Cu‐Al2O3/H2O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

The resent development of research in the field of nano technology introduced hybrid nanofluids which are advanced classes of fluids with augmented thermal properties and it gives better results comparing to regular nanofluid. The aim of the present work is to study the significant effects of variable viscosity and viscous dissipation on a porous stretching sheet in the presence of hybrid nanofluid and radiative heating. In this model, two types of nanoparticles, namely copper (Cu) and alumina oxide (Al₂O₃), are suspended in the base fluid H₂O to form a hybrid nanoliquid. The novelty of this study is to introduce variable viscosity along with natural convection in the momentum equation and viscous dissipation in the energy equation. Mathematical modeling is employed in this study, whereby partial differential equations for the fluid flow are constructed and transformed to a set of ordinary differential equations, and hence resolved computationally by Runge‐Kutta‐Fehlberg method along with shooting scheme. The most important results for relevant parameters concerning the flow heat measure, surface drag, and heat transfer coefficients are thoroughly examined and presented graphically for both Cu‐Al₂O₃/water hybrid nanofluids. There is an increase in hybrid nanofluid velocity profile with mounting values of $\lambda$, and the Cu‐water nanofluid converges to the boundary more quickly than the hybrid nanofluid due to the occurrence of variable viscosity. The results concluded that the Nusselt number of the viscous fluid is lower than that of the nanofluid and hence the hybrid nanofluid (ie, heat transfer rate: normal fluid < nanofluid < hybrid nanofluid). The outcomes of present investigations are in close agreement with the viscous fluid as a particular case.     

The viscous dissipation effect on heat transfer and fluid flow in micro-tubes

The numerical modeling of the conjugate heat transfer and fluid flow through the micro-tube was presented in the paper, considering the viscous dissipation effect. Three different fluids with temperature dependent fluid properties are considered: water and two dielectric fluids, HFE-7600 and FC-70. The diameter ratio of the micro-tube was D_i/D_o = 0.1/0.3 mm with a tube length L = 100 mm. The laminar fluid flow regime is analyzed. Two different heat transfer conditions are considered: heating and cooling and three different Br = 0.01, 0.1 and 0.5. The influence of the viscous heating on Nu and Po is analyzed and compared with Br = 0.     

The effects of Ohmic heating and viscous dissipation on unsteady MHD and slip flow over a porous rotating disk with variable properties in the presence of Hall and ion-slip currents

The effects of Ohmic heating and viscous dissipation on unsteady laminar magneto-hydrodynamics (MHD) flow of a viscous Newtonian and electrically conducting fluid over a rotating disk taken into account the variable fluid properties (density, (ρ), viscosity, (μ) and thermal conductivity, (κ)) in the presence of Hall and ion-slip currents effects have been examined. These fluid properties are taken to be dependent on temperature. The unsteady Navier–Stokes equations along with the energy equation are reduced to a system of ordinary differential equations by using similarity transformations and the resulting equation system is solved numerically by using a shooting method. Results for the details of the velocity as well as temperature are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tables.     

Entropy generation of viscous dissipative nanofluid flow in microchannels

An analytical study on the viscous dissipation effect on entropy generation in laminar fully developed forced convection of water–alumina nanofluid in circular microchannels is reported. In the first-law analysis, closed form solutions of the temperature distributions in the radial direction for the models with and without viscous dissipation term in the energy equation are obtained. The results show that the heat transfer coefficient decreases with nanoparticle volume fraction largely in the laminar regime of nanofluid flow in microchannel when the viscous dissipation effect is taken into account. In the second-law analysis, the two models are compared by analyzing their relative deviations in entropy generation for different Reynolds number and nanoparticle volume fraction. When the viscous dissipation is taken into account, the temperature distribution is prominently affected and consequently the entropy generation ascribable to the heat transfer irreversibility is significantly increased. The increase of entropy generation induced by the increase of nanoparticle volume fraction is attributed to the increase of both the thermal conductivity and viscosity of nanofluid which causes augmentation in the heat transfer and fluid friction irreversibilities, respectively. By incorporating the viscous dissipation effect, both thermal performance and exergetic effectiveness for forced convection of nanofluid in microchannels dwindle with nanoparticle volume fraction, contrary to the widespread conjecture that nanofluids possess advantage over pure fluid associated with higher overall effectiveness from the aspects of first-law and second-law of thermodynamics.     

Effects of viscous dissipation on forced convective heat transfer in a channel embedded in a power-law fluid saturated porous medium

The convective heat transfer analysis in a channel embedded in a power-law fluid saturated porous medium subject to uniform heat flux is presented and compared with a Newtonian fluid concerning the effects of viscous dissipation. Governing momentum and energy equations for non-Newtonian fluids which accounts for the viscous dissipation effects are solved numerically. The temperature profiles of the non-Newtonian fluids are found to relate closely to the velocity profiles. When viscous dissipation is taken account of, Nusselt numbers for non-Newtonian fluid are found to deviate more from Newtonian fluid with increasing Brinkman number for a certain range of the Darcy number.     

Effects of viscous dissipation and fluid axial heat conduction on heat transfer for non-Newtonian fluids in ducts with uniform wall temperature: Part I: Parallel plates and circular ducts

Laminar heat transfer in parallel plates and circular ducts subject to uniform wall temperature is studied by taking into account both viscous dissipation and fluid axial heat conduction in an infinite region. Developing temperature fields are evaluated numerically by a finite-difference method for various Brinkman numbers (Br) and Peclet numbers (Pe). Nusselt numbers are presented graphically for Pe = 10 and Pe → ∞, and Br = 0, ± 0.5 and ± 1 for non-Newtonian fluids described by the power-law model with the flow index of n = 0.5, 1.0 and 1.5. It is shown that Nusselt number has a single fixed value independent of Br in the thermally developing region and its numerical value is equal to that at the fully developed region for non-zero Br, when the preheating of incoming fluid due to both viscous dissipation and fluid axial heat conduction is considered.     

Design optimization of heat exchangers with high‐viscosity fluids

The thermal effectiveness and entropy generation of parallel and counter‐flow heat exchangers handling high‐viscosity fluids have been numerically investigated. Both the viscous friction and the viscosity variations with temperature were considered in the analysis. The results show that the thermal effectiveness–NTU curves deviate gradually from the curves obtained using the assumption that the effect of viscosity is negligible. Moreover, the consideration of the viscous frictional heating effect results in a considerable increase in the heat exchanger entropy. An optimum heat exchanger size could be determined from both first law and second law of thermodynamics points of view. The results show also that the effect of viscous friction with variable viscosity becomes more significant for lower inlet temperatures of high‐viscosity fluid. Copyright © 2002 John Wiley & Sons, Ltd.     

Slip-flow and heat transfer of gaseous flows in the entrance of a wavy microchannel

The present work investigates the developing fluid flow and heat transfer through a wavy microchannel with numerical methods. Governing equations including continuity, momentum and energy with the velocity slip and temperature jump conditions at the solid walls are discretized using the finite-volume method and solved by SIMPLE algorithm in curvilinear coordinate. The effects of creep flow and viscous dissipation are assumed. The numerical results are obtained for various Knudsen numbers. The results show that Knudsen number has declining effect on both the C_f.Re and Nusselt number on the undeveloped fluid flow. Significant viscous dissipation effects have been observed for large Knudsen number. Also, viscous dissipation causes a singular point in Nusselt profiles.     

Effects of viscous dissipation on the heat transfer in a forced pipe flow. Part 2: Thermally developing flow

In this part of the study, consideration is given to thermally developing laminar forced convection in a pipe including viscous dissipation. The axial heat conduction in the fluid is neglected. Two different thermal boundary conditions are considered: the constant heat flux (CHF) and the constant wall temperature (CWT). Both the wall heating (the fluid is heated) case and the wall cooling (the fluid is cooled) case are considered. The distributions for the developing temperature and local Nusselt number in the entrance region are obtained. Results show that the temperature profiles and local Nusselt number are influenced by the Brinkman number (Br) and the thermal boundary condition used for the wall. Significant viscous dissipation effects have been observed for large Br.     

Heat transfer due to electroosmotic flow of viscoelastic fluids in a slit microchannel

The bio-microfluidic systems are usually encountered with non-Newtonian behaviors of working fluids. The rheological behavior of some bio-fluids can be described by differential viscoelastic constitutive equations that are related to PTT and FENE-P models. In the present work, thermal transport characteristics of the steady fully developed electroosmotic flow of these fluids in a slit microchannel with constant wall heat fluxes have been investigated. The Debye–Huckel linearization is adopted and the effects of viscous dissipation and Joule heating are taken into account. Analytical solutions are obtained for the transverse distributions of velocity and temperature and finally for Nusselt number. Two different behaviors are observed for the Nusselt number variations due to increasing ?_geWe² which are an increasing trend for positive wall heat flux and a decreasing one for negative wall heat flux. However, the influence of ?_geWe² on Nusselt number vanishes at higher values of the dimensionless Debye–Huckel parameter. It is also realized that the effect of viscous heating is more important at small values of both ?_geWe² and the dimensionless Debye–Huckel parameter. Furthermore, the results show a singularity in Nusselt number at higher negative values of the dimensionless Joule heating parameter.     

Asymptotic approximations for the flow field in a free convective flow of a non-Newtonian fluid past a vertical porous plate

The problem of suction/injection on free convective flow of a non-Newtonian fluid past a vertical porous plate is modeled in this study. Adopting a series expansion technique about a small parameter E_c and making fairly realistic assumptions, the coupled non-linear partial differential equations are decoupled and expressions for the temperature, velocity, skin-friction and rate of heat transfer are obtained. This is based on the fact that for fairly slow motions of all incompressible fluids, the viscous dissipation heat parameter E_c is small. Our results show that the velocity distribution is highly dependent on the visco-elastic parameter L and we also observe that the rate of heat transfer does not depend on the free convection parameter G_r. Other observations are depicted in Fig. 1, Fig. 2, Fig. 3, Fig. 4.     

Conjugated heat transfer in circular ducts with a power-law laminar convection fluid flow

This work deals with the study of the steady-state analysis of conjugated heat transfer process for the thermal entrance region of a developed laminar-forced convection flow of a power-law fluid in a circular tube. A known uniform heat flux is applied at the external surface of the tube. The energy equation in the fluid is solved analytically using the integral boundary layer approximation by neglecting the heat generation by viscous dissipation and the axial heat conduction in the fluid. This solution is coupled to the Laplace equation for the solid, where the axial heat conduction effects are taken into account. The governing equations are reduced to an integro-differential equation which is solved by analytical and numerical methods. The results are shown for different parameters such as conduction parameter, α, the aspect ratio of the tube, ε and the index of power-law fluid, n.     

HEAT TRANSFER TO SPHERES FROM A POLYMER MELT

A Galerkin mixed finite-element method was used to predict the effect of fluid elasticity, temperature-dependent fluid properties, shear-dependent fluid properties, and viscous dissipation on the overall rate of heat transfer between a polymer melt and a sphere. A correlation is developed for the Nusselt number that accounts for changes in Péclet number, viscous dissipation, and a temperature-dependent viscosity function     

Viscous dissipation effect on entropy generation in curved square microchannels

The viscous dissipation effect on the thermodynamic performance of the curved square microchannels in laminar flow is numerically investigated. The classical Navier-Stokes equations are adopted; aniline and ethylene glycol are selected as the working fluids. The results show that the heat transfer entropy generation number and frictional entropy generation number augment relatively under viscous dissipation effect for the case of fluid heated, and the opposite results can be found for the case of fluid cooled. The heat transfer entropy generation number increases with Reynolds number at large Reynolds number region under viscous dissipation effect when ethylene glycol is heated. The total entropy generation number extremum exists for aniline, and the extremum happens earlier when aniline is heated than when aniline is cooled. The smaller the curvature radius is, the earlier the extremum appears. The extremum does not occur for ethylene glycol due to the predomination of frictional entropy generation in the total entropy generation.     

Assessment of heat transfer in large parallel plates with a narrow gap maintained at a constant temperature

Investigations are conducted on electromagnetohydrodynamic (EMHD) flow and heat transfer in a third-grade fluid flowing through large parallel plates, which are maintained at constant temperatures. The impact of convective heat transmission is disregarded since the space between the plates is small. The influence of viscous dissipation is considered. Despite being addressed for Newtonian fluids, the conduction problem with the viscous dissipation effect is not examined in third-grade fluids for EMHD flow and heat transfer behavior. The least-square method is adopted to solve nondimensional, nonlinear momentum and energy conservation equations to get the dimensionless velocity, temperature distribution, and heat flux. Temperature and heat flux are investigated in relation to the third-grade fluid parameter, the Hartmann number, the electric field parameter, and the Brinkman number. The findings show a rise in the Brinkman number dramatically increases heat transfer from both walls, necessitating cooling of both plates. The heat flow from both walls increases as the parameters of third-grade fluid increases.     

The effect of combined viscous dissipation and Joule heating on unsteady mixed convection MHD flow on a rotating cone in a rotating fluid with variable properties in the presence of Hall and ion-slip currents

This paper is concerned with the effect of combined viscous dissipation and Joule heating on unsteady mixed convention magnetohydrodynamics (MHD) flow on a rotating cone in an electrically conducting rotating fluid in the presence of Hall and ion-slip currents. The fluid properties (density, (ρ), viscosity, (μ) and thermal conductivity, (κ)) are taken to be dependent on temperature and a strong uniform magnetic field is applied in the z-direction. It has been shown that a self-similar solution is possible when the free stream angular velocity and the angular velocity of the cone vary inversely as a linear functions of time. The unsteady Navier–Stokes equations along with the energy equation are reduced to a system of ordinary differential equations by using similarity transformations and the resulting equation system is solved numerically by using a shooting method. Results for the details of the velocity as well as temperature are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tables.     

Effects of viscous dissipation during forced convection of power-law fluids in microchannels

The effect of viscous dissipation in forced convection of power-law fluids through microchannels of different cross-sectional geometries is studied numerically over the ranges of power-law index, 0.8 ≤ n ≤ 1.2 and Brinkman number, 0.001 ≤ Br ≤ 0.1 while keeping Péclet number constant at Pe = 10. Two types of thermal boundary conditions, namely, uniform wall temperature (T₂) and uniform heat flux (H₂), have been employed at the microchannel wall and the results of the temperature fields are expressed in terms of Nusselt number. The interplay between the fluid rheology and viscous dissipation effect gives rise to significant alteration in the net convective transport and thus can be beneficial in the thermal design of biofluidic devices.     

Analysis of Unsteady Rotor–Stator Flow with Variable Viscosity Based on Experiments and CFD Simulations

In recent years, computational fluid dynamics (CFD) has been widely used in calculating flow characteristics and heat–flow coupling. However, heat generated during fluid transportation is always ignored and the density and viscosity of the working medium are supposed to be constant. In this article, heat generation was taken into consideration. Accordingly, the thermophysical properties working of the medium are variable. A typical rotor–stator fluid machine, a hydraulic retarder, was chosen to investigate the relationship between the heat transfer characteristics of the fluid and the braking torque. The conclusions were obtained by analyzing the flow conditions which involved Re, vorticity, and rothalpy in the flow passage and viscous dissipation. When the viscous dissipation generated heat in the passage, temperature was increased and viscosity was decreased, thus accelerating the development of turbulence. Moreover, Re was increased at the same time. Furthermore, the dissipation of vorticity was reduced constantly and rothalpy reduced. The braking torque was decreased finally because the wall shear stress was decreased. The conclusions in this article are of practical significance for forecasting other turbomachine characteristics.     

Effect of pressure stress work and viscous dissipation in some natural convection flows

A regular two-parameter perturbation analysis is presented here to study the effects of both viscous dissipation and pressure stress on natural convection flows. Four different vertical flows have been analyzed, those adjacent to an isothermal surface and uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source on a vertical adiabatic surface, or wall-plume. For high gravity levels, stress work effects may be important for gases at very low temperatures, and for high Prandtl number liquids. Significant changes in heat transfer and flow quantities are observed even at moderate values of the perturbation parameters. For the entire range of Prandtl number values considered, the viscous dissipation term is seen to inhibit heat transfer from the surface for heated upward flows. The pressure term enhances heat transfer from the surface for lower Prandtl numbers. However, this effect is seen to reverse at Pr = 100, for both the isothermal and uniform flux surfaces. It is observed that viscous dissipation effects on heat transfer are much smaller than those due to the pressure stress, for many practical circumstances.     

Viscous dissipation and heat transfer in pulsatile flows of a yield-stress fluid

The convective heat transfer phenomenon due to viscous dissipation associated with the low Reynolds number pulsatile flow of a non-Newtonian inelastic fluid exhibiting a yield-stress (Bingham fluid) through a circular pipe is studied numerically. The problem is of interest in a number of industrial applications such as the processing of industrial slurries and plastic melts. The singularities due to the infinite value attained by the effective viscosity at zero rates of deformation is avoided by adopting a bi-viscosity model. The flow enhancement characteristic of the pulsatile flows of non-Newtonian fluids affects the associated heat transfer rates in the case of non-isothermal flows. The emphasis in this study is on investigating the effects of the fluid rheology, characterized by the yield number, as well as the frequency of the imposed pulsatile pressure gradient on the fluid flow and its heat transfer characteristics. The presented results reveal the instataneous as well as the time averaged characteristics of the flow and heat transfer phenomena.