known as COMSOL is used for simulations and discretization of differential equations and is executed incorporating a weak formulation. Domain discretization is performed by dividing it into triangular and rectangular elements at different refinement level...