Numerical Simulation of Mixed‐Convection Flow in a Lid‐Driven Porous Cavity Using Different Nanofluids

In this study, the effect of mixed convection flow in a lid‐driven porous cavity using different nanoparticles, such as aluminum oxide (Al ₂ O ₃), copper (Cu), silver (Ag), and titanium dioxide (TiO ₂), are investigated. The base fluid is considered as water. The transport equations are solved numerically by finite volume method on a co‐located grid arrangement using quadratic upwind interpolation for convective kinematics (QUICK) scheme. A two‐dimensional square cavity is considered for the present investigation whose horizontal walls are insulated. The cold left wall is moving up and hot right wall is moving down with equal velocities. The variations of temperature distribution, stream function, and Nusselt number (Nu) are analyzed at constant Grashof numbers (Gr), Richardson numbers (Ri), and Darcy numbers (Da) as 1 × 10 ⁴, 100, and 0.1, respectively, for different nanoparticles. The present results are validated by favorable comparison with previously published literature. The predicted results clearly indicate that the presence of nanoparticles inside the porous media enhances the heat transfer significantly. It is observed from the numerical results that the average Nusselt numbers (Nu) were found to increase linearly with an increase in volume fraction (χ). For the given volume fraction, the average Nu is maximum for a silver‐based nanoparticle. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(1): 1–16, 2014; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21075     

Numerical Investigation of Nanofluid Mixed‐Convection Flow in the Entrance Region of a Vertical Channel Partially Filled with Porous Medium

In this article, transient two‐dimensional mixed convection of nanofluids in the entrance region of a vertical channel has been studied carefully. The geometry under consideration consisted of a parallel‐plate channel partly filled with a porous medium with a constant wall temperature. In the free flow region, the two‐dimensional flow field has been governed by the Navier–Stokes equations. The general formulation of the momentum equations accounting for the inertial and the viscous effects in the presence of a porous medium has been used. Viscous dissipation effects have also been incorporated in the thermal energy equation. Effects of Brownian diffusion and thermophoresis have also been included for nanoparticles in the nanofluid. The governing equations have been given in terms of the stream function‐vorticity formulation and have been non‐dimensionalized and then solved numerically subject to appropriate boundary conditions. The characteristics of the flow and temperature fields have been presented in the terms of mixed‐convection parameter (GR), Brinkman number (Br), Darcy number (Da), Lewis number (Le), and other important parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 607–627, 2014; Published online 21 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21099     

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid‐saturated non‐Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far‐field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite‐difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non‐dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21083     

Influence of Viscous Dissipation on non‐Darcy Mixed Convection Flow of Nanofluid

In this paper, the steady fully developed non‐Darcy mixed convection flow of a nanofluid in a vertical channel filled with a porous medium with different viscous dissipation models is analyzed. The Brinkman‐Forchheimer extended Darcy model is used to describe the fluid flow pattern in the channel. The transport equations for a nanofluid are solved analytically using the seminumerical‐analytical method known as differential transformation method, and numerically with the Runge‐Kutta shooting method. Finally, the influence of pertinent parameters, such as solid volume fraction, different nanoparticles, mixed convection parameter, Brinkman number, Darcy number, and inertial parameter on the velocity and temperature fields are shown graphically. The results show that velocity and temperature are enhanced when the mixed convection parameter, Brinkman number, and Darcy number increases whereas solid volume fraction and inertial parameter decreases the velocity and temperature fields. The obtained results show that the nanofluid enhances the heat transfer process significantly.     

Natural Convection Heat Transfer of Liquid Metal Gallium Nanofluids in a Rectangular Enclosure

A new mixed nanofluid (Cu/diamond–gallium [Cu/diamond–Ga] nanofluid) is proposed, and the mass ratio of Cu nanoparticles and diamond nanoparticles in the new mixed nanofluid is 10:1. The natural convection heat transfer of Cu/diamond–Ga nanofluid, Cu–gallium (Cu–Ga) nanofluid, and liquid metal gallium with different volume fractions in a rectangular enclosure is investigated by a single‐phase model in this paper. The effects of temperature difference, nanoparticle volume fraction and the kinds of nanofluid on the natural convection heat transfer are discussed. The natural convection heat transfer of the three kinds of fluids is compared. It is found that Nusselt numbers of the Cu/diamond–Ga nanofluid along with X direction increases with the nanoparticle volume fraction and temperature difference. Cu/diamond–Ga nanofluid can enhance the heat transfer by 73.0% and 9.7% at low‐temperature difference (ΔT = 1 K) compared with liquid metal gallium and Cu–Ga nanofluid, respectively. It also can enhance the heat transfer by 85.9% and 5.2% at high‐temperature difference (ΔT = 11 K) compared with liquid metal gallium and Cu–Ga nanofluid, respectively.     

Entropy Analysis of a Coupled‐Convection Flow through a Vertical Channel Partially Filled by a Porous Medium with Injection/Suction and Slip Boundary Conditions

Flow fields, thermal fields, and entropy generation have been investigated for fully developed mixed convection flow between two vertical porous plates. The vertical channel is partially filled by a porous medium, and channel walls are subjected to a constant injection velocity at the left wall and constant suction velocity at the right wall. The viscous dissipation effects and velocity slip for the longitudinal component of the velocity at the channel walls are also taken into account. The momentum and energy equations for the mixed convection problem in the vertical channel are solved by means of the perturbation series method, by taking perturbation parameter proportional to the Brinkman number. For the present problem, numerical solution is also obtained and compared with the analytical solution. The effects of various pertinent parameters on the velocity distribution, temperature distribution, entropy generation rate, and Bejan number are investigated and discussed graphically.     

Mixed Convection Over a Vertical Plate in a Doubly Stratified Fluid‐Saturated Non‐Darcy Porous Medium with Cross‐Diffusion Effects

The present article investigates the influence of Dufour and Soret effects on mixed convection heat and mass transfer over a vertical plate in a doubly stratified fluid‐saturated porous medium. The plate is maintained at a uniform and constant wall heat and mass fluxes. The Darcy–Forchheimer model is employed to describe the flow in porous medium. The nonlinear governing equations and their associated boundary conditions are initially transformed into dimensionless forms. The resulting system of nonlinear partial differential equations is then solved numerically by the Keller‐box method. The variation of the dimensionless velocity, temperature, concentration, heat, and mass transfer rates for different values of governing parameters involved in the problem are analyzed and presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21114     

Mixed Convection Effect on Melting from a Vertical Plate Embedded in Porous Medium with Soret and Dufour Effects

The present work analyzed the impact of mixed convection on melting from a vertical flat plate embedded in porous medium in the presence of Dufour and Soret effects. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equation which is solved numerically by Runge–Kutta–Gill methods. Dimensionless velocity, temperature, and concentration profiles are presented graphically for various values of the Dufour number (Df), Soret number (Sr), melting parameter (M), and buoyancy parameter (Gr/Re). During the investigation, it was found that the melting phenomenon decreases the local Nusselt number and local Sherwood number at the solid–liquid interface. Also, it is interesting to note that the velocity as well as temperature increases while the concentration decreases with an increase in the Dufour number Df (or simultaneous decrease in the Soret number Sr). © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 667–676, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21113     

Natural Convection of Nanofluid in Cylindrical Enclosure Filled with Porous Media

A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady state, axisymmetric two-dimensional in a vertical cylindrical channel filled with porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations using Darcy law and Boussinesq＇s approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 program. The parameters affected on the system are Rayleigh number ranging within （10≤ Ra ≤ 103）, aspect ratio （1 ≤ As 〈 5） and the volume fraction （0 ≤0 〈 0.2）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that as ~ increase from 0.01 to 0.2 the value of the mean Nusselt number increase 50.4% for Ra = 1,000.     

Numerical Investigation of Double Diffusive Mixed Convection Laminar Flow in Two Sided Lid Driven Porous Cavity

This paper presents the numerical study of mixed convection in a two‐sided lid driven porous cavity due to temperature and concentration gradients. The top and bottom walls are stationary and insulated. The left and right walls are moving at an equal velocity (V_o) in the same direction. The temperature and concentration are kept high at the right wall and low at the left wall. The governing equations are discretized using finite volume method. The pressure–velocity coupling is performed by the SIMPLE algorithm. A third order differed QUICK scheme is applied at the inner nodes and a second order central difference scheme is used at the boundary nodes. The flow behavior and heat transfer are analyzed for different nondimensional numbers, such as, 1 × 10^?4 ≤ Ri ≤ 10, 1 × 10^?4 ≤ Da ≤ 0.1 and 0.7 < Pr < 10. The present numerical results are compared with the literature and are in good agreement. For the above selected nondimensional numbers, the heat and fluid flow behavior is investigated using local and average Nusselt (Nu) and Sherwood (Sh) numbers. Results show that the convection flow is significant up to Da = 0.1, beyond that the effect of porosity is negligible. The effect of Prandtl number (Pr) on average Nu is found to increase significantly.     

Finite Element Analysis of Radiative Mixed Convection Magneto‐Micropolar Flow in a Darcian Porous Medium with Variable Viscosity and Convective Surface Condition

A mathematical study is presented for the collective influence of the buoyancy parameter, convective boundary parameter and temperature dependent viscosity on the steady mixed convective laminar boundary flow of a radiative magneto‐micropolar fluid adjacent to a vertical porous stretching sheet embedded in a Darcian porous medium. The fluid viscosity is assumed to vary as an inverse linear function of temperature. Using appropriate transformations, the governing equations of the problem under consideration are transformed into a system of dimensionless nonlinear ordinary differential equations, which are then solved with the well‐tested, efficient finite element method. The results obtained are depicted graphically to illustrate the effect of the various important controlling parameters on velocity, microrotation, and temperature functions. The skin friction coefficient, wall couple stress, and the rate of heat transfer have also been computed and presented in tabular form. Comparison of the present numerical results with earlier published data has been performed and the results are found to be in good agreement, thus validating the accuracy of the present numerical code. The study finds applications in conducting polymer flows in filtration systems, trickle bed magnetohydrodynamics in chemical engineering, electro‐conductive materials processing, and so on.     

Double‐Diffusive Convective Transport in a Nanofluid‐Saturated Porous Layer with Cross Diffusion and Variation of Viscosity and Conductivity

The onset of double‐diffusive nanofluid convection in a fluid‐saturated horizontal porous layer is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. The Darcy model has been used for the porous medium, while the nanofluid incorporates the effects of Brownian motion along with thermophoresis. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation in the vertical direction of conductivity and viscosity. In addition, the thermal energy equation includes regular diffusion and cross diffusion terms. The linear stability analysis is based on the normal mode technique, while for nonlinear analysis, minimal representation of the truncated Fourier series representation involving only two terms has been used. It is found that for the stationary mode the Soret parameter, Dufour parameter, viscosity ratio, and conductivity ratio have a stabilizing effect, while the solutal Rayleigh number destabilizes the system. For the oscillatory mode, the Soret parameter, Dufour parameter, and viscosity ratio have a stabilizing effect while the solutal Rayleigh number and conductivity ratio destabilize the system. For steady finite amplitude motions, the heat and mass transport decreases with an increase in the values of the Dufour parameter and solutal Rayleigh number. The Soret parameter enhances the solute concentration Nusselt number while it retards the thermal Nusselt number and concentration Nusselt number. The viscosity ratio and conductivity ratio enhances the heat and mass transports. We also study the effect of time on transient Nusselt numbers which is found to be oscillatory when time is small. However, when time becomes very large, all three transient Nusselt values approach a steady value. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 628–652, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21102     

Soret Effect on Darcy–Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer

A linear and weakly nonlinear stability analyses is performed to study the onset of Darcy–Brinkman double diffusive convection in a binary viscoelastic fluid‐saturated porous layer in the presence of the Soret effect. The modified Darcy–Brinkman–Oldroyd model including the time derivative term is employed for the momentum equation. The expressions for stationary, oscillatory, and finite amplitude Rayleigh number are obtained as a function of the governing parameters. There is a competition between the processes of the Soret coefficient, viscoelasticity, thermal diffusion, and solute diffusion that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effects of the Soret parameter, Darcy number, relaxation and retardation parameters, and Darcy–Prandtl number on the stationary, oscillatory, and finite amplitude convection is shown graphically. The weakly nonlinear theory is based on truncated representation of the Fourier series method and is used to find the Nusselt and Sherwood numbers. Further, the transient behavior of the Nusselt and Sherwood numbers is investigated by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta method. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 297–320, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21076     

Solutal Dispersion and Viscous Dissipation Effects on Non‐Darcy Free Convection Over a Cone in Power‐Law Fluids

The effects of viscous dissipation and solutal dispersion on free convection about an isothermal vertical cone with a fixed apex half angle, pointing downwards in a power‐law fluid‐saturated non‐Darcy porous medium are analyzed. The governing partial differential equations are transformed into partial differential equations using non‐similarity transformation. The resulting equations are solved numerically using an accurate local non‐similarity method. The accuracy of the numerical results is validated by a quantitative comparison of the heat and mass transfer rates with previously published results for a special case and the results are found to be in good agreement. The effects of viscous dissipation, solutal dispersion, and/or buoyancy ratio on the velocity, temperature, and concentration field as well as on the heat and mass transfer rates are illustrated, by insisting on the comparison between pseudo‐plastic, dilatant, and Newtonian fluids. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 476–488, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21095     

Modelling and experimental studies on heat transfer in the convection section of a biomass boiler

This paper describes a model of heat transfer for the convection section of a biomass boiler. The predictions obtained with the model are compared to the measurement results from two boilers, a 50 kW_th pellet boiler and a 4000 kW_th wood chips boiler. An adequate accuracy was achieved on the wood chips boiler. As for the pellet boiler, the calculated and measured heat transfer rates differed more than expected on the basis of the inaccuracies in correlation reported in the literature. The most uncertain aspect of the model was assumed to be the correlation equation of the entrance region. Hence, the model was adjusted to improve the correlation. As a result of this, a high degree of accuracy was also obtained with the pellet boiler. The next step was to analyse the effect of design and the operating parameters on the pellet boiler. Firstly, the portion of radiation was established at 3–13 per cent, and the portion of entrance region at 39–52 per cent of the entire heat transfer rate under typical operating conditions. The effect of natural convection was small. Secondly, the heat transfer rate seemed to increase when dividing the convection section into more passes, even when the heat transfer surface area remained constant. This is because the effect of the entrance region is recurrent. Thirdly, when using smaller tube diameters the heat transfer area is more energy‐efficient, even when the bulk velocity of the flow remains constant. Copyright © 2006 John Wiley & Sons, Ltd.     

Onset of Darcy‐Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer with Internal Heat Source

The onset of Darcy‐Brinkman convection in a binary viscoelastic fluid‐saturated sparsely packed porous layer with an internal heat source is studied using both linear and nonlinear stability analyses. The Oldroyd‐B model is employed to describe the rheological behavior of binary fluid. An extended form of the Darcy‐Oldroyd law incorporating Brinkman's correction and time derivative is used to describe the flow through a porous layer. The onset criterion for stationary, oscillatory, and finite amplitude convection is derived analytically. There is a competition between the processes of thermal diffusion, solute diffusion, and viscoelasticity that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effect of internal Rayleigh number, relaxation and retardation parameters, solute Rayleigh number, Darcy number, Darcy‐Prandtl number, and Lewis number on the stability of a system is investigated and is shown graphically. The nonlinear theory based on the truncated representation of the Fourier series method is used to find heat and mass transfer. The transient behavior of the Nusselt and Sherwood numbers is obtained using numerical methods. Some known results are recovered for the particular cases of the present study. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(8): 676–703, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21056     

Effects of the Caputo fractional derivatives on convective flow in wavy vented enclosures filled with a porous medium using Al2O3‐Cu hybrid nanofluids

This paper studies the effect of fractional derivatives on the fractional convective flow of hybrid nanofluids in a wavy enclosure that has inlet and outlet parts near the left wall and is filled with a porous medium. The Caputo definition of the fractional derivatives is applied on the partial differential equations governing flow. The complex shape is mapped to a rectangular domain using appropriate transformations. The finite difference method is used to solve the resulting system. The results showed that an increase in order of the fractional derivatives causes a low activity of the fluid flow and a reduction in the rate of heat transfer. Also, an increase in the nanoparticles volume fractions reduces the activity of the fluid flow and, as a result, the rate of heat transfer is diminished. An enhancement in fluid motion and rate of the heat transfer is obtained by increasing the amplitude of the wavy wall.     

Analysis of Flow and Heat Transfer in a Parallelogram Non‐Uniformly Heated Enclosure Filled with Porous Medium

The flow and heat transfer in a parallelogram enclosure filled with a porous medium is analyzed numerically. The heated bottom wall has a sinusoidal temperature distribution and side walls cooled isothermally while the upper wall is well insulated. Dimensionless Darcy law and energy equations are solved using the finite difference method along with the corresponding boundary condition. Computations were carried out for four inclination angles of side walls (γ = 45°, 60°, 75°, 90°) with different Rayleigh numbers (100≤Ra≤1000) and their effects on the flow field and heat transfer are discussed. It is found that the inclination angle has a significant effect on flow pattern and heat transfer and an increase in the angle leads to a decrease in the strength of the right vortex. The study also revealed that as the Rayleigh number increases at γ = 45°, another (third) vortex develops along the left wall and its strength enhances with Rayleigh number. At the end, a correlation is extracted from the numerical data which represents the relation between the Nusselt number, inclination angle, and the Rayleigh number. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; 39(7): 497–506, 2010; Published online in Wiley Online Library ( wileyOnlinelibrary.com ). DOI 10.1002/htj.20312     

Unsteady Mixed Convection Flow of a Rotating Second‐Grade Fluid on a Rotating Cone

In the present article, we have investigated the unsteady mixed convection flow of a rotating second‐grade fluid in a rotating cone with time‐dependent angular velocities. Two cases of heat transfer are presented which are known as (i) prescribed wall temperature (PWT) and (ii) prescribed heat flux (PHF). The governing coupled nonlinear partial differential equations are simplified with the help of transformations and non‐dimensional similar and non‐similar variables, and solved analytically with the help of the homotopy analysis method (HAM). The effects of pertinent parameters on the velocity, temperature, concentration, skin friction coefficients, Nusselt number, and Sherwood number have been examined through graphs. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 204–220, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21072     

Flow of mixed convection for radiative and magnetic hybrid nanofluid in a porous material with Joule heating

This paper analyzes the mixed convection flow and transport of heat in a hybrid nanofluid via an exponentially extending/contracting surface. Joule heating, magnetic field, permeability of a porous medium, thermal radiation, and slip condition are taken into consideration. Magnetite (Fe₃O₄) and copper (Cu) are used as a mixture of nanoparticles while ethylene glycol as a regular liquid. The paradigm is dissolved by utilizing the method of Runge–Kutta–Fehlberg with the shooting technique in MATLAB software. The effect of controlling parameters on the coefficient of drag force, heat transfer coefficient, and the distributions of temperature and velocity for physical parameters are discussed numerically, physically, and graphically. The outcomes ended up illustrating that the transport of heat is diminished by upsurging the Joule heating and magnetic field parameters for both contracting and extending states. For larger values of permeability parameter and parameter of mixed convection, the coefficient of local skin friction upsurges in extending situations.