scholarly journals On power-law fluids with the power-law index proportional to the pressure

2016 ◽  
Vol 62 ◽  
pp. 118-123 ◽  
Author(s):  
J. Málek ◽  
K.R. Rajagopal ◽  
J. Žabenský
Keyword(s):  
Power Law ◽  
Power Law Fluids ◽  
Power Law Index

Unsteady Flow of Power Law Fluids With Wall Slip in Microducts

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
F. Talay Akyildiz ◽  
Dennis A. Siginer ◽  
M'hamed Boutaous
Keyword(s):  
Power Law ◽  
Nonlinear Partial Differential Equation ◽  
Slip Flow ◽  
Wall Slip ◽  
Nonlinear Boundary Conditions ◽  
Velocity Profiles ◽  
Momentum Balance ◽  
Power Law Fluids ◽  
Power Law Index ◽  
Pseudo Spectral

Unsteady laminar nonlinear slip flow of power law fluids in a microchannel is investigated. The nonlinear partial differential equation resulting from the momentum balance is solved with linear as well as nonlinear boundary conditions at the channel wall. We prove the existence of the weak solution, develop a semi-analytical solution based on the pseudo-spectral-Galerkin and Tau methods, and discuss the influence and effect of the slip coefficient and power law index on the time-dependent velocity profiles. Larger slip at the wall generates increased velocity profiles, and this effect is further enhanced by increasing the power law index. Comparatively, the velocity of the Newtonian fluid is larger and smaller than that of the power law fluid for the same value of the slippage coefficient if the power index is smaller and larger, respectively, than one.

Numerical Simulation for Heat Transfer of Nanofluid in a Rotating Circular Groove Using a Continuous Finite Element Scheme

2014 ◽  
Vol 1081 ◽  
pp. 175-179 ◽  
Author(s):  
Yong Yue Jiang ◽  
Ping Lin ◽  
Bo Tong Li ◽  
Lin Li
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Power Law ◽  
Initial Time ◽  
The Finite Element Method ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Circular Groove ◽  
Power Law Fluids ◽  
Power Law Index

In this paper, we investigate the heat transfer of the power-law-fluids-based nanofluids in a rotating circular groove. The circular groove rotates with a constant speed and the temperature on the wall of the groove is different from the temperature inside in the initial time. The effects of thermophoresis and Brownian are considered. The thermal conductivity of the nanofluids is taken as a constant. We solve the model with the finite element method directly and discretize them using a continuous finite element scheme in space and a modified midpoint scheme in time. From the results we can find that the heat transfer enhancement of the nanofluids increases as the power law index of the base fluid decreases.

scholarly journals Finite Volume Simulation of Natural Convection for Power-Law Fluids with Temperature-Dependent Viscosity in a Square Cavity with a Localized Heat Source

2021 ◽  
Vol 39 (5) ◽  
pp. 1405-1416
Author(s):  
Hamza Daghab ◽  
Mourad Kaddiri ◽  
Said Raghay ◽  
Ismail Arroub ◽  
Mohamed Lamsaadi ◽  
...  
Keyword(s):  
Natural Convection ◽  
Heat Source ◽  
Finite Volume ◽  
Power Law ◽  
Numerical Study ◽  
Staggered Grid ◽  
Cooling Performance ◽  
Coupled Equations ◽  
Power Law Fluids ◽  
Power Law Index

In this paper, numerical study on natural convection heat transfer for confined thermo-dependent power-law fluids is conducted. The geometry of interest is a fluid-filled square enclosure where a uniform flux heating element embedded on its lower wall is cooled from the vertical walls while the remaining parts of the cavity are insulated, without slipping conditions at all the solid boundaries. The governing partial differential equations written in terms of non-dimensional velocities, pressure and temperature formulation with the corresponding boundary conditions are discretized using a finite volume method in a staggered grid system. Coupled equations of conservation are solved through iterative Semi Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. The effects of pertinent parameters, which are Rayleigh number (103 ≤ Ra ≤ 106), power-law index (0.6 ≤ n ≤ 1.4), Pearson number (0 ≤ m ≤ 20) and length of the heat source (0.2 ≤ W ≤ 0.8) on the cooling performance are investigated. The results indicate that the cooling performance of the enclosure is improved with increasing Pearson and Rayleigh numbers as well as with decreasing power-law index and heat source length.

Unsteady Forced Convection Heat Transfer for Power Law Fluids in a Pipe

2010 ◽  
Author(s):  
Botong Li ◽  
Liancun Zheng ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Forced Convection ◽  
Power Law ◽  
Control Volume ◽  
Convection Heat Transfer ◽  
Inlet Temperature ◽  
Convection Heat ◽  
Forced Convection Heat Transfer ◽  
Power Law Fluids ◽  
Power Law Index

This paper studied the problem of forced convection heat transfer for power law fluids in a pipe which was affected by the varying inlet temperature. The fluid flow was hydrodynamically fully-developed and laminar while the effects of viscous dissipation and the power law kinematic viscosity on heat transfer were considered. A control volume technique based on the finite difference model coupled with the LU decomposition method was adopted and the least squares polynomial was introduced to approximate the non-linear items. The results show that the heat transfer behaviors are strongly depending on the value of the power law index. It is found that the thermal wave of the inlet temperature has less penetration with the increasing axial coordinate, and the effect of heat transfer is dominant away from the wall. The temperature profile is flatter as the power law index increases, which is implies that the shear-thickening non-Newtonian flows are affected easier by the inlet temperature than the shear-thinning fluids.

Non-Newtonian Power-Law Flows around Circular Cylinder under Aiding/Opposing Thermal Buoyancy

2018 ◽  
Vol 16 ◽  
pp. 45-56
Author(s):  
Houssem Laidoudi ◽  
Mohamed Bouzit
Keyword(s):  
Heat Transfer ◽  
Circular Cylinder ◽  
Power Law ◽  
Flow Separation ◽  
Vertical Channel ◽  
Buoyancy Effect ◽  
Thermal Buoyancy ◽  
Power Law Fluids ◽  
Recirculation Length ◽  
Power Law Index

This paper presents a comprehensive computational work on hydrodynamic and thermal phenomena of upward flow separation around a confined circular cylinder by aiding/opposing thermal buoyancy. For that purpose, let us consider a confined flow of Non-Newtonian power-law fluid around a heated/cooled circular cylinder in a two-dimensional vertical channel. The effects of thermal buoyancy and power-Law index on the flow separation and the average Nusselt number are studied for the conditions: (10 ≤ Re ≤ 40), (0.4≤ n ≤ 1.2), (-0.5 ≤ Ri ≤ 0.8), Pr = 50 and blockage ratio β = 0.2. In the steady flow regime the results show that the augmentation of the power-law index in the absence of thermal buoyancy causes a separation to grow. The adding buoyancy effect delays the separation in different power-law indices gradually and at some critical value of the buoyancy parameter it completely disappears resulting a stuck flow around a cylinder, whereas the opposing buoyancy effect causes an earlier wake behind cylinder. Moreover, the recirculation length is calculated to support the above finding. The decrease in the power-Law index increases the heat transfer rate. The Nusselt numbers are computed to predict the heat transfer rates of power-law fluids under the aiding/opposing thermal buoyancy condition.

scholarly journals Numerical Analysis and Entropy Generation of Electrokinetic Flow of Power-Law Fluid in a Microtriangular Prism

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Fehaid Salem Alshammari
Keyword(s):  
Nusselt Number ◽  
Entropy Generation ◽  
Power Law ◽  
Second Law Of Thermodynamics ◽  
Physical Parameters ◽  
Electrokinetic Flow ◽  
Power Law Fluids ◽  
Transfer Equations ◽  
Constant Wall Heat Flux ◽  
Power Law Index

This research aims to study the characteristics of thermal transport and analyse the entropy generation of electroosmotic flow of power-law fluids in a microtriangular prism in the presence of pressure gradient. Considering a fully developed flow subject to constant wall heat flux, the nonlinear electric potential, momentum, and linear heat transfer equations are solved numerically by developing an iterative finite difference method with a nonuniform grid. The thermal efficiency of the model is explored under the light of the second law of thermodynamics. Effect/impact of governing physical parameters on velocity, temperature, Nusselt number, and entropy distributions is studied, and the results are demonstrated graphically; we found that the Nusselt number decreases with the increase of power-law index, and average entropy generation increases with power-law index. We believe that the obtained result in the present study shall be useful for design of energy efficient microsystems which utilize the dual electrokinetic and centrifugal pumping effects.

Mixed Convection From a Heated Square Cylinder to Newtonian and Power-Law Fluids

2006 ◽  
Vol 129 (4) ◽  
pp. 506-513 ◽  
Author(s):  
A. K. Dhiman ◽  
N. Anjaiah ◽  
R. P. Chhabra ◽  
V. Eswaran
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Power Law ◽  
Richardson Number ◽  
Square Cylinder ◽  
Laminar Mixed Convection ◽  
Power Law Fluids ◽  
Power Law Index

Steady laminar mixed convection flow and heat transfer to Newtonian and power-law fluids from a heated square cylinder has been analyzed numerically. The full momentum and energy equations along with the Boussinesq approximation to simulate the buoyancy effects have been solved. A semi-explicit finite volume method with nonuniform grid has been used for the range of conditions as: Reynolds number 1–30, power-law index: 0.8–1.5, Prandtl number 0.7–100 (Pe⩽3000) for Richardson number 0–0.5 in an unbounded configuration. The drag coefficient and the Nusselt number have been reported for a range of values of the Reynolds number, Prandtl number, and Richardson number for Newtonian, shear-thickening (n>1) and shear-thinning (n<1) fluids. In addition, detailed streamline and isotherm contours are also presented to show the complex flow field, especially in the rear of the cylinder. The effects of Prandtl number and of power-law index on the Nusselt number are found to be more pronounced than that of buoyancy parameter (Ri⩽0.5) for a fixed Reynolds number in the steady cross-flow regime (Re⩽30).

scholarly journals High mixing performances of shear-thinning fluids in two-layer crossing channels micromixer at very low Reynolds numbers

2019 ◽  
Vol 13 (4) ◽  
pp. 5938-5960
Author(s):  
A. Kouadri ◽  
Y. Lasbet ◽  
M. Makhlouf
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Transport Model ◽  
Tangential Velocity ◽  
Reynolds Numbers ◽  
Mixing Efficiency ◽  
Species Transport ◽  
Industrial Sectors ◽  
Power Law Fluids ◽  
Power Law Index

In a recent study, the Two-Layer Crossing Channels Micromixer (TLCCM) exhibited good mixing capacities in the case of the Newtonian fluids (close to 100%) for all considered Reynolds number values. However, since the majority of the used fluids in the industrial sectors are non-Newtonians, this work details the mixing evolution of power-law fluids in the considered geometry. In this paper, the power-law index ranges from 0.73 to 1 and the generalized Reynolds number is bounded between 0.1 and 50. The conservation equations of momentum, mass and species transport are numerically solved using a CFD code, considering the species transport model. The flow structure at the cross-sectional planes of our micromixer was studied using the dynamic systems theory. The evolutions of the intensity, also the axial, radial and tangential velocity profiles were examined for different values of the Reynolds number and the power-law index. Besides, the pressure drop of the power-law fluids under different Reynolds number was calculated and represented. Furthermore, the mixing efficiency is evaluated by the computation of the mixing index (MI), based on the standard deviation of the mass fraction in different cross-sections. In such geometry, a perfect mixing is achieved with MI closed to 99.47 %, at very small Reynolds number (from the value 0.1) whatever the power-law index and generalized Reynolds numbers taken in this investigation. Consequently, the targeted channel presents a useful tool for pertinent mass transfer improvements, it is highly recommended to include it in various microfluidic systems.

Numerical Investigation of Natural Convection Heat Transfer From an Array of Horizontal Fins in Non-Newtonian Power-Law Fluids

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Jacob K. Mulamootil ◽  
Sukanta K. Dash
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Power Law ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Flat Plates ◽  
Power Law Fluids ◽  
Power Law Index ◽  
Fin Length

Natural convection heat transfer from an array of horizontal rectangular fins on a vertical flat plate in non-Newtonian power-law fluids has been studied. The underlying physical principles affecting heat transfer were studied using comprehensive solutions obtained from numerical investigations. Heat transfer to the power-law fluid was found to depend on the fluid rheology (power-law index) and significantly on the geometric parameters (interfin spacing, fin length) as well. The dependence was quantified using the Nusselt number (Nu) and fin effectiveness (Q/Q0). The present study shows that compared to a fin analyzed in isolation, the spatial arrangement of multiple fins relative to one another in an array does have a significant effect on the flow field around subsequent fins in power-law fluids. Therefore, the average heat transfer coefficient of the natural convection system is affected significantly. The variation of Nu with the dimensionless fin length (l/L), dimensionless interfin spacing (S/L), and fluid power-law index (n) was plotted. The dependence was found to be counter intuitive to expectations based on studies for natural convection from vertical flat plates to power-law fluids. In the present study involving fins, shear-thinning fluids (n < 1) show a decrease in heat transfer and shear-thickening fluids (n > 1) show an enhancement in heat transfer for higher l/L values. The results of the study may be useful in the design of natural convection systems that employ power-law fluids to enhance or control heat transfer.

Lattice Boltzmann Modelling for Natural Convection in Power-Law Fluids within a Partially Heated Square Enclosure

2020 ◽  
Author(s):  
Siva Subrahmanyam Mendu ◽  
P.K. Das
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Source ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Collision Term ◽  
Square Enclosure ◽  
Power Law Fluids ◽  
Power Law Index

Abstract The present 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 and, temperature contours, velocity profiles and variation of heat transfer on the non-adiabatic 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.

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