Convection Of non-Newtonian Fluids Research Articles

A fractional time-stepping method for unsteady thermal convection in non-Newtonian fluids

We propose a fractional-step method for the numerical solution of unsteady thermal convection in non-Newtonian fluids with temperature-dependent physical parameters. The proposed method is based on a viscosity-splitting approach, and it consists of four uncoupled steps where the convection and diffusion terms of both velocity and temperature solutions are uncoupled while a viscosity term is kept in the correction step at all times. This fractional-step method maintains the same boundary conditions imposed in the original problem for the corrected velocity solution, and it eliminates all inconsistencies related to boundary conditions for the treatment of the pressure solution. In addition, the method is unconditionally stable, and it allows the temperature to be transported by a non-divergence-free velocity field. In this case, we introduce a methodology to handle the subtle temperature convection term in the error analysis and establish full first-order error estimates for the velocity and the temperature solutions and 1/2-order estimates for the pressure solution in their appropriate norms. Three numerical examples are presented to demonstrate the theoretical results and examine the performance of the proposed method for solving unsteady thermal convection in non-Newtonian fluids. The computational results obtained for the considered examples confirm the convergence, accuracy, and applicability of the proposed time fractional-step method for unsteady thermal convection in non-Newtonian fluids.

Rayleigh–Bénard convection in non-Newtonian fluids: Experimental and theoretical investigations

We present an experimental and theoretical study of Rayleigh–Bénard convection in shear-thinning fluids with temperature-dependent properties. Experiments were performed using a cylindrical cell with a radius R̂=60 mm and height adjustable at d̂=15 and 20 mm giving a radius-to-height ratio L = 4 and 3, respectively. The fluids used are glycerol (Newtonian fluid) and aqueous xanthan gum solutions (shear-thinning fluids) at 1000 and 1200 ppm. Convection patterns are visualized by the shadowgraph method. In the theoretical part of this study, the weakly nonlinear analysis performed by Varé et al. [J. Fluid Mech. 905, A33 (2020)] is extended to take into account the variation of the thermal expansion coefficient with temperature. For the xanthan gum solutions used, the temperature dependence of the fluid parameters is sufficiently strong to obtain hexagonal cells at the onset of convection. It has been observed that their size decreases with the increase in the temperature difference across the fluid layer above the critical value. This result provides an experimental support to our theoretical study where it is shown that for hexagons, the band of stable wavenumbers is bent toward higher wavenumbers. For the glycerol, Newtonian fluid with a large Prandtl number, a slight increase in the wavelength of rolls is observed in agreement with the literature.

Viscous Dissipation Effect in the Free Convection of Non-Newtonian Fluid with Heat Generation or Absorption Effect on the Vertical Wavy Surface

The present article analyzes the effect of viscous dissipations on natural convection heat transfer. The power law model for non-Newtonian fluid with heat generation or absorption effect along a sinusoidal wavy surface with isothermal boundary condition is investigated. A simple coordinate transform is employed to map the wavy surface into a flat surface, and also, the fully implicit finite difference method is incorporated for the numerical solution. The findings of this study can help better understand the effect of parameters such as the Brinkman number, heat generation/absorption, wave amplitude magnitude, and generalized Prandtl number on convective heat transfer in dilatant and pseudoplastic non-Newtonian. Results show that as the Brinkman number increases, the amount of heat transfer decreases. This is physically justifiable considering that the fluid becomes warmer due to the viscous dissipation, decreasing its temperature difference with the constant temperature surface. Also, the effect of the power law viscosity index is surveyed. It is demonstrated that the magnitude of the local Nusselt number in the plane leading edge has the smallest quantity for pseudoplastic fluids compared to dilatant Newtonian fluids. Additionally, as the distance from the plane leading edge increases, the heat transfer declines.

Numerical simulation on convection of non-Newtonian fluid in a porous enclosure with non-uniform heating and thermal radiation

The aim of the numerical simulation is to explore the laminar, incompressible, buoyant induced convection flow and heat transfer of Casson fluid in a porous square box in the presence of thermal radiation. Thermal insulation is imposed on horizontal walls. The vertical boundaries of the closed box are maintained with sinusoidal thermal distribution. The non-Darcy porous model is adopted in the present study along with Navier-Stokes equations. The solution is obtained by finite volume method with SIMPLE algorithm. The results are explored over a range of radiation parameter, Casson fluid parameter, and Darcy numbers. It is found that thermal stratification is found for higher values of Casson liquid parameter in the presence of radiation. The kinematic energy enhances on rising the values of Casson liquid parameter & radiation parameter. The heat transport deteriorates on growing the values of radiation parameter and it enhances on growing the Casson fluid parameter.

Heat and Mass Transfer on the Mixed Convection of Non-Newtonian Fluids Over a Vertical Wedge with Soret/Dufour Effects and Internal Heat Generation: Variable Wall Temperature/Concentration

This numerical analysis investigated the effects of heat and mass transfer characteristics on the mixed convection flow of non-Newtonian fluids over the vertical wedge in a saturated porous medium with Soret/Dufour effects and internal heat generation. The numerical modeling of this problem has attracted considerable attention from researchers because it has practical applications in biological sciences, electronic cooling, advanced nuclear systems, etc. The internal heat generation is assumed to be an exponential decaying form. The power-law model of Ostwald–de Waele for non-Newtonian fluids is considered. The surface of the vertical wedge is kept at variable wall temperature and concentration. In the analysis of mixed convection, which included free convection and forced convection, parameter varies from 0 (pure free convection) to 1 (pure forced convection). The transformed equations are obtained by using a suitable coordinate transformation, and then, Keller box method is utilized to solve the non-similar equations. Comparisons with data published previously showed good agreement. Both the local Nusselt number and the local Sherwood number increase with increasing the exponent of variable wall temperature/concentration. Increasing the internal heat generation coefficient decreases (increases) the local Nusselt (Sherwood) number. As the power-law index is increased, the local Nusselt and Sherwood numbers are decreased.

Конвективный теплоперенос степенной жидкости в полости с источником энергии нестационарного объемного тепловыделения

Numerical analysis of transient natural convection of non-Newtonian fluid in an enclosure with a local heat source of variable volumetric heat generation is carried out. The power-law fluid model of Ostwald-De-Waele is used for description of the non-Newtonian fluid behavior. The governing partial differential equations have been formulated in dimensionless variables «stream function–vorticity». The obtained boundary-value problem of mathematical physics has been solved numerically by the finite difference method using the uniform mesh. Investigations have been conducted in a wide range of the fluid power-law index and oscillation frequency of the heat source volumetric heat generation. Distributions of streamlines and isotherms as well as average Nusselt number at heater surface and average temperature within the heater illustrating the effects of the governing parameters on the fluid flow and heat transfer have been obtained.

Influence of Internal Heat Generation on the Natural Convection of Non-Newtonian Fluids over a Vertical Plate in Porous Media with Thermal Radiation and Soret/Dufour Effects: Variable Wall Temperature/Concentration

The heat and mass transfer characteristics of the influence of internal heat generation on the natural convection of non-Newtonian fluids over a vertical plate in porous media with thermal radiation and Soret/Dufour effects are numerically analyzed. The surface of the vertical plate has a variable wall temperature and variable wall concentration (VWT/VWC). The similarity solution is obtained by assuming internal heat generation to be in exponential decaying form. The Rosseland diffusion approximation is employed to describe the radiative heat flux. Similar governing equations are solved by Keller box method. Comparisons showed excellent agreement with the numerical data of previous works. Numerical data for the dimensionless temperature profile, the dimensionless concentration profile, the local Nusselt number and the local Sherwood number are presented for the buoyancy ratio $$ N $$, the Lewis number $$ Le $$, the power-law index of the non-Newtonian fluid $$ n $$, the Soret parameter $$ S $$, the Dufour parameter $$ D $$, the exponent of VWT/VWC $$ \lambda $$, the internal heat generation coefficient $$ A^{*} $$ and the thermal radiation parameter $$ R_{d} $$. The physical aspects of the problem are discussed in detail.

Simulation of forced convection in non-Newtonian fluid through sandstones

ABSTRACTNumerical simulation is carried out to study forced convection in non-Newtonian fluids flowing through sandstones. Simulation is carried out using lattice Boltzmann method (LBM) for both shear-thinning and shear-thickening, by varying the power law index from 0.5 to 1.5 in Carreau–Yasuda model. Parameters involved in LBM and Carreau model are identified to achieve numerical convergence. Permeability and porosity are varied in the range of 10−10–10−6 and 0.1–0.7, respectively, to match actual geometrical properties of sandstone. Numerical technology is validated by establishing Darcy's law by plotting the graph between velocity and pressure gradient. Consequently, investigation is carried out to study the influence of material properties of porous media on flow properties such as velocity profiles, temperature profiles, and Nusselt number.

Influence of Uniform Blowing/Suction on the Free Convection of Non-Newtonian Fluids Over a Vertical Cone in Porous Media With Thermal Radiation and Soret/Dufour Effects: Uniform Wall Temperature/Uniform Wall Concentration

This work studies numerically the combined heat and mass transfer of uniform blowing/suction, non-Newtonian power-law fluid, and thermal radiation effects on free convection adjacent to a vertical cone within a porous medium in the presence of Soret/Dufour effects. The surface of the vertical cone has a uniform wall temperature and uniform wall concentration (UWT/UWC). The Rosseland diffusion approximation is employed to describe the radiative heat flux. A nonsimilarity analysis is performed, and the transformed governing equations are solved by Keller box method (KBM). The effects of these major parameters of the Dufour parameter, Soret parameter, Lewis number, buoyancy ratio, power-law index of the non-Newtonian fluids, blowing/suction parameter, and thermal radiation parameter on the heat and mass transfer characteristics have been carried out. In general, for the case of blowing, both the local Nusselt number and the local Sherwood number decrease. This trend reversed for suction of fluid. The physical aspects of the problem are discussed in detail.

Rayleigh–Bénard convection in non-Newtonian Carreau fluids with arbitrary conducting boundaries

The objective of the present work is to investigate the Rayleigh–Bénard convection in non-Newtonian fluids with arbitrary conducting boundaries. A linear and weakly nonlinear analysis is performed. The rheological behavior of the fluid is described by the Carreau model. As a first step, the critical Rayleigh number and wavenumber for the onset of convection are computed as a function of the ratios ξb and ξt of the thermal conductivities of the bottom and top slabs to that of the fluid. In the second step, the preferred convection pattern is determined using an amplitude equation approach. The stability of rolls and squares is investigated as a function of (ξb,ξt) and the rheological parameters. The bounded region of (ξb,ξt) space where squares are stable decreases with increasing shear-thinning effects. This is related to the fact that shear-thinning effects increase the nonlinear interactions between sets of rolls that constitute the square patterns [1]. For a significant deviation from the critical conditions, the nonlinear convection terms and nonlinear viscous terms become stronger, reducing overall the stability domain of squares. The largest Nusselt number, Nu, is obtained for perfectly conducting boundaries. For a given (ξb,ξt), the stable solution yields the largest Nusselt number. The enhancement of heat transfer due to shear-thinning effects is significantly reduced for poorly heat conducting plates.

Mixed convection in non-Newtonian fluids along a vertical plate in a liquid-saturated porous medium with melting effect

A boundary-layer analysis is presented for the problem of mixed convection in a flow of a non-Newtonian fluid from a vertical plate in a liquid-saturated porous medium in the presence of the melting effect. Aiding and opposing external flows are considered. The power-law model for non-Newtonian fluids is used. After a suitable coordinate transformation, the governing boundary-layer equations are reduced to nonlinear coupled differential ones which are solved numerically by employing an implicit finite difference scheme. A discussion of the effect of the viscosity index and melting parameter on the surface heat transfer rate, as well as on the temperature and velocity distributions, is presented. It is shown that melting decreases the local Nusselt number. A comparison with previous published results at various values of the governing parameters for a Newtonian fluid reveals an excellent agreement.

Second law analysis for free convection in non-newtonian fluids over a horizontal plate embedded in a porous medium: (prescribed heat flux)

Second law characteristics of heat transfer and fluid flow due to free convection of non-Newtonian fluids over a horizontal plate with prescribed surface heat flux in a porous medium are analyzed. Velocity and temperature fields are obtained numerically using an implicit finite difference method under the similarity assumption and these results are used to compute the entropy generation rate Ns, irreversibility ratio φ and the Bejan number Be for both Newtonian and non-Newtonian fluids. The effects of power-law index n, heat flux variation parameter λ , and modified duty parameter, G on the dimensionless entropy generation rate Ns, and the Bejan number Be are investigated and presented graphically.

Second Law Analysis for Free Convection in Non-Newtonian Fluids Over a Horizontal Plate Embedded in a Porous Medium: Prescribed Surface Temperature

Second law characteristics of heat transfer and fluid flow due to free convection of non-Newtonian fluids over a horizontal plate with prescribed surface temperature in a porous medium are analyzed. Velocity and temperature fields are obtained numerically using an implicit finite difference method under the similarity assumption and these results are used to compute the entropy generation rate Ns, irreversibility ratio Φ, and the Bejan number Be for both Newtonian and non-Newtonian fluids. The effects of viscous frictional parameter G, Rayleigh number Ra, temperature variation λ, axial distance (x) on the dimensionless entropy generation rate Ns, and the Bejan number Be are investigated for Newtonian and non-Newtonian fluids and presented graphically.

Integral method for analyzing natural convection of non-newtonian fluid along a vertical heated plate in anisotropic porous medium

An analytical study of natural convection boundary-layer flow along a vertical plate embedded in an anisotropic porous medium saturated by a non-Newtonian fluid has been conducted. The principal axis of permeability ani-sotropy was oriented in oblique direction to the gravity vector. A power-law variation of wall temperature was prescribed at the vertical plate, and in the Darcy-Rayleigh number limit (Rax > 100), a boundary-layer solution based on the integral relations approach was assumed. Scale analysis was applied to determine the order of magnitudes involved in the boundary-layer regime. Analytical expressions were obtained for the boundary-layer thickness and the mean Nusselt number in terms of the governing parameters of the problem. When the power-law exponent was made smaller, the convective flow along the plate became stronger. When the porous matrix was oriented such that the principal axis of higher permeability was parallel to the gravity, the convective heat transfer along the plate attained maximum value. Journal of Applied Science and Technology Vol. 13 (1 & 2) 2008: pp. 1-7

Theoretical study of hydrodynamics and heat transfer by free convection of non-Newtonian fluids near a cooled surface with regard for variable viscosity

We have made a theoretical study of the hydrodynamics and heat transfer of non-Newtonian fluids near a cooled isothermal surface by laminar free convection with regard for the change in the fluid viscosity with temperature. A power rheological model has been used. The solutions to the systems of differential equations for the boundary layer have been obtained numerically. It has been shown that the strongest influence in the considered kinds of convection is produced by the relative viscosity. Moreover, of great importance is the nonlinearity index of the medium. With increasing rheological parameter the influence of variable viscosity decreases. Criteria equations for calculating the local and mean Nusselt numbers and friction coefficients have been obtained.

Validation of the Local Thermal Equilibrium Assumption in Forced Convection of Non-Newtonian Fluids through Porous Channels

In this paper, we assess the validity of the local thermal equilibrium assumption in the non-Newtonian forced convection flow through channels filled with porous media. For this purpose, the problem is solved numerically using local thermal non-equilibrium and non-Darcian models. Numerical solutions obtained over broad ranges of representative dimensionless parameters are utilized to map conditions at which the local thermal equilibrium assumption can or cannot be employed. The circumstances of a higher modified Peclet number, a lower modified Biot number, a lower fluid-to-solid thermal conductivity ratio, a lower power-law fluid index, and a lower microscopic and macroscopic frictional flow resistance coefficients, are identified as unfavorable circumstances for the local thermal equilibrium (LTE) condition to hold. Quantitative LTE validity maps that reflect the proportional effect of each parameter as related to others are presented.

Nonsimilar Solutions for Free Convection in non-Newtonian Fluids along a Horizontal Plate in a Porous Medium

Nonsimilar Solutions for Free Convection in non-Newtonian Fluids along a Horizontal Plate in a Porous Medium

Free convection in non-newtonian fluids along a horizontal plate in a porous medium

A similarity solution is presented for the problem of free convection boundary layer in power-law type non-Newtonian fluids along a horizontal plate with variable wall temperature or heat flux distribution. The effects of surface mass transfer are included. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.

Combined convection in non-Newtonian fluids along a nonisothermal vertical plate in a porous medium with lateral mass flux

A boundary layer analysis has been presented for interaction of combined convection from vertical surface in a porous medium saturated with a power-low type non-Newtonian fluid with presence suction and injection. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The effect of fluid suction/injection on the heat transfer rate is discussed.

Thermal Dispersion Effects on Combined Convection in Non-Newtonian Fluids Along a Nonisothermal Vertical Plate in a Porous Medium

The method of non-similarity solution is used to study the influence of thermal dispersion on combined convection from vertical surfaces in a porous medium saturated with a power-law type non-Newtonian fluid. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented.