Forced Convection Heat Transfer of Nanofluids in a Porous Channel

This article is concerned with the effects of flow and migration of nanoparticles on heat transfer in a straight channel occupied with a porous medium. Investigation of force convective heat transfer of nanofluids in a porous channel has not been considered completely in the literature and this challenge is generally considered to be an open research topic that may require more study. The fully developed flow and steady Darcy?CBrinkman?CForchheimer equation is employed in porous channel. The thermal equilibrium model is assumed between nanofluid and solid phases. It is assumed that the nanoparticles are distributed non-uniformly inside the channel. As a result the volume fraction distribution equation is also coupled with governing equations. The effects of parameters such as Lewis number, Schmidt number, Brownian diffusion, and thermophoresis on the heat transfer are completely studied. The results show that the local Nusselt number is decreased when the Lewis number is increased. It is observed that as the Schmidt number is increased, the wall temperature gradient is decreased and as a consequence the local Nusselt number is decreased. The effects of Lewis number, Schmidt number, and modified diffusivity ratio on the volume fraction distribution are also studied and discussed.     

Numerical investigation of Dufour and Soret effects on unsteady MHD natural convection flow past vertical plate embedded in non-Darcy porous medium

The Dufour and Soret effects on the unsteady two-dimensional magnetohydro-dynamics(MHD) double-diffusive free convective flow of an electrically conducting fluidpast a vertical plate embedded in a non-Darcy porous medium are investigated numeri-cally.The governing non-linear dimensionless equations are solved by an implicit finitedifference scheme of the Crank-Nicolson type with a tridiagonal matrix manipulation.The effects of various parameters entering into the problem on the unsteady dimension-less velocity,temperature,and concentration profiles are studied in detail.Furthermore,the time variation of the skin friction coefficient,the Nusselt number,and the Sherwoodnumber is presented and analyzed.The results show that the unsteady velocity,tem-perature,and concentration profiles are substantially influenced by the Dufour and Soreteffects.When the Dufour number increases or the Soret number decreases,both the skinfriction and the Sherwood number decrease,while the Nusselt number increases.It isfound that,when the magnetic parameter increases,the velocity and the temperaturedecrease in the boundary layer.     

Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity

The present paper is concerned with the study of radiation effects on the combined (forced-free) convection flow of an optically dense viscous incompressible fluid over a vertical surface embedded in a fluid saturated porous medium of variable porosity with heat generation or absorption. The effects of radiation heat transfer from a porous wall on convection flow are very important in high temperature processes. The inclusion of radiation effects in the energy equation leads to a highly non-linear partial differential equations which are transformed to a system of ordinary differential equations using non-similarity transformation. These equations are then solved numerically using implicit finite-difference method subject to appropriate boundary and matching conditions. A parametric study of the physical parameters such as the particle diameter-based Reynolds number, the flow based Reynolds number, the Grashof number, the heat generation or absorption co-efficient and radiation parameter is conducted on temperature distribution. The effects of radiation and other physical parameters on the local skin friction and on local Nusselt number are shown graphically. It is interesting to observe that the momentum and thermal boundary layer thickness increases with the radiation and decrease with increase in the Prandtl number.     

Non-Darcy effects on convective boundary layer flow past a semi-infinite vertical plate in saturated porous media

The composite effects of viscosity, porosity, buoyancy parameter, thermal conductivity ratio and non-Darcy effects of Brinkman friction and Forscheimmer quadratic drag on the mixed convection boundary layer flow past a semi-infinite plate in a fully-saturated porous regime are theoretically and numerically investigated using Keller’s implicit finite-difference technique and a double-shooting Runge-Kutta method. The Brinkman Forcheimer-extended Darcy model is implemented in the hydrodynamic boundary layer equation. The effects of the various non-dimensional thermofluid parameters, viz Grashof number, Darcy number, and Forchheimer number, and also porosity, thermal conductivity and viscosity parameters on the velocity and temperature fields are discussed. Computations for both numerical schemes are made where possible and found to be in excellent agreement.     

Analysis of Thermal Flow in a Rotating Porous U-Turn Duct Using Lattice Boltzmann Method

The lattice Boltzmann method is carried out to investigate the heat transfer enhancement in a U-turn duct which is partially filled with a porous media. The porous layer is inserted at the core of the duct and is modeled using the Brinkman–Forchheimer assumptions. In order to validate the results, first a channel flow problem without any porous layer is compared with available data. Second, the porous Couette flow and partially porous channel flow are successfully compared with the studies of other researchers. Then, fluid flow in a clear U-turn duct is studied looking carefully at the velocity, curvature and rotation effects. Finally, the effects of porous layer thickness on the rate of heat transfer and pressure drop are investigated. Parametric studies are conducted to evaluate the effects of various parameters (i.e., Reynolds number, Darcy number, rotation number), highlighting their influences on the thermo-hydrodynamics behavior of the flow. The optimum values of porous layer thickness are presented for specific flow parameters.     

Slip effects on a mixed convection flow of a third-grade fluid near the orthogonal stagnation point on a vertical surface

A mixed convection flow of a third-grade fluid near the orthogonal stagnation point on a vertical surface with slip and viscous dissipation effects is investigated. The governing partial differential equations for the third-grade fluid are converted into a system of nonlinear ordinary differential equations by using a similarity transformation. The effects of various parameters, including the Weissenberg number, third-grade parameter, local Reynolds number, Prandtl number, Eckert number, mixed convection parameter, velocity slip, and thermal slip on the velocity and temperature profiles, local skin friction coefficient, and local Nusselt number are discussed.     

Instability of binary nanofluids with magnetic field

The present paper investigates the effects of a vertical magnetic field on the double diffusive nanofluid convection. The effects of the Brownian motion and thermophoresis due to the presence of nanoparticles and the effects of the Dufour and Soret parameters due to the presence of solute are included in the investigated model. The normal mode technique is used to solve the conservation equations. For the analytical study, valid approximations are made in the complex expression for the Rayleigh number to get useful and interesting results. The bottom heavy binary nanofluids are more stable than the regular binary fluids, while the top heavy binary nanofluids are less stable than the regular binary fluids. The critical wave number and the critical Rayleigh number increase whereas the frequency of oscillation (for the bottom heavy configuration) decreases when the Chandrasekhar number increases. The numerical results for the alumina-water nanofluid are studied by use of the MATHEMATICA software.     

Forced convection of a power-law fluid in a porous channel – numerical solutions

A detailed numerical study of laminar forced convection in a porous channel which contains a fibrous medium saturated with a power-law fluid was performed. Hydrodynamic and heat transfer results are presented for a configuration that has uniform heat flux or uniform temperature heating at the walls. The flow in the porous medium was modeled using the modified Brinkman-Forchheimer-extended Darcy model for power law fluids in which the non-Darcy effects of inertia and boundary were considered. Parametric studies were conducted to examine the effects of Darcy number, power law index, inertia parameter and Prandtl number. The results indicate that when the power law index is decreased, the velocity gradient near the walls increases but these effects are reduced gradually as the Darcy number decreases until the Darcy regime (Da≤10⁻⁶) is reached in which case the effects of power law index become negligible. As the power law index is decreased, the thermal boundary layer thickness decreases significantly only in the non-Darcy regime. Consequently, as the power law index decreases, the fully developed Nusselt number increases considerably in the non-Darcy regime whereas in the Darcy regime the change in Nusselt number is very small. As the Prandtl number increases, the local Nusselt number increases and this effect is more significant for shear thinning fluids (n<1.0). Received on 2 March 1998     

Viscous dissipation effects on fully developed combined free and forced non-Newtonian convection in a vertical tube

An investigation which includes the simultaneous effects of viscous dissipation and combined free and forced laminar non-Newtonian convection is presented. The problem under consideration is that of fully developed upflow in a vertical, circular tube which is heated with a constant wall heat flux. All properties are assumed to be constants in the analysis except for a temperature dependent density in the body force term which generates the free convection effects. The coupled continuity, momentum, and energy equations are solved using a finite difference technique. Numerical solutions are presented as a function of the parameters of the problem-flow behavior index n, Grashof number over Reynolds number ratio Gr/Re, and the Eckert number-Prandtl number product E Pr. The results show that heating due to viscous dissipation distorts the velocity profile, increases the friction factor, and decreases the Nusselt number.     

Buoyancy effects on the mass transfer in absorption with a nonabsorbable gas

This paper describes the vapor side buoyancy effects on the mass transfer in absorption in the presence of a nonabsorbable gas. Experimental results on a diffusion-absorption refrigerator (DAR) indicate that the vapor side buoyancy effects on the mass transfer are significant when the density of the nonabsorbable gas is significantly less than that of the absorbable gas. A rectangular enclosure absorption problem is first solved to demonstrate the buoyancy effects without the presence of a forced flow. Then, mixed convection heat transfer in a circular pipe is simulated in such a way as to be analogous to the mixed convection mass-transfer problem in the DAR absorber. Finally, the vapor side mixed convection absorption between parallel plates is simulated including the effects of the absorbed mass on the mass balance. The Sherwood number dependence on the mass transfer Grashof number and Reynolds number as well as the effects of the suction boundary conditions are discussed. Each of these simulations had individual limitations, but, taken together, they illuminate the major aspects of the absorption physics.     

Coriolis effects on the stability of pulsed flows in a Taylor–Couette geometry

Results steming from the linear stability of time-periodic flows in a Taylor–Couette geometry with cylinders oscillating in phase or out-of-phase are presented. Our analysis takes into account the gap size effects and investigates the influence of a superimposed mean angular rotation of the whole system.In case of no mean rotation, the finite gap geometry is found to affect the shape of the stability diagrams (critical Taylor number versus the frequency parameter) which consist of two distinct branches as opposed to being continuous in the narrow gap approximation. In particular, in the out-of-phase configuration a new branch for low frequencies was found, thus enabling better agreement with available experimental results.When cylinders are co-rotating and subject to rotation effects, our calculations provide the evolution of the critical Taylor number versus the rotation number for two values of the frequency. The stability curves are found to be in qualitative agreement with available experimental data revealing a maximum of instability for a rotation number of about 0.3.In the high rotation regime, enhancement of the critical Taylor number is investigated through an asymptotic analysis and the value of the rotation number at which restabilization occurs is found to depend on the frequency parameter.A restabilization of the flow also occurs when the rotation number and the gap size are of the same order, a phenomenon already pointed out in the case of steady flows and attributed to the near cancellation of Coriolis and centrifugal effects. Our investigation proves that the same mechanism still holds for time-periodic flows.     

Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with Soret and Dufour effects

In this paper, we study the unsteady coupled heat and mass transfer of two-dimensional MHD fluid over a moving oscillatory stretching surface with Soret and Dufour effects. Viscous dissipation effects are adopted in the energy equation. A uniform magnetic field is applied vertically to the flow direction. The governing equations are reduced to non-linear coupled partial differential equations and solved by means of homotopy analysis method （HAM）. The effects of some physical parameters such as magnetic parameter, Dufour number, Soret number, the Prandtl num- ber and the ratio of the oscillation frequency of the sheet to its stretching rate on the flow and heat transfer characteristics are illustrated and analyzed.     

Effects of the particle Stokes number on wind turbine airfoil erosion

Under natural conditions, wind turbines are inevitably eroded by the action of sand-wind flow. To further investigate the effects of dust drift on the erosion of the wind turbine blades in sand-wind environments, the effects of the wind velocity, particle diameter, and particle density on the erosion of wind turbine airfoils are studied, and the effects of the particle Stokes number on the airfoil erosion are discussed. The results show that, when the angle of attack(AOA) is 6.1°, there will be no erosion on the airfoil surface if the particle Stokes number is lower than 0.013 5, whereas erosion will occur if the particle Stokes number is higher than 0.015 1. Therefore, there exists a critical range for the particle Stokes number. When the particle Stokes number is higher than the maximum value in the critical range, airfoil erosion will occur. The result is further confirmed by changing the particle diameter, particle density, and inflow speed. It is shown that the erosion area on the airfoil and the maximum erosion rate are almost equal under the same particle Stokes number and AOA. The extent of airfoil erosion increases when the particle Stokes number increases, and the critical particle Stokes number increases when the AOA increases. Moreover, the geometric shape of the airfoil pressure surface greatly affects the airfoil erosion, especially at the curvature near the leading edge.     

The Onset of Bioconvection in a Horizontal Porous-Medium Layer

In this note the problem of the onset of bioconvection in a horizontal layer occupied by a saturated porous medium is analyzed. Gyrotactic effects are incorporated in the analysis. The Darcy flow model is employed, and it is assumed that the bioconvection Péclet number is not greater than unity. Critical values of the bioconvection Rayleigh number and the corresponding critical Rayleigh number are obtained for various values of the bioconvection Péclet number, the gyrotaxis number and the cell eccentricity.     

Experimental study on influence of microscale effects on liquid flow characteristic in microtubes

Using deioned water as a working fluid, the influence of the microscale effects on liquid flow resistance in microtubes with inner diameters of 19.6 and 44.2 μm, respectively, is experimentally studied. The temperature rise resulted from the microscale effects, such as viscous dissipation, electric double layer, wall rough on the wall surface, etc., is obtained by an IR camera with a special magnified lens adopting micro-area thermal image technology and the corresponding pressure drop and the flux are also measured, so the relationship among friction factor, temperature rise and Reynolds number is obtained. Investigation shows that experimental data are almost equal to those of Hagen–Poiseuille when Reynolds number is low. With the increase of Reynolds number, the values of the friction factor depart from that of classical theory due to the microscale effects. Moreover, the values of the experimental friction factor considering various microscale effects is the maximal 10–15% deviation from that of friction factor without considering various microscale effects with further increase of Reynolds number.     

Linear and Nonlinear Double-Diffusive Convection in a Fluid-Saturated Porous Layer with Cross-Diffusion Effects

The double-diffusive convection in a horizontal fluid-saturated porous layer, which is heated and salted from below in the presence of Soret and Dufour effects, is studied analytically using both linear and nonlinear stability analyses. The linear analysis is based on the usual normal mode technique, while the nonlinear analysis is based on truncated representation of Fourier series. The generalized Darcy model that includes the time derivative is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effects of solute Rayleigh number, Lewis number, normalized porosity parameter, Vadasz number, Soret and Dufour parameters on the stationary, oscillatory convection, and heat and mass transfers are shown graphically. The Vadasz number has dual effect on the threshold of the oscillatory convection. Some known results are recovered as special cases of the present problem.     

Comparison of low Mach number models for natural convection problems

 We investigate in this paper two numerical methods for solving low Mach number compressible flows and their application to single-phase natural convection flow problems. The first method is based on an asymptotic model of the Navier–Stokes equations valid for small Mach numbers, whereas the second is based on the full compressible Navier–Stokes equations with particular care given to the discretization at low Mach numbers. These models are more general than the Boussinesq incompressible flow model, in the sense that they are valid even for cases in which the fluid is subjected to large temperature differences, that is when the compressibility of the fluid manifests itself through low Mach number effects. Numerical solutions are computed for a series of test problems with fixed Rayleigh number and increasing temperature differences, as well as for varying Rayleigh number for a given temperature difference. Numerical difficulties associated with low Mach number effects are discussed, as well as the accuracy of the approximations. Received on 17 January 2000     

Numerical investigation of turbulent flow,heat transfer and entropy generation in a helical coiled tube with larger curvature ratio

Three-dimensional turbulent forced convective heat transfer and flow characteristics, and the non-dimensional entropy generation number in a helical coiled tube subjected to uniform wall temperature are simulated using the k–ε standard turbulence model. A finite volume method is employed to solve the governing equations. The effects of Reynolds number, curvature ratio, and coil pitch on the average friction factor and Nusselt number are discussed. The results presented in this paper cover a Reynolds number range of 2 × 10⁴ to 6 × 10⁴, a pitch range of 0.1–0.2 and a curvature ratio range of 0.1–0.3. The results show that the coil pitch, curvature ratio and Reynolds number have different effects on the average friction factor and Nusselt number at different cross-sections. In addition, the flow and heat transfer characteristics in a helical coiled tube with a larger curvature ratio for turbulent flow are different from that of smaller curvature ratio for laminar and turbulent flow in certain ways. Some new features that are not obtained in previous researches are revealed. Moreover, the effects of Reynolds number, curvature ratio, and coil pitch on the non-dimensional entropy generation number of turbulent forced convection in a helical coiled tube are also discussed.     

LAMINAR DISSIPATIVE FLOW IN A POROUS CHANNEL BOUNDED BY ISOTHERMAL PARALLEL PLATES

IntroductionTheproblemofforcedconvectioninaporousmediumchannelorductisaclassicalone (atleastforthecaseofslugflow (Darcymodel) .Therehasrecentlybeenrenewedinterestintheproblembecauseoftheuseofhyperporousmediainthecoolingofelectronicequipment.Recently ,NieldandBejan[1]refertomorethan 3 0papersonthetopic ,butnoneofthemdealsexplicitlywiththecaseofthermaldevelopment.ThisgapintheliteraturehasbeenpartlyfilledbyNieldetal.[2 - 4 ].Lahjomrietal.[5 ,6 ]havesolvedmathematicallysimilarproblemsbyusingthe…     

LAMINAR DISSIPATIVE FLOW IN A POROUS CHANNEL BOUNDED BY ISOTHERMAL PARALI,EL PLATES

The effects of viscous dissipation on thermal entrance heat transfer in a parallel plate channel filled with a saturated porous medium, is investigated analytically on the basis of a Darcy model. The case of isothermal boundary is treated. The local and the bulk temperature distribution along with the Nusselt number in the thermal entrance region were found. The fully developed Nusselt number, independent of the Brinkman number, is found
to be 6. It is observed that neglecting the effects of viscous dissipation would lead to the well-known case of internal flows, with Nusselt number equal to 4.93. A finite difference numerical solution is also utilized. It is seen that the results of these two methods, analytical and numerical, are in good agreement.