Convection Of Power-law Fluids Research Articles

Numerical modeling of magnetohydrodynamic thermosolutal free convection of power law fluids in a staggered porous enclosure

In this study, the influence of a magnetic field on thermosolutal free convective flow inside a staggered porous enclosure, filled with non-Newtonian power-law fluids is investigated using the Galerkin finite element method. The computational model has been validated against available data from the literature. Results indicate that the augmentation of Hartmann number (Ha) causes heat and mass transport to decrease significantly. However, the magnetic field has a greater influence on mass transfer in comparison with heat transfer. The maximum local Nu and Sh numbers are decreased respectively by 55% and 43% at Ha = 75. This reduction becomes more significant for Hartmann number values higher than 25. However, the increase of Darcy number reduces the influence of the magnetic field. In the presence or absence of magnetic field, the alteration of power law index provides different trends for the prediction of the convective flow intensity. The increase in Lewis (Le) number has a smaller effect on the heat transfer rate compared to the mass transfer rate. Increase in Le augments mass transfer rate by 230% but decreases heat transfer rate by 37%. Further, the augmentation of the buoyancy ratio causes a significant increase in the heat and mass transfer rates.

Numerical Study of Natural Convection of Power Law Fluid in a Square Cavity Fitted with a Uniformly Heated T-Fin

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 levels. A grid independence test is accomplished for quantities of engineering interest like local and average Nusselt numbers to attain accuracy and validity in results. Variation in the momentum and thermal distributions against pertinent parameters is analyzed through stream lines and isothermal contour plots. Measurement of the heat flux coefficient along with the calculation of kinetic energy against involved parameters is displayed through graphs and tables. After the comprehensive overview of attained results it is deduced that kinetic energy elevates against the upsurging magnitude of the Rayleigh number, whereas contrary behavior is encapsulated versus power-law index n. Elevation in the Nusselt number for the shear thinning case i.e., n=0.5 adheres as compared to Newtonian i.e., n=1 and shear thickening cases i.e., n=1.5. It is perceived that by the upsurging power-law index viscosity augmentations and circulation zones increases. Heat is transferred quickly against Rayleigh number (Ra) due to production of temperature difference in flow domain.

Natural Convection of Power Law Fluid through a Porous Deposit: MRT-LBM Approach

Natural Convection of Power Law Fluid through a Porous Deposit: MRT-LBM Approach

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.

Comparison of two and three-dimensional Rayleigh-Bénard convection of power-law fluids in cylindrical and annular enclosures

In the present study, three-dimensional steady-state laminar Rayleigh-Bénard convection (RBC) of power-law fluids in cylindrical and annular enclosures with a square cross-section has been investigated numerically. The simulations have been carried out for a range of power-law exponents for different non-dimensional parameters such as nominal Rayleigh number (Ra) (from 103 to 105), internal radius to enclosure height ratio (ri/L) (from 0 to 2), for a single representative value of Prandtl number (i.e. Pr=102) and an aspect ratio of unity together with Dirichlet boundary conditions. It has been found that convection augments with decreasing n values due to the shear-thinning character of viscosity. As a reflection of this, the mean Nusselt number (Nu¯) increases with decreasing n values and the flow patterns show multiple torus like structures. These findings have been compared with previous findings where the same analysis has been conducted for two-dimensional axisymmetric simulations of cylindrical enclosures. It has been revealed that the results of the two-dimensional analysis are not representative for a three-dimensional configuration in terms of flow pattern and the Nusselt number at Ra > 104 for both the Newtonian (i.e. n=1.0) and shear-thinning (i.e. n < 1) fluids for high values of Rayleigh number. Additionally, the values of critical Rayleigh numbers Racrit (RaNu¯=1) (where Nu¯ values deviate from unity for n ≤ 1 (n > 1)) have been found to be almost insensitive to the change in ri/L, but they decrease with decreasing value of n. Finally, a new correlation for Nu¯, Racrit and RaNu¯=1 has been proposed for the range of parameters considered in this study, based on three-dimensional analysis, which can be very useful for practical applications.

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

Numerical investigation of aspect ratio influences on Rayleigh-Bénard convection of power-law fluids in vertical cylindrical annuli

The influences of aspect ratio on laminar Rayleigh-Bénard convection of power-law fluids in cylindrical annular enclosures have been numerically investigated for Neumann and Dirichlet boundary conditions for the differentially heated horizontal walls. The axisymmetric simulations have been carried out for a range of different Rayleigh number (i.e. Ra=103-105), aspect ratio (i.e. AR=H/L where H is the enclosure height and L is the difference between outer and inner radii) (i.e. AR=0.25-4), power-law index (i.e. n=0.6-1.8) and normalised inner radius (i.e. ri/L=0-16 where ri is internal cylinder radius) for a nominal representative Prandtl number (i.e. Pr=103). It has been found that thermal convection weakens with an increase in AR and conductive thermal transport becomes dominant for AR>3 irrespective of the values of Ra, n and ri/L for both boundary conditions. The mean Nusselt number Nu‾cy exhibits a complex non-monotonic behaviour with the variations of above parameters due to the changes in flow pattern (e.g. number of cells) for shear-thinning fluids (i.e. n<1). However, this tendency is much weaker for shear-thickening fluids (i.e. n>1) for both boundary conditions. Moreover, the critical Rayleigh number Racrit for the onset of convection of power-law fluids is found to be largely independent of ri/L for both Neumann and Dirichlet boundary conditions.

Developing laminar natural convection of power law fluids in vertical open ended channel

Steady, developing laminar natural convection heat transfer for power law fluids between two parallel vertical plates where the fluid is entrained from the bottom and exiting from top is studied. The results for asymmetric and symmetric configurations of the heated plates, which are kept at uniform temperatures with an aspect ratio of 40, are presented. For the numerical computations, the ANSYS Workbench Fluent commercial package is used to solve the governing equations and its numerical output is post-processed. Various range values of Rayleigh number (Ra = 104, 105, 106) Prandtl number (Pr = 10, 100, 1000), non-Newtonian power law indexes (0.6⩽n⩽1.4) of the fluids and the temperature ratios of colder and hotter walls (rT = 0, 0.5, 1.0) are considered. The temperature and velocity profiles, and the average Nusselt number distributions are presented. Comparisons between Newtonian and non-Newtonian fluids are made in terms of the variations of the average Nusselt number as a function of the non-dimensional governing parameters.

Laminar Free Convection in Power-law Fluids in a Right Angle Triangular Duct with Heated Base

ABSTRACTLaminar free convection in power-law fluids in a triangular duct is studied numerically to delineate the effects of the height-to-base ratio of the enclosure (0.2 to 2), power-law index (0.2 to 1.8), Grashof number (10 to 104) and Prandtl number (0.7 to 100). The heat transfer is analyzed for the heated base with the other two walls being cold. Detailed kinematics is characterized by the formation of multiple recirculating zones ranging from two to four cells. Shear rate contours provide additional insights about the variation of the local viscosity in the fluid. Heatlines and the values of the Bejan number over the range of conditions are calculated to delineate the contributions of the entropy generation due to thermal effects and viscous dissipation. At low Grashof and/or Prandtl numbers, conduction dominates the overall heat transfer and this transition between the conduction and convection-dominated regimes is captured in terms of a modified Rayleigh number. The effect of aspect ratio on the Nusselt number is modulated by the values of Grashof and Prandtl numbers and power-law index. The present results have been consolidated via the use of a modified Rayleigh number for estimating the value of average Nusselt number in a new application.

Steady Mixed Convection in Power-Law Fluids from a Heated Triangular Cylinder

ABSTRACTThe steady mixed convective transport from a heated triangular cylinder immersed in power-law fluids in an unconfined vertical domain is investigated numerically. Two different configurations of the cylinder are chosen; one when the base of the cylinder is facing the flow and the other when the apex of the triangle is facing the flow. The simulation is performed for: Reynolds number (1 to 35), Richardson number (0 to 2), power law index (0.4 to 1.8) and Prandtl number, 50. The flow and thermal fields are visualized through the streamlines and isotherm contours at the close proximity of the heated object for various Reynolds numbers, Richardson numbers and power law indices. The distributions of the surface pressure coefficient and local Nusselt number provide further insight of the hydrodynamic and thermal characteristics. Finally, the total drag coefficient and average Nusselt numbers on the surface of the cylinder are computed to explore the overall macroscopic behavior of the involved thermo-hydrodynamics. The flow separation is observed to be more when the apex of the cylinder is facing the flow. The average heat transfer, measured in terms of the Nusselt number, and the total drag on the cylinder are also found higher for that configuration.

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.

Laminar forced convection in power-law fluids from two heated cylinders in a square duct

Forced convection heat transfer has been investigated numerically for a pair of identical circular cylinders in side-by-side and in tandem arrangements confined in an adiabatic square enclosure filled with a power-law fluid with single inlet and outlet ports. The governing equations for the laminar, steady, 2-D and incompressible flow have been solved using a finite-element based method, COMSOL Multiphysics (Version 4.3a) for the following ranges of parameters: 5≤Re≤200; 0.7≤Pr≤100, 0.2≤n≤2 and 0.1≤D/L≤0.3. The numerical results obtained in terms of the velocity and temperature fields have been interpreted using streamlines, isotherm contours, plots of the individual and the total drag coefficients and the local and average Nusselt number. Further insights are developed with the help of velocity vectors and shear-rate contours prevailing in the flow domain, especially adjacent to the two cylinders. Owing to the symmetry, the two cylinders in side-by-side arrangement show identical momentum and heat transfer characteristics. The corresponding values for the upstream and downstream cylinders in the tandem arrangement differ from each other depending upon the values of the Reynolds and Prandtl numbers, power-law index and the diameter of the cylinders. In both cases, an increase in heat transfer is obtained at high values of the Reynolds and Prandtl number in shear-thinning fluids. Moreover, the upstream cylinder exhibits a higher drag and heat transfer as compared to the downstream cylinder. The non-linearity in the definitions of Reynolds and Prandtl numbers due to the occurrence of the power-law index leads to non-monotonic trends in the results. The flow and heat transfer phenomena are strongly influenced by the formation of secondary flows, reverse flow and the varying level of fluid acceleration due to the space constriction in the flow domain. Thus, the overall values of the pressure drop and Nusselt number are determined by a complex interplay between the kinematic conditions, fluid properties and geometric details of the system.

Rayleigh–Bénard Power-Law Fluid Convection in Rectangular Enclosures

The influences of the aspect ratio (ratio of height to length) on the laminar Rayleigh–Bénard convection of power-law fluids in rectangular enclosures have been numerically investigated for the constant wall heat flux boundary condition for horizontal walls. The steady-state simulations have been conducted for a range of aspect ratios of 0.25 to 4, a nominal Rayleigh number range of to , and a power-law index of 0.6 to 1.8 for a representative single value of the nominal Prandtl number (). It has been found that convective transport weakens with an 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 the power-law index and aspect ratio for both shear-thinning and Newtonian fluids. Thermal convection, irrespective of the value of the aspect ratio, has been found to augment with an increasing (decreasing) Rayleigh number (power-law index) due to strengthening of the buoyancy force in comparison to viscous resistance with an increasing Rayleigh number (shear-thinning behavior with decreasing power-law index). The simulations revealed that the 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 used to propose a correlation for the mean Nusselt number.

Marangoni Convection Heat and Mass Transport of Power-Law Fluid in Porous Medium with Heat Generation and Chemical Reaction

ABSTRACTThis article presents a study for Marangoni convection of power-law fluid in a porous medium driven by a power-law temperature and a power-law concentration with heat generation and first-order chemical reaction. It is assumed that the surface tension varies linearly with both the temperature and the concentration. The effects of power-law viscosity on temperature and concentration fields are taken into account bya modified Fourier law and Darcy's Law for power-law fluid. An approximate analytical solution is obtained using a homotopy analytical method, which is verified by numerical ones with good agreement. The transport characteristics of velocity, temperature, and concentration fields are analyzed in detail.

Numerical investigation of laminar Rayleigh–Bénard convection of power-law fluids in square cross-sectional cylindrical annular enclosures

Steady-state laminar Rayleigh–Bénard convection (i.e. differentially heated horizontal walls heated from below) of power-law fluids in square cross-sectional cylindrical annular enclosures has been numerically investigated under the assumption of axisymmetry. The numerical simulations have been conducted for a range of different values of nominal Rayleigh number Ra, nominal Prandtl number Pr, power-law index n, and internal radius to enclosure height ratio ri/L (i.e. 103≤Ra≤105; 10≤Pr≤104; 0.6≤n≤1.8; 0≤ri/L≤24) for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for differentially heated horizontal walls. It has been found that convective transport is stronger for CWT boundary condition than for CWHF boundary condition for large (small) values of Ra (n) for a given set of values of n (Ra), Pr, and ri/L, but an opposite trend is observed for small (large) values of Ra (n). The mean Nusselt number Nu−cy does not show a monotonic increase with increasing (decreasing) Ra (n) especially for small values of ri/L for a given value of Pr due to changes in flow patterns (i.e. number of convection cells). However, the mean Nusselt number Nu−cy and flow patterns for large values of ri/L approach those for square enclosures (ri/L→∞) for both CWT and CWHF boundary conditions. Additionally, the critical Rayleigh number Racrit for the onset of convection has been found to be mostly insensitive to the value of ri/L for both CWT and CWHF boundary conditions.

Marangoni Effects on Forced Convection of Power Law Fluids in Thin Film over an Unsteady Horizontal Stretching Surface with Heat Source

Objectives: In this paper, the effect of surface tension gradient on the transport phenomenon and temperature differences within a power-law liquid film on an unsteady horizontal stretching sheet with heat source is been investigated. Method: The flow of a fluid film and the heat transfer from the subsequent stretching surface is been found by applying similarity transformation. The numerical computation of the problem is done with aid of Maple. The system of governing non-linear partial differential equation is converted to a set of nonlinear ordinary differential equation using local similarity transformations, then solved numerically applying the Runge Kutta Felhberg-45 method. The effect of power law index n, Prandtl number Pr, the unsteadiness parameter S, Space dependent heat source parameter α 1 , temperature dependent heat source parameter β 1 , and film thickness parameter β(=η) on heat transfer and flow are studied and graphically presented. And it was found that the surface tension gradient and nonuniform heating source have tremendous impact on controlling the rate of convective heat transfer near the boundary layer region.

Mixed Convection in Power-Law Fluids from a Heated Semicircular Cylinder: Effect of Aiding Buoyancy

Laminar aiding-buoyancy mixed-convection heat transfer in power-law fluids from a heated semicircular cylinder with its flat base facing the oncoming flow was studied in this work. The coupled momentum and energy equations were solved numerically over the following ranges of conditions: Richardson number (0 ≤ Ri ≤ 2), Reynolds number (0.1 ≤ Re ≤ 25), Prandtl number (1 ≤ Pr ≤ 100), and power-law index (0.3 ≤ n ≤ 1.8). Extensive results on the velocity and temperature fields are presented and discussed in terms of the streamline and isotherm contours adjacent to the heated object. Similarly, the distribution of the pressure coefficient and the local Nusselt number along the surface of the semicircular cylinder are analyzed to delineate the influence of the relevant dimensionless parameters listed above. Next, the pressure and total drag coefficient and surface average values of the Nusselt number describe the momentum and heat transfer aspects at the gross macroscopic level. Both the pressure and total drag coefficient exhibit the expected dependence on Richardson number, Prandtl number, and Reynolds number. Similarly, the average Nusselt number bears a positive dependence on each Richardson number, Prandtl number, and Reynolds number. Broadly, under otherwise identical conditions, heat transfer is augmented in shear-thinning fluids (n < 1) whereas it is somewhat impeded in shear-thickening fluids (n > 1) with reference to that in Newtonian fluids. Finally, the present numerical results of the average Nusselt number (recast in terms of the Colburn j H factor) were correlated as functions of the modified Reynolds number, Prandtl number, and power-law index thereby enabling its prediction in a new application.

Laminar Free Convection in Power-Law Fluids from a Heated Hemisphere

Extensive results are presented on the laminar free convection heat transfer in power-law fluids from a heated hemisphere in two orientations, namely, its flat base oriented upward (inverted) or downward (upright). The coupled field equations have been numerically solved over wide ranges of conditions as follows: Grashof number (), Prandtl number () and power-law index (). Detailed flow and temperature fields are visualized in terms of the streamline and isotherm contours, respectively. At the next level, the results are analyzed in terms of the total drag coefficient and local Nusselt number variation along the surface of the hemisphere, together with its surface averaged value. The average Nusselt number increases with both the Grashof and Prandtl numbers. Furthermore, for fixed values of the Grashof and Prandtl numbers, and for a given orientation, shear-thinning behavior () enhances the rate of heat transfer whereas shear-thickening () impedes it with reference to that in Newtonian fluids, especially when there is a reasonable degree of advection. Finally, the present numerical results of drag coefficient and Nusselt number have been correlated using a general composite parameter, which is essentially a modified Rayleigh number. The use of such a Rayleigh number also emphasizes the varying nature of dependence of the average Nusselt number on the Grashof and Prandtl numbers governed by the type of fluid behavior, i.e., shear-thinning () or shear-thickening ().

Laminar and steady free convection in power-law fluids from a heated spheroidal particle: A numerical study

In this work, the effects of aspect ratio and shear-dependent viscosity on the laminar free convection heat transfer from a heated spheroid immersed in unbounded quiescent power-law fluids have been investigated. In particular, the coupled momentum and energy equations have been solved numerically over the following ranges of the pertinent governing parameters: Grashof number, 10⩽Gr⩽105; Prandtl number, 0.72⩽Pr⩽100; power-law index, 0.3⩽n⩽1.5 and aspect ratio, 0.2⩽e⩽5. Detailed structures of the flow and temperature fields in the vicinity of the spheroid are visualized in terms of the streamline and isotherm patterns, whereas the gross flow and heat transfer phenomena are resolved in terms of the local Nusselt number and its surface averaged value and drag coefficient (CD). Broadly speaking, shear-thinning fluid behaviour (n<1) facilitates heat transfer whereas shear-thickening (n>1) impedes it in comparison to that seen in Newtonian fluids (n=1) under otherwise identical conditions. At fixed values of the Grashof number (Gr), Prandtl number (Pr) and power-law index (n), the value of Nusselt number gradually increases as the spheroid shape progressively passes from the oblate (e>1) to the prolate (e<1) configurations via the spherical shape (e=1). The reverse trend occurs, however, for the drag coefficient (CD). Finally, the present values of the average Nusselt number and drag coefficient are correlated using a simple analytical form based on a general composite parameter proposed for power-law fluids. The paper is concluded by presenting some comparisons with the limited previous analytical and experimental results available in the literature which are limited to Newtonian fluids.