Heat Transfer To Power-law Fluids Research Articles

Pulsating non-Newtonian heat and fluid flow in a concentric annular duct: An analysis using perturbation series method

In the current study, an analytical analysis is conducted to examine laminar pulsating flow and heat transfer of power-law fluid in a concentric annular channel that is uniformly heated. The momentum and energy balance equations are solved analytically using the perturbation series method under the assumption that fully developed hydrodynamic and thermal conditions exist. Nondimensional frequency and amplitude effects on periodic and period-averaged friction factor and Nusselt number are obtained for various power-law index values, representing pseudoplastic, Newtonian, and dilatant fluids. The results from the present study are compared to those from the literature for some specific cases, and an excellent agreement is observed.

Unsteady Pressure-Driven Electrokinetic Slip Flow and Heat Transfer of Power-Law Fluid through a Microannulus

To guarantee the transporting efficiency of microdevices associated with fluid transportation, mixing, or separation and to promote the heat transfer performance of heat exchangers in microelectronics, the hydrodynamic behaviors at unsteady and steady states, as well as the thermal characteristics at the steady state in a pressure-driven electrokinetic slip flow of power-law fluid in a microannulus are studied. To present a more reliable prediction, the slip phenomenon at walls and nonlinear rheology of liquid are incorporated. The modified Cauchy momentum equation applicable to all time scales and energy equations, are analytically solved in the limiting case of a Newtonian fluid and numerically solved for power-law fluids. The transient velocity profile, time evolution of flow rate, temperature profile, and heat transfer rate are computed at different flow behavior indices, electrokinetic width, slip lengths, and Brinkman numbers, thereby, the coupling effect of nonlinear rheology, slip hydrodynamics, and annular geometry on flow and thermal behaviors is explored. The unsteady flow takes a longer time to achieve the steady state for shear thinning fluids or greater slip lengths. The flow behavior index and slip length play a significant role in the flow rate and heat transfer performance. The relevant discussion can serve as a theoretical guide for the operation and thermal management of annular geometry-related flow actuation systems.

Pulsating flow and heat transfer of power-law fluid in a circular pipe

In this study, the pulsating flow of a non-Newtonian fluid and heat transfer in a pipe with uniform heat flux at its wall is examined analytically. The flow is assumed to be both hydrodynamically and thermally fully developed. The perturbation method based on the series expansion is used in the analysis. The periodic change and period-averaged values of the friction factor and Nusselt number as well as velocity and temperature profiles are obtained at varying values of dimensionless frequency and amplitude for shear-thinning, Newtonian and shear-thickening fluids. It is shown that the frequency is effective on the friction factor for a specific range of the dimensionless frequency. For some specific cases, excellent agreements are obtained with the literature. It is disclosed that the dimensionless frequency, the amplitude and the power-law index are interactively effective on the friction and heat transfer.

Using active/passive methods to control of MHD conjugate heat transfer of power-law fluids: a numerical entropy analysis by LBM

Using active/passive methods to control of MHD conjugate heat transfer of power-law fluids: a numerical entropy analysis by LBM

Heat transfer of power-law fluids with slip-dependent zeta potential

In this work, the influence of slip-dependent (S.D.) zeta potential on the heat transfer characteristics for power-law fluids is analyzed with consideration of overlapping electric double layer (EDL) and high zeta potential. Based on the non-linear electric potential distribution, the flow velocity, fluid temperature and convective heat transfer are discussed numerically. Results reveal that the shear-thinning fluids are more susceptible to the S.D. zeta potential as compared to Newtonian and shear-thickening fluids. The fluid temperature can be reduced obviously for shear-thinning fluids when the S.D. zeta potential is considered. However, the S.D. zeta potential has little impact on the temperature of shear-thickening fluids even for a large pressure gradient value. In addition, the convective thermal transfer is enhanced by the power-law behavior index and overlapping EDL. The present study aims to regulate the fluid temperature and enhance the convective thermal transfer by selecting appropriate salt concentration and power-law behavior index.

Analysis of Heat Transfer of Power-Law Fluid Along a Vertical Stretching Cylinder

The aim of this paper is to study the heat transfer enhancement of power-law fluid over a vertical stretching cylinder. The model is governed by partial differential equations (PDEs) which is then converted into a coupled system of non-linear ordinary differential equations (ODEs). Here both velocity and temperature profiles have been constructed for different physical parameters such as, Reynold number, Prandtl number, Eckert number, unsteadiness, mixed convective and magnetic-parameters. The obtained results have been compared with the existing literature that reveals the accuracy of the proposed scheme. Moreover, it has been noticed during the study that the power-law energy is getting enhanced corresponding to these parameters, which can be viewed in graphical simulations. In addition, the numerical computations of local-skin friction coefficient and Nusselt number are tabulated.

Heat transfer of power-law fluids under electrowetting actuation in structured microchannels

The dynamics and heat transfer performance of droplets play an important role in electrowetting systems. Contrary to the growing trend towards non-Newtonian fluids in electrotechnical systems, most researchers have focused on Newtonian fluids. In the current study, the interface is tracked by the phase-field method and afterwards, the numerical model is confirmed by comparing the results obtained from previous experimental and theoretical works. Several parameters such as power-law index and contact angle are analyzed. Furthermore, the dynamics and heat transfer of the droplets on chemically or topographically structured substrates in the presence of electrowetting are examined. It has been shown that increasing the power-law index Increases the heat transfer. Also, shear-thinning fluids exhibit more dynamics. The results also suggest that an increase in the contact angle of chemical heterogeneity leads to increase in average Nusselt number. Finally, in larger microgrooves, the shear thickening fluids has the higher Prandtl and average Nusselt number.

Conjugated heat transfer of power-law fluids in double-pass concentric circular heat exchangers with sinusoidal wall fluxes.

An analytical formulation, referred to as conjugated Graetz problems, is developed to predict the temperature distribution and Nusselt numbers for the power-law fluid flowing in a double-pass concentric circular heat exchanger under sinusoidal wall fluxes. A new design of inserting an impermeable sheet into a concentric tube, in parallel, to conduct recycling double-pass operations has been studied theoretically in the fully developed region, resulting in substantial improvements in the performance of heat exchanger device. The analytical solution was derived using the complex functions by transforming the boundary value problem into ordinary differential equations with the aid of the Frobenius method. The influences of power-law index and impermeable-sheet position on average Nusselt numbers with various designs and operating parameters are also delineated. The theoretical predictions show that the heat transfer efficiency is considerably improved through operating the double-pass device compared to via a single-pass circular heat exchanger (where an impermeable sheet is not inserted). The economic feasibility of operating double-pass concentric circular heat exchanger for power-law fluids is exemplified by the ratio of the heat-transfer efficiency enhancement and the increment in power consumption. The double-pass effect from increasing the convective heat-transfer coefficient can compensate for the rise in power consumption, which serves as important economic advantage of this design.

Effect of Non-Newtonian Fluid Behavior on Forced Convection from a Cluster of Four Circular Cylinders in a Duct, Part I: Power-Law Fluids

Forced convection heat transfer in power-law fluids has been investigated numerically around four identical circular cylinders in a diamond array in a square enclosure. For the laminar flow, the governing equations have been solved numerically over the following ranges of parameters: Reynolds number (5 − 200), Prandtl number (0.7 − 100), power-law index (0.2 − 2) and center-to center gap between cylinders (0.3 − 0.7) to elucidate their influence. The detailed kinematics and engineering parameters are influenced by the gap between the cylinders via the development of multiple secondary flow regions and/or the splitting of incoming fluid stream. The drag on the trailing cylinders with reference to the lead cylinder can be up to ± ∼ 80% higher or lower depending upon the gap between the cylinders, power-law index and Reynolds numbers. In compact arrays, the drag becomes slightly negative due to the reverse flow for certain combinations of power-law index (< 1) and high Reynolds numbers (100 and 200). Similarly, the heat transfer affected by the subsequent cylinders ranges from 50-60% for the second cylinder which drops to ∼10% for the last cylinder. Finally, the functional dependence of the Nusselt number has been consolidated in terms of Reynolds number, Prandtl number, power-law index and the gap ratio.

Heat Transfer of Power-Law Fluids in Plane Couette–Poiseuille Flows with Viscous Dissipation

Analytical expressions for the velocity and temperature profiles, bulk temperature and Nusselt numbers, in a fully-developed laminar Couette–Poiseuille flow between parallel plates of a power-law fluid with constant, and distinct, wall heat fluxes, in the presence of viscous dissipation are deduced and presented. Both favorable and adverse pressure gradient cases were analyzed. The walls’ shear stresses ratio, which arises naturally when the dimensionless hydrodynamic solution is obtained, together with the fluid power-law index Brinkman number and the walls’ heat fluxes ratio are the independent variables in the heat transfer solutions. With the exception of Newtonian fluids, there are in general two distinct analytical solutions, one for positive and another for negative values of the walls’ shear stresses ratio. The existence of singular points are also observed, where for a given value of the power-law index, there are values of the walls’ shear stresses ratio for which the Nusselt number becomes independent of the Brinkman number. It was also found that in a Couette–Poiseuille flow, for each value of the power-law index there exists a certain negative value of the walls’ shear stresses ratio that makes the Nusselt numbers at both walls identically zero.

Flow and heat transfer of non-Newtonian power-law fluids over a stretching surface with variable thermal conductivity

PurposeThe purpose of this paper is to investigate the flow and heat transfer of power-law fluids over a non-linearly stretching sheet with non-Newtonian power-law stretching features.Design/methodology/approachThe governing non-linear partial differential equations are reduced to a series of ordinary differential equations by suitable similarity transformations and the numerical solutions are obtained by the shooting method.FindingsAs the temperature power-law index or the power-law number of the fluids increases, the dimensionless stream function, dimensionless velocity and dimensionless temperature decrease, while the velocity boundary layer and temperature boundary layer become thinner for other fixed physical parameters. The thermal diffusivity varying as a function of the temperature gradient can be used to present the characteristics of flow and heat transfer of non-Newtonian power-law fluids.Originality/valueUnlike classical works, the effect of power-law viscosity on the temperature field is considered by assuming that the temperature field is similar to the velocity field with modified Fourier’s law heat conduction for power-law fluid media.

Coupling Effects of Viscous Sheet and Ambient Fluid on Boundary Layer Flow and Heat Transfer in Power-Law Fluids

This paper investigates the flow and heat transfer of power-law fluids over a stretching sheet where the coupling dynamics influence of viscous sheet and ambient fluid is taken into account via the stress balance. A modified Fourier's law is introduced in which the effects of viscous dissipation are taken into account by assuming that the thermal conductivity is to be shear-dependent on the velocity gradient. The conditions for both velocity and thermal boundary layers admitting similarity solutions are found, and numerical solutions are computed by a Bvp4c program. The results show that the viscous sheet and rheological properties of ambient fluids have significantly influences on both velocity and temperature fields characteristics. The formation of sheet varies with the viscosity of fluid and draw ratio, which then strongly affects the relations of the local skin friction coefficient, the local Nusselt number, and the generalized Reynolds number. Moreover, for specified parameters, the flow and heat transfer behaviors are discussed in detail.

Discussion: “Convection Heat Transfer of Power-Law Fluids Along the Inclined Nonuniformly Heated Plate With Suction or Injection” [Sui, J., Zheng, L., and Zhang, X., 2016, ASME J. Heat Transfer, 138(2), p. 021701

The present comment concerns some doubtful results in the above paper.

Non-linear Differential Equations and Rotating Disc Electrodes: Padé approximationTechnique

Rotating disc electrodes are preferred devices to analyze electrochemical reactions in electrochemical cellsand various rotating machinery such as fans, turbines, and centrifugal pumps. This model contains system of fully coupled and highly non-linear equations. This manuscript outlines the steady state solution of rotating disc flow coupled through the fluid viscosity, to the mass-concentration field of chemical species and heat transfer of power-law fluid over rotating disk. Furthermore, a simple analytical expression (Padé approximation) of velocity component/ self-similar velocity profiles is derived from the short and long distance expression. Our analytical results for all distance are compared with previous small and long distance and numerical solutions (Runge-Kutta method), which are in satisfactory agreement.

On heat transfer of weakly compressible power-law flows

This paper completes a numerical research on steady momentum and heat transfer in power-law fluids in a channel. Weakly compressible laminar fluids are studied with no slip at the walls and uniform wall temperatures. The full governing equations are solved by continuous finite element method. Three thermal conductivity models are adopted in this paper, that is, constant thermal conductivity model, thermal conductivity varying as a function of temperature gradient, and a modified temperature-gradient-dependent thermal conductivity model. The results are compared with each other and the physical characteristics for values of parameters are also discussed in details. It is shown that the velocity curve from the solution becomes straight at higher power-law index. The effects of Reynolds numbers on the dilatant fluid and the pseudo-plastic look similar to each other and their trends can be easily predicted. Furthermore, for different models, the temperature curves also present pseudo-plastic and dilatant properties.

Lie group analysis of hydromagnetic flow and heat transfer of a power-law fluid over stretching surface with temperature-dependent viscosity and thermal conductivity

The symmetry group of MHD boundary layer flow and heat transfer of a non-Newtonian power-law fluid over a stretching surface under the effects of variable fluid properties is investigated. The similarity equations with the corresponding boundary conditions are solved numerically by using a shooting method with the fourth order Runge–Kutta integration scheme. Comparisons of the numerical method with the existing results in the literature are made and obtained an excellent agreement. It is observed that the heat transfer rate diminishes with an increase in magnetic parameter and variable thermal conductivity parameter. Further, the opposite influence is found with an increase in variable viscosity parameter.

Flow and heat transfer of power-law fluid over a rotating disk with generalized diffusion

The study of swirling flows and heat transfer near various rotating machines, such as fans, turbines and centrifugal pumps, is necessary and important for many manufacturing processes in industry, especially the cooling of turbojet engines. The flow and heat transfer of power-law fluids over an infinite rotating disk is investigated in this paper. A generalized Fourier heat transfer model is introduced in which the thermal conductivity is assumed to depend on temperature gradient. New similarity variables are defined and the governing equations in the boundary layer are reduced to a set of coupling ordinary differential equations. An improved multi-shooting method is proposed to solve the resulting singular boundary value problems. The effects of the power-law index and local Prandtl number on velocity, pressure and temperature fields are analyzed. Especially, the viscosity coefficient and heat conductivity are discussed.

Free Convection in Confined Power-Law Fluids From Two Side-by-Side Cylinders in a Square Enclosure

Laminar free convection heat transfer in power-law fluids from two side-by-side cylinders (one hot and one cold) confined in a square duct has been studied numerically in the two-dimensional flow regime. For a fixed value of the ratio of cylinder radius to size of the enclosure, the effect of geometrical placement of the cylinders is studied on the resulting velocity and temperature fields in the laminar free convection regime by considering six asymmetric locations of the two cylinders. In particular, extensive results reported herein span the range of conditions of Grashof number, 10 to 105; Prandtl number, 0.7 to 100, thereby yielding the range of the Rayleigh number as 7 to 107; power-law index, 0.3 to 1.8; and the relative positions (dimensionless) of the cylinders with respect to the centerline, –0.25 to 0.25. The heat transfer characteristics are analyzed in terms of the local Nusselt number along the surfaces of the two cylinders and the enclosure walls. Overall, the average Nusselt number shows a positive dependence on both the Grashof number and the Prandtl number irrespective of the values of power-law index and relative positioning of the cylinders. Also, all else being equal, shear-thinning fluid behavior promotes heat transfer with reference to that in Newtonian fluids. When the two cylinders are situated close to the bottom wall, the rate of heat transfer is augmented with reference to that for the symmetric positioning of the cylinders along the horizontal mid-plane of the enclosure. Conversely, heat transfer deteriorates as the cylinders are located above the centerline of the enclosure. The present numerical results have been consolidated via the use of a modified Rayleigh number, thereby enabling the estimation of the average Nusselt number in a new application.

Lie group method for the modified model of MHD flow and heat transfer of a non-Newtonian fluid with prescribed heat flux over a moving porous plate

The modified model of magneto-hydrodynamic (MHD) flow and heat transfer of power-law fluid over a stretching permeable surface with prescribed heat flux in the presence of heat generation or absorption is investigated. The thermal conductivity is assumed to be dependent on the power law of velocity gradient. The general boundary conditions are given and Lie-group method is used to determine the appropriate boundary conditions suitable for the similarity solution. By using the achieved similarity transformations, the similarity equations are obtained and solved numerically by Bvp4c with Matlab. Graphical solutions for the dimensionless velocity and temperature as well as skin-friction coefficient and Nusselt number for various parameters are presented and discussed.

Convection Heat Transfer of Power-Law Fluids Along the Inclined Nonuniformly Heated Plate With Suction or Injection

A comprehensive analysis to convection heat transfer of power-law fluids along the inclined nonuniformly heated plate with suction or injection is presented. The effects of power-law viscosity on temperature field are taken into account in highly coupled velocity and temperature fields. Analytical solutions are established by homotopy analysis method (HAM), and the effects of pertinent parameters (velocity power-law exponent, temperature power index, suction/injection parameter, and inclination angle) are analyzed. Some new interesting phenomena are found, for example, unlike classical boundary layer problem in which the skin friction monotonically increases (decreases) with suction increases (injection increases), but there exists a special region where the skin friction is not monotonic, which is strongly bound up with Prandtl number, which have never been reported before. The nonmonotony occurs in suction region for Prandtl number Npr &lt; 1 and injection region for Npr &gt; 1. Results also illustrate that the velocity profile decreases but the heat convection is enhanced obviously with increasing in temperature power exponent m (generalized Prandtl number Npr has similar effects), the decreases in inclination angle lead to the reduction in convection and heat transfer efficiency.