Convection Of non-Newtonian Power-law Fluids Research Articles

Double-diffusive convection of non-newtonian power-law fluids in an inclined porous layer

This paper presents a numerical study of Double-Diffusive convection within an inclined porous medium saturated by a non-Newtonian fluid. The power-law model is utilized for modelling the behavior of the flow in the porous layer. The given statement implies that the long side of the cavity experience thermal and solutal flux rates, whereas the other walls are impermeable and thermally isolated. The issue is characterized by a set of tightly linked non-linear differential equations, termed governing equations, encompassing the mass conservation equation (known as the continuity equation), the momentum equation, the energy equation, and the species equation. The relevant factors that govern the problem being investigated are the Rayleigh number, R_T, the power-law index, n, the angle of inclination, Φ, the cavity aspect ratio, A, the Lewis number, Le, the normalized porosity, ξ, and the buoyancy ratio, N, two types of cavity configuration have been studied: inclined cavity (i.e. Φ≠0°), then we have studied the case of a vertical cavity (i.e. Φ=90°) where the buoyancy forces induced by the thermal and solutal effects are opposing each other and of equal intensity (N=-1). A semi-analytical solution, valid for an infinite layer (A>>1), is derived on the basis of the parallel flow approximation, A numerical approach utilizing the finite differences method was utilized to resolve the governing equations within the porous medium. It is demonstrated that both the inclination of the layer, Φ, and the power-law index, n, have a strong influence on the strength of the intensity of flow, Ψ_0, the heat transfer rate, Nu, and the mass transfer rate, Sh, within the enclosure. A good agreement is found between the predictions of the parallel flow approximation and the numerical results obtained by solving the full governing equations.

Relative importance of temperature-dependent properties in non-Newtonian natural convection around curved surfaces

Natural convection of non-Newtonian power-law fluids around curved surfaces is a ubiquitous phenomenon in industrial applications and research. In this context, the importance of temperature-dependent properties combined with the power-law behavior of the fluid was studied numerically to elucidate the extent and significance of non-Boussinesq effects. An order-of-magnitude-analysis (OMA) indicated that both the thermal expansion coefficient and consistency index had significant temperature dependencies for the class of fluids considered. These dependencies were incorporated in the governing equations applicable over practical temperature ranges. It was found that the effect of curvature on the local shear rate distribution for flow around the object lends additional significance to the non-Oberbeck-Boussinesq (NOB) effects augmented or diminished by power-law behavior. The importance of using actual temperature differences in the analysis because of a complete reversal of trends at very low temperatures was demonstrated. The influence of NOB effects in studies where the fluid and geometrical parameters are optimized was found to be significant. Comprehensive numerical studies to estimate the extent of NOB effects due to the inadequacy of OMA were found necessary. The solutions provided additional insight to the relative importance of thermo-dependent viscosity and thermal expansion coefficient for the class of power-law fluids considered.

Laminar natural convection of non-Newtonian power-law fluid in an eccentric annulus

This work is about studying the natural convection of two-dimensional steady state non-Newtonian power law fluid numerically. The inner cylinder was put eccentrically into the outer one. The cylinders are held at constant temperatures with the inner one heated isothermally at temperature Th and the outer one cooled isothermally at temperature Tc (Th>Tc). The simulations have been taken for the parameters 103?Ra?105, 10?Pr?103, 0.6?n?1.4, 0???0.9 and an inclination angle ? from 0? up to 90?. The average Nusselt numbers for the previous parameters are obtained and discussed numerically. The results revealed that the average Nusselt number has the highest values when n=0.6, Ra=105 at ?=0 which is a signal for the large transfer herein and has the lowest values for n=1.4, Ra=103 at ?=90? which is a signal that the transfer is by conduction more than convection. Furthermore, the increasing of eccentricity causes an increase in the Nusselt number for all the cases. Finally, the best case where we can get the best heat transfer is at ? = 0, ?=0.9 among them all. The results have compared with some precedent works and showed good agreement.

Natural Convection Heat Transfer of Non-Newtonian Power-Law Fluids Within an Array of Elliptic Cylinders

Abstract In this study, natural convection of non-Newtonian power-law fluids around an array of elliptic cylinders has been investigated numerically. The governing equations have been solved using an in-house computational fluid dynamics code based on the well-known finite volume method. It is assumed that the flow and temperature fields are laminar, steady, and two-dimensional. Furthermore, due to the low-temperature difference between the tube walls and the surrounding fluid, the changes in the physical properties of the fluids are neglected. The numerical results are validated against the available experimental and numerical results. The results show that by increasing the non-Newtonian fluid power-law index, the ratio of average Nusselt number of the ith cylinder to the average Nusselt number of a single cylinder under identical thermal conditions decreases. Moreover, it is found that the increase in the ratio of the distance between elliptic centers and the elliptic vertical diameter increases the ratio of the average Nusselt number of ith cylinder to the average Nusselt number for a single cylinder. Finally, a mathematical expression is given for the array averaged Nusselt number.

Natural Convection of Non-Newtonian Power-Law Fluid in a Square Cavity with a Heat-Generating Element

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.

Magnetohydrodynamic free convection of non-Newtonian power-law fluids over a uniformly heated horizontal plate

The MHD free convection flow of non-Newtonian power-law fluids over a horizontal plate subjected to a constant heat flux is studied. The results are presented for various values of the three influential parameters, i. e. the generalized Hart?mann number, the generalized Prandtl number, and the non-Newtonian power-law viscosity index. Increasing the Hartmann number increases the thermal boundary-layer thickness and the surface temperature and consequently decreases the wall skin friction and Nusselt number. A lower generalized Prandtl number results in a larger skin friction coefficient and higher wall temperature as well as thicker thermal boundary-layer. The viscosity index is predicted to influence the flow conditions depending on the value of generalized Hartmann number. At high generalized Prandtl number numbers, by decreasing non-Newtonian power-law index, the wall skin friction, temperature scale, and thermal boundary-layer thickness are increased and the Nusselt number is decreased, while the opposite trend is observed for low generalized Prandtl number. A general correlation for the Nusselt number is derived using the numerical results

Natural convection of power-law fluids under wall vibrations: A lattice Boltzmann study

ABSTRACTThe natural convection of non-Newtonian power-law fluids in a rectangular cavity in the presence of wall vibrations has been investigated by the lattice Boltzmann method. The longitudinal and transverse vibrations are applied to the horizontal walls of the cavity separately, and the two vertical walls are set as high and low temperatures, respectively. The velocity fields and temperature distributions of power-law fluids are visualized with respect to the streamlines and isotherm contours. The heat transfer characteristics are interpreted in terms of averaged Nusselt number () near the surface of heated wall. The effects of power-law index n in the range of 0.5–1.2 on momentum transport and heat transfer are investigated for Rayleigh number (Ra) in the range of 103–105 and Prandtl number (Pr) of 10. near the hot wall is increased significantly with the fluid exponent increase at high Ra, but it is smaller than that without wall vibrations. Moreover, wall vibrations show slight and even no influence on of power-law fluids at low Ra. The maximum velocity components of shear-thinning fluids are both decreased under wall vibrations with increasing n, but it is unchanged in shear-thickening fluids. The velocity components along the central lines of the cavity are decreased significantly for power-law fluids under wall vibrations. It is concluded that wall vibrations influence the streamlines, isotherm contours, and heat transfer characteristics of power-law fluids significantly at high Ra (∼105). In addition, it has been found that the heat transfer rate is decreased as both aspect ratio and Pr increase.

Three-dimensional numerical investigation on thermosolutal convection of power-law fluids in anisotropic porous media

The present study simulates the 3D unsteady double-diffusive natural convection subject to opposing thermal and solutal buoyancy forces (N<0) in a porous cubic by a generalized non-Darcy model, in which the effects of the crucial parameters such as the porous thermal Rayleigh numbers, buoyancy ratio and anisotropy ratio on the flow structure, heat and mass transfer of power-law fluids are investigated independently. The top and bottom walls are given different temperatures and concentrations, while the other walls are adiabatic and impermeable. A compact high order finite volume method is adopted to describe the flow structure and the resulting heat and mass transfer characteristic of non-Newtonian fluids in the anisotropy porous cubic. Our simulations show that the flow structure develops from conduction-dominated to convection-dominated as buoyancy ratio or anisotropy ratio or porous thermal Rayleigh number increases. The average Nusselt and Sherwood numbers keep constants during the conduction-dominated stage, then increase along the transition route. On the other hand, the impacts of different power-law indexes on the convection are mainly manifested in rheological properties, which elucidate that the shear-thinning fluids is more effective in heat and mass transfer enhancement than shear-thickening fluids. The studies may help us establish a physically reasonable methodology to systemically assess double-diffusive convection of non-Newtonian power-law fluids in anisotropy porous media in the real world.

Simulation of double diffusive MHD (magnetohydrodynamic) natural convection and entropy generation in an open cavity filled with power-law fluids in the presence of Soret and Dufour effects (Part I: Study of fluid flow, heat and mass transfer)

In this paper, double diffusive natural convection of non-Newtonian power-law fluids in an open cavity in the presence of a horizontal magnetic field, studying Soret and Dufour parameters has been analyzed by FDLBM (Finite Difference Lattice Boltzmann method). This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 104 and 105), Hartmann number (Ha = 0, 15, and 30), power-law index (n = 0.6, 1, and 1.4), Lewis number (Le = 2.5 and 5), Dufour parameter (Df = 0, 1, and 5), Soret parameter (Sr = 0, 1, and 5) and the buoyancy ratio (N = −1and 1). Results indicate that the augmentation of the Hartmann number provokes heat and mass transfer to drop for different power-law indexes. As the Soret and Dufour numbers equal zero, the heat and mass transfer decrease with the increment of the power-law index in different Rayleigh numbers for various Hartmann numbers. The heat transfer increases with the rise of the Dufour parameter and the mass transfer enhances as the Soret parameter increases for different power-law indexes and Rayleigh numbers. The augmentation of Soret and Dufour parameters alters the behavior of heat and mass transfer against the change of the power-law index.

Simulation of double diffusive MHD (magnetohydrodynamic) natural convection and entropy generation in an open cavity filled with power-law fluids in the presence of Soret and Dufour effects (part II: entropy generation)

In this paper, entropy generation of associated with double diffusive natural convection of non-Newtonian power-law fluids in an open cavity in the presence of a horizontal magnetic field, studying Soret and Dufour parameters has been analyzed by FDLBM (Finite Difference Lattice Boltzmann method). This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 104 and 105), Hartmann number (Ha = 0, 15, and 30), power-law index (n = 0.6, 1, and 1.4), Lewis number (Le = 2.5 and 5), Dufour parameter (Df = 0, 1, and 5), Soret parameter (Sr = 0, 1, and 5) and the buoyancy ratio (N = −1and 1). Results indicate that the augmentation of the thermal Rayleigh number enhances different entropy generations and declines the average Bejan number. The increase in the Hartmann number provokes various irreversibilities to enhance and the average Bejan number decreases significantly. The enhancement of Lewis number and buoyancy ratio affect various entropy generations and the average Bejan number. The rise of Soret and Dufour parameters enhances the entropy generations due to heat transfer and fluid friction. The change of power-law index alters various entropy generations, but the alteration does not follow a specific manner in different studied parameters.

Simulation of double diffusive natural convection and entropy generation of power-law fluids in an inclined porous cavity with Soret and Dufour effects (Part I: Study of fluid flow, heat and mass transfer)

In this paper, double diffusive natural convection of non-Newtonian power-law fluids in an inclined porous cavity in the presence of Soret and Dufour parameters has been analyzed by Finite Difference Lattice Boltzmann Method (FDLBM). This study has been performed for the certain pertinent parameters of thermal Rayleigh number (RaT=104 and 105), Darcy number (Da=10−4, 10−3, and 10−2), power-law index (n=0.6–1.4), Lewis number (Le=2.5 and 5), inclined angles (θ=0°, 40°, 80°, and 120°), Dufour parameter (Df=0, 1, and 5), Soret parameter (Sr=0, 1, and 5) and the buoyancy ratio (N=−1 and 1). Results indicate that the augmentation of the Darcy number causes heat and mass transfer to rise for different power-law indexes. At Da=10−4, the heat and mass transfer increase with the augmentation of the power-law index in the absence of the Soret and Dufour parameters. The rise of the inclined angle from θ=0° to 40° and from θ=80° to 120° provokes heat and mass transfer to augment. As the Soret and Dufour numbers equal zero, the heat transfer enhances with the increment of the power-law index at Da=10−3. The heat transfer increases with the rise of the Dufour parameter and the mass transfer enhances as the Soret parameter increases for different power-law indexes and thermal Rayleigh numbers. In some cases, the augmentation of Soret and Dufour parameters alter the behavior of heat and mass transfer against the alteration of the power-law index.

Simulation of double diffusive natural convection and entropy generation of power-law fluids in an inclined porous cavity with Soret and Dufour effects (Part II: Entropy generation)

In this paper, entropy generation of associated with double diffusive natural convection of non-Newtonian power-law fluids in an inclined porous cavity has been analyzed by Finite Difference Lattice Boltzmann Method (FDLBM). The entropy generations due to fluid friction, heat and mass transfer have been simulated and analyzed for the certain pertinent parameters of thermal Rayleigh number (RaT=104 and 105), Darcy number (Da=10−4, 10−3, and 10−2), power-law index (n=0.6–1.4), Lewis number (Le=2.5 and 5), inclined angles (θ=0°, 40°, 80°, and 120°), Dufour parameter (Df=0, 1, and 5), Soret parameter (Sr=0, 1, and 5) and the buoyancy ratio (N=−1 and 1). Results indicate that the augmentation of the thermal Rayleigh number enhances different entropy generations and declines the average Bejan number. The increase in the Darcy number provokes various irreversibilities to enhance and the average Bejan number decreases significantly. The augmentation of the inclined angle from θ=0° to 40° enhances various total entropy generations and plummets the average Bejan number. The increase in the inclined angle from θ=40° to 80° results in the drop of different total entropy generations and rises the average Bejan number. The rise of Soret and Dufour parameters enhances the entropy generations due to heat transfer and fluid friction. The change of power-law index alters various entropy generations, but the alteration does not follow a specific manner in different studied parameters.

Mesoscopic simulation of magnetic field effect on natural convection of power-law fluids in a partially heated cavity

In this paper, effect of a magnetic field on natural convection of non-Newtonian power-law fluids in a partially heated cavity, has been analyzed by using the Finite-Difference Lattice Boltzmann Method (FDLBM). This study has been conducted for certain pertinent parameters of Rayleigh number (Ra=104 and 105), Hartmann number (Ha=0–60), power-law index (n=0.5–1.5), and length of heated section (H/L=0.25, 0.5, and 0.75), as the magnetic field is applied horizontally. Results indicate that the augmentation of the power-law index in the absence of the magnetic field causes heat transfer to drop. Generally, the magnetic field decreases heat transfer in different power-law indexes. The increment of the magnetic field power declines the effect of the power-law index on heat transfer. The magnetic field for various Hartmann numbers at Ra=104; has different effects on heat transfer with the enhancement of power-law index. At Ra=105 and for Ha=0 to 30, heat transfer falls with rise of the power-law index as the effect is weakened by increase in Hartmann number significantly. The influence of power-law index on heat transfer augments with increase in the size of the heated section.

Simulation of magnetic field effect on natural convection of non-Newtonian power-law fluids in a sinusoidal heated cavity using FDLBM

In this paper, the effect of a magnetic field on natural convection of non-Newtonian power-law fluids in a cavity with a sinusoidal heated wall has been analyzed by finite difference Lattice Boltzmann method (FDLBM). This study has been performed for the certain pertinent parameters of Rayleigh number (Ra=104 and 105), Prandtl number (Pr=10), Hartmann number (Ha=0–60) and power-law index (n=0.5–1.5) as the magnetic field is applied at different inclinations of γ=0° and 90°. Results indicate that the augmentation of the power-law index in the absence of the magnetic field causes heat transfer to drop. The magnetic field decreases heat transfer in different power-law indexes generally. The increment of the magnetic field power decreases the effect of the power-law index on heat transfer. The magnetic field for various Hartmann numbers at Ra=104 has different effects on heat transfer against the enhancement of power-law index. At Ra=105 and in the presence of the magnetic field, the heat transfer falls with the rise of the power-law index as the effect is weakened by the increase of Hartmann number significantly. The amount of the magnetic field influence on the heat transfer and the fluid flow is different in the vertical and horizontal ones.

FDLBM simulation of magnetic field effect on natural convection of non-Newtonian power-law fluids in a linearly heated cavity

In this paper, the effect of a magnetic field on natural convection of non-Newtonian power-law fluids in a cavity with a linearly heated wall has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). This study has been performed for the certain pertinent parameters of Rayleigh number (Ra=104 and 105), Hartmann number (Ha=0, 15, 30 and 60) and power-law index (n=0.5-1.5) as the magnetic field is applied horizontally. Results indicate that the augmentation of the power-law index in the absence of the magnetic field causes heat transfer to drop. The magnetic field decreases heat transfer in different power-law indexes generally. The increment of the magnetic field power declines the effect of the power-law index on heat transfer. The magnetic field for various Hartmann numbers at Ra=104 provokes heat transfer to increase with the enhancement of power-law index. At Ra=105, the heat transfer falls with the rise of the power-law index for Ha=15 and 30 as the effect is weakened by the increase of Hartmann number significantly. However, the increase in power-law index augments heat transfer at Ha=60.

Natural convection of non-Newtonian power-law fluids on a horizontal plate

The problem of natural convective boundary layer flow of a non-Newtonian power-law fluid over an isothermal horizontal plate, which does not admit a similarity solution, has been solved numerically using a time-marching finite difference method. The analysis shows that the velocity, temperature and pressure inside the boundary layer depend on two parameters, the non-Newtonian power-law index (n) and the generalised Prandtl number (Pr∗). For n>1 (dilatant fluids), the u-velocity profiles reveal that the maximum velocity attained increases but the thickness of the boundary layer decreases as the value of n is progressively increased above unity. For n<1 (pseudoplastic fluids), the reverse occurs and the boundary layer thickness increases to a great extent while the maximum velocity is reduced as the value of n is progressively decreased below unity. The magnitude of the normal velocity component at the edge of the boundary layer is found to be smaller for dilatant fluids and larger for pseudoplastic fluids as compared to Newtonian fluids. It has been found that the dilatant fluids show improved heat transfer characteristics as compared to Newtonian and pseudoplastic fluids at the same generalised Prandtl number. The non-existence of self-similar solutions for non-Newtonian power-law fluids has been established, thus showing the utility of the numerical method developed to solve the system of partial differential equations.

Laminar natural convection of power-law fluids in a square enclosure submitted from below to a uniform heat flux density

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 103–105 and a Prandtl number (Pr) range of 10–106. 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.

Laminar natural convection of non-Newtonian power-law fluids between concentric circular cylinders

The two-dimensional steady-state natural convection of power-law fluids is studied numerically between two concentric horizontal cylinders with different constant temperatures. The governing equations are discretized using finite volume technique based on second order upwind and are solved using the SIMPLE algorithm. The effects of Rayleigh number (103≤Ra≤105) and Prandtl number (10≤Pr≤103) on the dimensionless velocity and temperature are investigated for both pseudoplastic and dilatant fluids. Also the mean Nusselt number for various values of governing parameters is obtained and discussed. The results indicate that with increasing the power-law index from 0.6 to 1.4, the mean Nusselt number decreases. In the best case among the range of parameters considered here the heat transfer rate for pseudo-plastic fluid (n=0.6) is 170% higher than the Newtonian one and for dilatant fluid (n=1.4) the heat transfer rate is 43% lower than the Newtonian fluid. So the pseudoplastic and dilatant fluids are more efficient than Newtonian fluids for cooling and insulating purposes, respectively. It is shown that as the Rayleigh number increases the cooling effect of pseudoplastic fluid and the insulating effect of dilatant fluid become more pronounced.

Natural convection of power-law fluid between two-square eccentric duct annuli

The present paper numerically studies two-dimensional steady-state natural convection of non-Newtonian power-law fluid between two eccentric horizontal square ducts with constant temperature. The inner and outer ducts are assumed to be held at hot and cold temperatures, respectively. The conservation equations of mass, momentum and energy are dicretized using finite volume technique based on second order upwind and finally SIMPLE algorithm is utilized to solve the resultant system of equations. The effects of power-law index (0.6⩽n⩽1.4), Rayleigh number (103⩽Ra⩽106), aspect ratio (0.25⩽AR⩽0.75), eccentricity (-0.2⩽e⩽+0.2) and Prandtl number (10⩽Pr⩽103) on heat and fluid flows are investigated. Also the Nusselt number for various values of governing parameters is obtained and discussed. The results indicate that with increasing the power-law index n from 0.6 to 1.4 the mean Nusselt number that indicates heat transfer rate decreases. It is shown that there is a minimum situation for the Nusselt number versus the eccentricity dependent on the other parameters. Also it is found that varying the Prandtl number almost does not affect heat transfer characteristics except for some cases.

Thermal radiation effect on mixed convection heat and mass transfer of a non-Newtonian fluid over a vertical surface embedded in a porous medium in the presence of thermal diffusion and diffusion-thermo effects

Thermal radiation, thermal diffusion, and diffusion-thermo effects on heat and mass transfer by mixed convection of non-Newtonian power-law fluids over a vertical permeable surface embedded in a saturated porous medium are investigated. The governing equations describing the problem are non-dimensionalized and transformed into a non-similar form. The transformed equations are solved by using the local non-similarity method combined with the shooting technique. The effects of the physical parameters of the problem on the fluid temperature and concentration are illustrated graphically and analyzed. Also, the effects of the pertinent parameters on the local Nusselt number and the local Sherwood number are presented.