Dynamics of Sutterby fluid flow due to a spinning stretching disk with non-Fourier/Fick heat and mass flux models

The magnetohydrodynamic Sutterby fluid flow instigated by a spinning stretchable disk is modeled in this study. The Stefan blowing and heat and mass flux aspects are incorporated in the thermal phenomenon. The conventional models for heat and mass flux, i.e., Fourier and Fick models, are modified using the Cattaneo-Christov(CC)model for the more accurate modeling of the process. The boundary layer equations that govern this problem are solved using the apt similarity variables. The subsequent system of equations is tackled by the Runge-Kutta-Fehlberg(RKF) scheme. The graphical visualizations of the results are discussed with the physical significance. The rates of mass and heat transmission are evaluated for the augmentation in the pertinent parameters. The Stefan blowing leads to more species diffusion which in turn increases the concentration field of the fluid. The external magnetism is observed to decrease the velocity field. Also,more thermal relaxation leads to a lower thermal field which is due to the increased time required to transfer the heat among fluid particles. The heat transport is enhanced by the stretching of the rotating disk.     

Transient flow of magnetized Maxwell nanofluid: Buongiorno model perspective of Cattaneo-Christov theory

The present research article is devoted to studying the characteristics of Cattaneo-Christov heat and mass fluxes in the Maxwell nanofluid flow caused by a stretching sheet with the magnetic field properties. The Maxwell nanofluid is investigated with the impact of the Lorentz force to examine the consequence of a magnetic field on the flow characteristics and the transport of energy. The heat and mass transport mechanisms in the current physical model are analyzed with the modified versions of Fourier’s and Fick’s laws, respectively. Additionally, the well-known Buongiorno model for the nanofluids is first introduced together with the Cattaneo-Christov heat and mass fluxes during the transient motion of the Maxwell fluid. The governing partial differential equations (PDEs) for the flow and energy transport phenomena are obtained by using the Maxwell model and the Cattaneo-Christov theory in addition to the laws of conservation. Appropriate transformations are used to convert the PDEs into a system of nonlinear ordinary differential equations (ODEs). The homotopic solution methodology is applied to the nonlinear differential system for an analytic solution. The results for the time relaxation parameter in the flow, thermal energy, and mass transport equations are discussed graphically. It is noted that higher values of the thermal and solutal relaxation time parameters in the Cattaneo-Christov heat and mass fluxes decline the thermal and concentration fields of the nanofluid. Further, larger values of the thermophoretic force enhance the heat and mass transport in the nanoliquid. Moreover, the Brownian motion of the nanoparticles declines the concentration field and increases the temperature field. The validation of the results is assured with the help of numerical tabular data for the surface velocity gradient.     

Electro-magneto-hydrodynamic flow of couple stress nanofluids in micro-peristaltic channel with slip and convective conditions

This study explores the effects of electro-magneto-hydrodynamics,Hall currents,and convective and slip boundary conditions on the peristaltic propulsion of nanofluids(considered as couple stress nanofluids)through porous symmetric microchannels.The phenomena of energy and mass transfer are considered under thermal radiation and heat source/sink.The governing equations are modeled and non-dimensionalized under appropriate dimensionless quantities.The resulting system is solved numerically with MATHEMATICA(with an in-built function,namely the Runge-Kutta scheme).Graphical results are presented for various fluid flow quantities,such as the velocity,the nanoparticle temperature,the nanoparticle concentration,the skin friction,the nanoparticle heat transfer coefficient,the nanoparticle concentration coefficient,and the trapping phenomena.The results indicate that the nanoparticle heat transfer coefficient is enhanced for the larger values of thermophoresis parameters.Furthermore,an intriguing phenomenon is observed in trapping:the trapped bolus is expanded with an increase in the Hartmann number.However,the bolus size decreases with the increasing values of both the Darcy number and the electroosmotic parameter.     

Numerical Simulation of Diesel Spray Evaporation in a “Stabilized Cool Flame” Reactor: A Comparative Study

The major objective of this work is to numerically investigate the interacting physical and chemical phenomena that characterize the flow in a stabilized cool flame diesel fuel spray evaporation system. A two-phase RANS computational fluid dynamics code has been developed and used to predict the characteristics of the developing turbulent, multiphase, multi-component, reactive flow-field. The code employs a Eulerian–Lagrangian approach, taking into account the mass, momentum, thermal and turbulent energy exchange between the phases. A variety of physical phenomena, such as turbulent dispersion, droplet evaporation, droplet-wall collision, conjugate heat transfer, drift correction, two-way coupling are taken into account by implementing respective sub-models. Two alternative modelling approaches for the simulation of cool flame reactions have been validated and evaluated by comparing numerical predictions with experimental data from two atmospheric pressure, evaporating Diesel spray, Stabilized Cool Flame reactors. Both models have achieved good quantitative agreement in the majority of the considered test cases. The results have been used to estimate the local physical and chemical characteristic time scales of the occurring phenomena, thus allowing, for the first time, the classification of stabilized cool flames.     

Boundary layer flow of Maxwell fluid due to torsional motion of cylinder: modeling and simulation

This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field. The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature. The torsional motion of the cylinder is considered with the constant azimuthal velocity E. The partial differential equations (PDEs) governing the torsional motion of the Maxwell fluid together with energy transport are simplified with the boundary layer concept. The current analysis is valid only for a certain range of the positive Reynolds numbers. However, for very large Reynolds numbers, the flow becomes turbulent. Thus, the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers. The numerical simulations for the flow, heat, and mass transport phenomena are carried out in view of the bvp4c scheme in MATLAB. The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid. It is also noted that the phenomenon of stress relaxation, described by the Deborah number, causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion. The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers. An excellent validation of the numerical results is assured through tabular data with the existing literature.     

Similarity solutions of mixed convection heat and mass transfer in combined stagnation and rotation-induced flows over a rotating disk

The objective of the present study is to develop a novel similarity model for analysis of mixed convection heat and mas transfer in combined stagnation and rotation-induced flows over a rotating disk. Thermal and concentration (solutal) buoyancy effects stemmed from temperature and concentration gradients in rotational as well as gravitational forces fields are all taken into account. The influences of the forced flow, disk rotation, thermal buoyancy, buoyancy ratio and the fluid properties, i.e. Prandtl and Schmidt numbers, on the flow, temperature and concentration fields and the associated friction factors, heat and mass transfer rates are investigated. The present results reveal the effects of various buoyancy modes with combined forces on the transport phenomena in rotating-disk flows, and the analysis is also useful in understanding the mechanisms of mixed convection in the class of rotating fluids. Received on 30 December 1997     

3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux

A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips (diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that the velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.     

Dual solutions of time-dependent magnetohydrodynamic stagnation point boundary layer micropolar nanofluid flow over shrinking/stretching surface

Time-dependent, two-dimensional(2 D) magnetohydrodynamic(MHD)micropolar nanomaterial flow over a shrinking/stretching surface near the stagnant point is considered. Mass and heat transfer characteristics are incorporated in the problem. A model of the partial differential expressions is altered into the forms of the ordinary differential equations via similarity transformations. The obtained equations are numerically solved by a shooting scheme in the MAPLE software. Dual solutions are observed at different values of the specified physical parameters. The stability of first and second solutions is examined through the stability analysis process. This analysis interprets that the first solution is stabilized and physically feasible while the second one is un-stable and not feasible. Furthermore, the natures of various physical factors on the drag force, skin-friction factor, and rate of mass and heat transfer are determined and interpreted. The micropolar nanofluid velocity declines with a rise in the suction and magnetic parameters, whereas it increases by increasing the unsteadiness parameter.The temperature of the micropolar nanofluid rises with increase in the Brownian motion,radiation, thermophoresis, unsteady and magnetic parameters, but it decreases against an increment in the thermal slip constraint and Prandtl number. The concentration of nanoparticles reduces against the augmented Schmidt number and Brownian movement values but rises for incremented thermophoresis parameter values.     

Flow of Oldroyd-B fluid with nanoparticles and thermal radiation

The two-dimensional boundary layer flow of an Oldroyd-B fluid in the presence of nanoparticles is investigated. Convective heat and mass conditions are considered in the presence of thermal radiation and heat generation. The Brownian motion and thermophoresis effects are retained. The nonlinear partial differential equations are reduced into the ordinary differential equation (ODE) systems. The resulting ODE systems are solved for the series solutions. The results are analyzed for various physical parameters of interest. Numerical values of the local Nusselt and Sherwood numbers are also computed and analyzed.     

Rotational flow of Oldroyd-B nanofluid subject to Cattaneo-Christov double diffusion theory

A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal conductivity of the nanofluid, and such an increment of thermal conductivity can play an important role in improving the heat transfer rate of the base fluid. Further, the dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The present predominately predictive modeling studies the flow of the viscoelastic Oldroyd-B fluid over a rotating disk in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov heat and mass flux expressions. The characteristic of the Lorentz force due to the magnetic field applied normal to the disk is studied. The Buongiorno model together with the Cattaneo-Christov theory is implemented in the Oldroyd-B nanofluid flow to investigate the heat and mass transport mechanism. This theory predicts the characteristics of the fluid thermal and solutal relaxation time on the boundary layer flow. The von K′arm′an similarity functions are utilized to convert the partial differential equations(PDEs) into ordinary differential equations(ODEs). A homotopic approach for obtaining the analytical solutions to the governing nonlinear problem is carried out. The graphical results are obtained for the velocity field, temperature, and concentration distributions. Comparisons are made for a limiting case between the numerical and analytical solutions, and the results are found in good agreement. The results reveal that the thermal and solutal relaxation time parameters diminish the temperature and concentration distributions, respectively. The axial flow decreases in the downward direction for higher values of the retardation time parameter. The impact of the thermophoresis parameter boosts the temperature distribution.     

Condensation models for the water–steam interface and the volume of fluid method

We assess the quantitative capabilities of three condensation models. These models are: (1) Numerical iteration technique; (2) heat flux balance equation; (3) phase field. The numerical iteration technique introduces a mass and energy transfer at the interface, if the temperature of the corresponding cell differs from the saturation value. The second approach solves the heat flux balance equation at the interface, hence, the resolution of the thermal boundary layer around the liquid-vapor interface is necessary to obtain an accurate value for the condensation rate. The third technique is based on a recently derived phase field model for boiling and condensation phenomena. The models were implemented in FLUENT and the interface was tracked explicitly with the volume of fluid (VOF) method. The models were tested on the LAOKOON facility, which measured direct contact condensation in a horizontal duct. The results showed that the phase field model fit best the experimental results.     

Heat and mass transfer in a visco–elastic fluid flow over an accelerating surface with heat source/sink and viscous dissipation

 In this paper we present a mathematical analysis of heat and mass transfer phenomena in a visco–elastic fluid flow over an accelerating stretching sheet in the presence of heat source/sink, viscous dissipation and suction/blowing. Similarity transformations are used to convert highly non-linear partial differential equations into ordinary differential equations. Several closed form analytical solutions for non-dimensional temperature, concentration, heat flux, mass flux profiles are obtained in the form of confluent hypergeometric (Kummer's) functions for two different cases of the boundary conditions, namely, (i) wall with prescribed second order power law temperature and second order power law concentration (PST), and (ii) wall with prescribed second order power law heat flux and second order power law mass flux (PHF). The effect of various physical parameters like visco–elasticity, Eckert number, Prandtl number, heat source/sink, Schmidt number and suction/blowing parameter on temperature and concentration profiles are analysed. The effects of all these parameters on wall temperature gradient and wall concentration gradient are also discussed. Received on 23 March 2000 / Published online: 29 November 2001     

Convective transport of nanoparticles in multi-layer fluid flow

Technologically, multi-layer fluid models are important in understanding fluid-fluid or fluid-nanoparticle interactions and their effects on flow and heat transfer characteristics. However, to the best of the authors’ knowledge, little attention has been paid to the study of three-layer fluid models with nanofluids. Therefore, a three-layer fluid flow model with nanofluids is formulated in this paper. The governing coupled nonlinear differential equations of the problem are non-dimensionalized by using appropriate fundamental quantities. The resulting multi-point boundary value problem is solved numerically by quasi-linearization and Richardson’s extrapolation with modified boundary conditions. The effects of the model parameters on the flow and heat transfer are obtained and analyzed. The results show that an increase in the nanoparticle concentration in the base fluid can modify the fluid-velocity at the interface of the two fluids and reduce the shear not only at the surface of the clear fluid but also at the interface between them. That is, nanofluids play a vital role in modifying the flow phenomena. Therefore, one can use nanofluids to obtain the desired qualities for the multi-fluid flow and heat transfer characteristics.     

In search of physical parameters influenced by flow patterns in a heterogeneous two-phase mixture in microchannels using concomitant measurements

Space transportation systems require high-performance thermal protection and fluid management for systems ranging from cryogenic fluid devices to primary structures, and for propulsion systems exposed to extremely high temperatures, and other space systems, e.g., integrated circuits and cooling/environment control devices for advanced space suits. Although considerable developmental effort is underway to bring promising technologies to a readiness level for practical use, new and innovative methods are still needed. One such method is the Advanced Micro Cooling Module (AMCM), essentially a compact two-phase heat exchanger constructed of microchannels and designed to rapidly remove large quantities of heat from critical systems by incorporating phase transition. This paper describes the results of experimental research in two-phase flow phenomena, encompassing both an experimental and an analytical approach to the incorporation of flow patterns for air–water mixtures flowing in microchannels. Specifically addressed are: (1) design and construction of a sensitive two-phase experimental system which measures both ac and dc components of in situ physical mixture parameters including spatial concentration, using concomitant methods; (2) data acquisition and analysis in the amplitude, time, and frequency domains; and (3) analysis of results including evaluation of in situ physical parameters, and assessment of their validity for application in flow pattern determination.     

A revised Cattaneo-Christov micropolar viscoelastic nanofluid model with combined porosity and magnetic effects

The dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The current predominately predictive modeling deals with the flow of the viscoelastic micropolar fluid in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov(C-C) heat and mass flux expressions. Besides, the thermal radiation effects are contributed in the energy equation and aspect of the radiation parameter, and the Prandtl number is specified by the one-parameter approach.The formulated expressions are converted to the dimensionless forms by relevant similarity functions. The analytical solutions to these expressions have been erected by the homotopy analysis method. The variations in physical quantities, including the velocity,the temperature, the effective local Nusselt number, the concentration of nanoparticles,and the local Sherwood number, have been observed under the influence of emerging parameters. The results have shown good accuracy compared with those of the existing literature.     

What physical phenomena can be neglected when modelling concrete at high temperature? A comparative study. Part 2: Comparison between models

The paper deals with modelling of hygro-thermal performance and thermo-chemical degradation of concrete exposed to high temperature. Several possible simplifications in modelling of heat and mass transport phenomena in heated concrete are considered and their effect on the results of numerical simulations is analyzed.In part I of the companion paper, the physical phenomena, and heat and mass flux and sources in a concrete element were studied, both during slow and fast heating process, to examine the relative importance of different flux components. Then, the mathematical model of concrete at high temperature, developed by Authors in the last 10 years, was briefly presented and for the first time all the constitutive relationships of the model are summarized and discussed in detail. Finally, the method of numerical solution of the model equations was thoroughly presented.In this part of the paper a brief literature review of the existing mathematical models of concrete at high temperature and a summary of their main features and physical assumptions is presented first. Then, extensive numerical study is performed with several simplified models, neglecting a chosen physical phenomenon or flux component, to evaluate a difference between the results obtained with the simplified models and with the reference model. The study concerns hygric, thermal and degradation performance of 1-D and 2-D axisymmetric concrete elements during fast and slow heating. The analysis will allow us to indicate which simplifications in modeling of concrete at high temperature are practically and physically possible, without generating excessive differences of the results with respect to the full reference model.     

Cattaneo-Christov heat and mass flux model for 3D hydrodynamic flow of chemically reactive Maxwell liquid

This research focuses on the Cattaneo-Christov theory of heat and mass flux for a three-dimensional Maxwell liquid towards a moving surface. An incompressible laminar flow with variable thermal conductivity is considered. The flow generation is due to the bidirectional stretching of sheet. The combined phenomenon of heat and mass transport is accounted. The Cattaneo-Christov model of heat and mass diffusion is used to develop the expressions of energy and mass species. The first-order chemical reaction term in the mass species equation is considered. The boundary layer assumptions lead to the governing mathematical model. The homotopic simulation is adopted to visualize the results of the dimensionless flow equations. The graphs of velocities, temperature, and concentration show the effects of different arising parameters. A numerical benchmark is presented to visualize the convergent values of the computed results. The results show that the concentration and temperature fields are decayed for the Cattaneo-Christov theory of heat and mass diffusion.     

Characteristics of air and water velocity fields during natural convection

Air and water velocity fields have been simulated during natural convection, using a two-dimensional volume of fluid (VOF) model. The results have shown that during unstable thermal stratification, the root-mean-square (RMS) airside velocities are an order of magnitude higher than the RMS waterside velocities, whereas, during the stable thermal stratification, the velocity magnitudes are comparable for air and water sides. Furthermore, the magnitude of the air velocity changed more rapidly with the change in the bulk air–water temperature difference than the water velocity, indicating that the air velocities are more sensitive to the bulk air and water temperature difference than the water velocities. A physical model of the heat and mass transfer across the air–water interface is defined. According to this model, the vortices on the air and water sides play an important role in enhancing the heat and mass transfer. Due to the significance of the flow velocities in the transport process, it has been proposed that the correlations for the heat and mass transfer during natural convection should be improved by incorporating the flow velocity as a parameter.     

Work optimization in continuous and discrete systems with complex fluids

We extend to the realm of complex fluids and finite durations the classical problem of extremum work delivered from (or consumed by) the nonequilibrium system composed of a complex fluid, a perfect thermal machine and the environment or an infinite reservoir. The fluid constitutes a valuable resource of a finite flow or amount “a finite resource”, and work production (consumption) takes place sequentially, in stages of “endoreversible” thermal machines. At each stage, heat and mass transfer takes place in boundary layers which play the role of resistances in the system model. For the fluid at flow, total specific work is extremized at constraints which take into account dynamics of heat and mass transport and rate of work generation. Finite rate limits are obtained for the work production and consumption, which provide stronger bounds that those predicted by classical thermodynamics. Optimal work functions, which incorporate an inevitable minimum of the entropy production are found as functions of end states, duration and (in discrete processes) number of stages. Formal analogies between the entropy production expressions for work-assisted and conventional mass transfer operations help formulate optimization models.     

Natural convection due to heat and mass transfer in a composite system

A numerical study is performed to analyse heat and mass transfer phenomena due to natural convection in a composite cavity containing a fluid layer overlying a porous layer saturated with the same fluid. The flow in the porous region is modelled using Brinkman–Forchheimer-extended Darcy model that includes both the effect of macroscopic shear (Brinkman effect) and flow inertia (Forchheimer effect). The vertical walls of the two-dimensional enclosure are isothermal whilst the horizontal walls are adiabatic. The two regions are coupled by equating the velocity and stress components at the interface. The resulting coupled equations in non-dimensional form are solved by an alternating direction implicit method by transforming them into parabolic form by the addition of false transient terms. The numerical results show that the amount of fluid penetration into the porous layer depends strongly upon the Darcy, thermal and solutal Rayleigh numbers. Average Nusselt number decreases while average Sherwood number increases with an increase of the Lewis number. The transfer of heat and mass on the heated wall near the interface depends strongly on the Darcy number. Received on 11 May 1998