Numerical study of dynamic thermal conductivity of nanofluid in the forced convective heat transfer

In this work, forced convective heat transfer of nanofluid in the developing laminar flow (entrance region) in a circular tube is considered. The nanofluid thermal conductivity, as an important parameter, is considered as two parts: static and dynamic part. Simulated results show that the dynamic part of nanofluid thermal conductivity due to the Brownian motion has a minor effect on the heat transfer coefficients, on the other hand, static part of thermal conductivity including nanolayer around nanoparticle has an important role in heat transfer.     

Similarity solution in MHD: Effects of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a stretching surface considering suction or injection

An analysis is carried out to study free convective heat and mass transfer of an incompressible, electrically conducting fluid over a stretching sheet in the presence of suction and injection with thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects. The similarity solutions are obtained using scaling transformations. Furthermore, the similarity equations are solved numerically by using shooting technique with fourth-order Runge–Kutta integration scheme. A comparison with previously published work is performed and the results are found to be in good agreement. Numerical results of the local skin friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, the temperature and the concentration profiles are presented for different physical parameters. The result indicates: (i) for fluids with medium molecular weight (H₂, air), Dufour and Soret effects should not be neglected; and (ii) the suction and injection parameter has significant impact in controlling the rate of heat transfer in the boundary layer.     

Flow and heat transfer of a nanofluid through a porous medium due to stretching/shrinking sheet with suction,magnetic field and thermal radiation

This study investigates the suction and magnetic field effects on the two-dimensional nanofluid flow through a stretching/shrinking sheet at the stagnation point in the porous medium with thermal radiation. The governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) using the similarity transformation. The resulting ODEs are then solved numerically by using the bvp4c solver in MATLAB software. It was found that dual solutions exist for the shrink...     

Effect of transverse magnetic field on heat transfer to an electrically conducting and thermal radiating fluid flowing in a parallel-plate channel

Zusammenfassung Der Einfluss eines magnetischen Feldes auf die Wärmeübertragung in einer ausgebildeten laminaren Strömung einer elektrisch leitenden, wärmestrahlenden, zähen und inkompressiblen Flüssigkeit zwischen zwei unendlichen parallelen Platten wird untersucht. Ein konstantes äusseres magnetisches Feld wirkt in der Richtung senkrecht zu den Platten und der Strömungsrichtung. Die auf einer konstanten Temperatur gehaltenen Kanalwände sollen Wärme ausstrahlen und diffus reflektieren.Die Temperaturverläufe wurden für einige Werte der interessierenden Parameter und für das ganze Gebiet der Hartmannschen Zahl numerisch gerechnet. Die entsprechenden Kennwerte der Wärmeübertragung zwischen den Kanalwänden und der Flüssigkeit sind im Text tabellarisch angegeben. Das Magnetfeld vergrössert sowohl die Wärmeübertragung durch Leitung als auch durch Strahlung. Die Vergrösserung ist jedoch gering.

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Work done under auspices of U.S. Atomic Energy Commission.     

Two-dimensional heat and mass transfer during drying of deformable media

Drying is an essential step in many production and treatment processes. The control of the dry product quality is more and more required in order to ensure effective use or handling of the material. The aim of this study is to develop a two-dimensional drying model which takes into account heat and mass transfer and the accompanying deformation of the dried material. The model tries to be relatively simple but sufficiently complete in order to predict and analyze the spatio-temporal distribution of the temperature, the moisture and the solid displacement during the process. The product was considered as a two-phases, homogeneous, hygroscopic, isotropic and highly shrinkable medium. The model was solved numerically by a finite difference method. The simulation allowed the obtention of the time and space evolutions of several parameters such as product temperature, moisture content and solid displacement.     

Analysis of flow and thermal field in nanofluid using a single phase thermal dispersion model

Flow and thermal field in nanofluid is analyzed using single phase thermal dispersion model proposed by Xuan and Roetzel [Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer 43 (2000) 3701–3707]. The non-dimensional form of the transport equations involving the thermal dispersion effect is solved numerically using semi-explicit finite volume solver in a collocated grid. Heat transfer augmentation for copper–water nanofluid is estimated in a thermally driven two-dimensional cavity. The thermo-physical properties of nanofluid are calculated involving contributions due to the base fluid and nanoparticles. The flow and heat transfer process in the cavity is analyzed using different thermo-physical models for the nanofluid available in literature. The influence of controlling parameters on convective recirculation and heat transfer augmentation induced in buoyancy driven cavity is estimated in detail. The controlling parameters considered for this study are Grashof number (10³ < Gr < 10⁵), solid volume fraction (0 < ? < 0.2) and empirical shape factor (0.5 < n < 6). Simulations carried out with various thermo-physical models of the nanofluid show significant influence on thermal boundary layer thickness when the model incorporates the contribution of nanoparticles in the density as well as viscosity of nanofluid. Simulations incorporating the thermal dispersion model show increment in local thermal conductivity at locations with maximum velocity. The suspended particles increase the surface area and the heat transfer capacity of the fluid. As solid volume fraction increases, the effect is more pronounced. The average Nusselt number from the hot wall increases with the solid volume fraction. The boundary surface of nanoparticles and their chaotic movement greatly enhances the fluid heat conduction contribution. Considerable improvement in thermal conductivity is observed as a result of increase in the shape factor.     

Convective thermal conditions and the thermophoretic effect's impacts on a hybrid nanofluid over a moving thin needle

This research focuses on the heat source/sink, chemical reaction, and thermophoretic particle deposition in the influence of hybrid nanofluid over a moving thin needle subjected to a magnetic field. Using the appropriate transformations, a group of nonlinear partial differential equations may be converted to ordinary differential equations. Additionally, with the aid of computational software, the RKF-45 approach is used for the numerical assessment, as well as the shooting operation. It should be mentioned that the results' approval demonstrates a strong association with the previous findings. The resulting graphs mainly explain the fundamental characteristics of hybrid nanofluids and nanofluids, as well as the consequences of different restrictions. An increase in needle size enhances the velocity profile, temperature profile, and concentration profile. The radial and axial velocity profiles are reduced when the magnetic constraint is increased, whereas the thermal and concentration patterns are reversed. Improved heat source-sink as well as Biot number values will enhance the thermal profile. The concentration profiles will decrease due to reaction rate restrictions and thermophoretic limits. The inclusion of solid volume fraction reduces surface drag forces while increasing the rate of mass transfer. In most circumstances, hybrid nanofluid plays a prominent role than nanofluid.     

Influence of fluctuating thermal and mass diffusion on unsteady MHD buoyancy-driven convection past a vertical surface with chemical reaction and Soret effects

The influence of thermal radiation and first-order chemical reaction on unsteady MHD convective flow, heat and mass transfer of a viscous incompressible electrically conducting fluid past a semi-infinite vertical flat plate in the presence of transverse magnetic field under oscillatory suction and heat source in slip-flow regime is studied. The dimensionless governing equations for this investigation are formulated and solved analytically using two-term harmonic and non-harmonic functions. Comparisons with previously published work on special cases of the problem are performed and results are found to be in excellent agreement. A parametric study illustrating the effects of various physical parameters on the fluid velocity, temperature and concentration fields as well as skin-friction coefficient, the Nusselt and Sherwood numbers in terms of amplitude and phase is conducted. The numerical results of this parametric study are presented graphically and in tabular form to highlight the physical aspects of the problem.     

Symmetry of heat and mass transfer equations in case of dependence of thermal diffusivity coefficient either on temperature or concentration

This paper describes the solution of group classification problem for heat and mass transfer equations with respect to 3 transport coefficients. Two coefficients depend on temperature and concentration, and the thermal diffusivity coefficient is the function of only one of these state parameters. The forms of the arbitrary elements providing the additional transformations are found. Examples of exact solutions of the governing equations are constructed.     

On the consistency of the mass transfer problem

Conditions are given under which the Monge-Kantorovich mass transfer problem on general metric spaces and with unbounded cost function has a feasible solution.     

Effects of thermophoresis on hydromagnetic mixed convection and mass transfer flow past a vertical permeable plate with variable suction and thermal radiation

The present paper deals with the effect of surface mass transfer on MHD mixed convection flow past a heated vertical flat permeable surface in the presence of thermophoresis, radiative heat flux and heat source/sink. Usual similarity transformations are introduced to obtain similarity solution, using regular perturbation technique. To observe physical insight and interesting aspects of the problem in the presence of thermophoresis, the non-dimensional velocity, temperature and concentration field are numerically studied and displayed graphically for pertinent parameters. It is observed that the thermophoresis has dominant effect on mass transfer mechanism in particle deposition process. The model finds applications in studying particulate deposition on turbine blades, removing small particles from gas streams and determining chemical vapor deposition rate in chemical industries.     

Variable electrical and thermal conductivity in the theory of generalized thermoelastic diffusion

This paper deals with the problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time and with variable electrical and thermal conductivity. The bounding surface of the half-space is taken to be traction free and subjected to a time dependent thermal shock. The solution is obtained in the Laplace transform domain by a direct approach. A numerical technique is employed to obtain the solution in the physical domain. It is found that there exist two coupled waves, one of which is elastic and the other is thermal, and a third wave affects diffusion mainly. A comparison is made with the results obtained in a thermoelastic medium with and without diffusion in the following cases : (a) the electrical and thermal conductivities have constant values, (b) the presence of magnetic field and (c) the generalized theory in thermoelasticity. Received: June 1, 2005     

Variable electrical and thermal conductivity in the theory of generalized thermoelastic diffusion

This paper deals with the problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time and with variable electrical and thermal conductivity. The bounding surface of the half-space is taken to be traction free and subjected to a time dependent thermal shock. The solution is obtained in the Laplace transform domain by a direct approach. A numerical technique is employed to obtain the solution in the physical domain. It is found that there exist two coupled waves, one of which is elastic and the other is thermal, and a third wave affects diffusion mainly. A comparison is made with the results obtained in a thermoelastic medium with and without diffusion in the following cases : (a) the electrical and thermal conductivities have constant values, (b) the presence of magnetic field and (c) the generalized theory in thermoelasticity.     

Effect of the cellular structure on thermal conductivity of rigid closed-cell foam polymers during long-term aging

The thermal conductivity of rigid closed-cell polyurethane foams during long-term aging has been studied. The similarity between the kinetics of changes in the physical and mechanical characteristics of PU foams on progressive aging is established, which is attributed to the effect of matrix destruction. It is found that rigid foams have cell walls of various strength, whose impact on the kinetics of changes in the physical characteristics of the foams during long-term aging is ascertained. The results of predicting the thermal conductivity of PU foams by the method of temperature-time analogy and establishing the limits of its application are discussed. The research presented is of interest both in determining the foam durability and in replacing freons by alternative, ecologically less harmful blowing agents.     

Buoyancy and chemical reaction effects on MHD mixed convection heat and mass transfer in a porous medium with thermal radiation and Ohmic heating

The combined effect of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous and electrically conducting fluid past a vertical permeable surface embedded in a porous medium is analyzed. The heat equation includes the terms involving the radiative heat flux, Ohmic dissipation, viscous dissipation and the internal absorption whereas the mass transfer equation includes the effects of chemically reactive species of first-order. The non-linear coupled differential equations are solved analytically by perturbation technique. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, thermal stratification and magnetic field. It is observed that the effect of thermal radiation and magnetic field is to decrease the velocity, temperature and concentration profiles in the boundary layer. There is also considerable effect of magnetic field and chemical reaction on skin-friction coefficient and Nusselt number.     

Effect of the cellular structure on thermal conductivity of rigid closed-cell foam polymers during long-term aging

The thermal conductivity of rigid closed-cell polyurethane foams during long-term aging has been studied. The similarity between the kinetics of changes in the physical and mechanical characteristics of PU foams on progressive aging is established, which is attributed to the effect of matrix destruction. It is found that rigid foams have cell walls of various strength, whose impact on the kinetics of changes in the physical characteristics of the foams during long-term aging is ascertained. The results of predicting the thermal conductivity of PU foams by the method of temperature-time analogy and establishing the limits of its application are discussed. The research presented is of interest both in determining the foam durability and in replacing freons by alternative, ecologically less harmful blowing agents.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 187–198, March–April, 1999.     

Numerical study of the influence of diffusion of magnetic particles on equilibrium shapes of a free magnetic fluid surface

A mathematical model and a computational method for studying the influence of the particle diffusion on equilibrium shapes of a magnetic liquid is developed. It is then applied on the ferrohydrostatic problem of doubly connected equilibrium shapes of a magnetic fluid located on a horizontal plate around a vertical cylindrical conductor with a direct current. Numerical simulations show the limits of the uniform concentration approximation.     

Effects of Soret Dufour,chemical reaction and thermal radiation on MHD non-Darcy unsteady mixed convective heat and mass transfer over a stretching sheet

A study has been carried out to analyze the combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) on unsteady MHD non-Darcy mixed convection over a stretching sheet embedded in a saturated porous medium in the presence of thermal radiation, viscous dissipation and first-order chemical reaction. Energy equation takes into account of viscous dissipation, thermal radiation and Soret effects. The governing differential equations are transformed into a set of non-linear coupled ordinary differential equations and solved using similarity analysis with numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing nonlinear boundary value problem is based on shooting algorithm with Runge–Kutta–Fehlberg integration scheme over the entire range of physical parameters. The effects of various physical parameters on the dimensionless velocity, temperature and concentration profiles are depicted graphically and analyzed in detail. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for local skin-friction, local Nusselt number, and local Sherwood number are tabulated for different physical parameters.