Effect of viscosity variation on natural convection flow of water–alumina nanofluid in an annulus with internal heat generation

Heat transfer enhancement in a horizontal annulus using the variable viscosity property of an Al₂O₃–water nanofluid is investigated. Two different viscosity models are used to evaluate heat transfer enhancement in the annulus. The base case uses the Pak and Cho model and the Brinkman model for viscosity which take into account the dependence of this property on temperature and nanoparticle volume fraction. The inner surface of the annulus is heated uniformly by a constant heat flux q_w and the outer boundary is kept at a constant temperature T_c. The nanofluid generates heat internally. The governing equations are solved numerically subject to appropriate boundary conditions by a penalty finite‐element method. It is observed that for a fixed Prandtl number Pr = 6.2, Rayleigh number Ra = 10⁴ and solid volume fraction ? = 10%, the average Nusselt number is enhanced by diminishing the heat generation parameter, mean diameter of nanoparticles, and diameter of the inner circle. The mean temperature for the fluids (nanofluid and base fluid) corresponding to the above mentioned parameters is plotted as well. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21016     

The effect of the top and bottom wall temperatures on the laminar natural convection in an air-filled square cavity

The effect of the top and bottom wall temperatures on the natural convection heat transfer characteristics in an air-filled square cavity driven by a difference in the vertical wall temperatures was investigated by measuring the temperature distributions along the heated vertical wall and visualizing the flow patterns in the cavity. The experiments were performed at a horizontal Grashof number of 1.9 × 10⁸. Increasing the top wall temperature resulted in a separated flow region on the top wall, which caused a secondary flow between the separated flow and the boundary layer on the heated vertical wall. This secondary flow had a significant effect on the heat transfer in this region. Changes in the top and bottom wall temperatures changed the temperature gradient and the average temperature of the air outside the thermal boundary layers in the cavity. The local heat transfer along much of the heated vertical wall could be correlated by Nu = C · Ra^0.32, but the constant C increased when the average of the top and bottom wall temperatures increased.     

Flow and heat transfer of natural convection around an upward‐facing horizontal plate with a vertical plate at the edge

Natural convective flows around an upward‐facing horizontal heated plate with a vertical plate at the edge were investigated experimentally. Of particular concern were the influences of the vertical plate on the fluid flow and the heat transfer of the horizontal plate. The flow and temperature fields adjacent to the horizontal plate were visualized with dye and a liquid‐crystal thermometry. The results show that the vertical plate obstructs the flow from the top of the vertical plate, while the flow from the open edge of the horizontal plate covers the whole horizontal surface when the height of the vertical plate exceed H/W = 0.14 for adiabatic vertical plate and H/W = 0.1 for the heated vertical plate. The local heat‐transfer‐coefficients of the horizontal plate were also measured. It was found that the vertical adiabatic plates deteriorate the heat transfer, while the heated vertical plates enhance the heat transfer from the horizontal plates. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(8): 527–539, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20033     

Non‐Darcy assisted flow along a channel with an open cavity filled with water–TiO2 nanofluid

Numerical investigation on forced (assisted) convection heat transfer in a two‐dimensional horizontal porous channel with an open cavity is studied in this article. A non‐uniform heat flux is considered to be located on the bottom surface of the cavity. The rest of the surfaces are taken to be perfectly insulated. The physical domain is filled with a water‐based nanofluid containing TiO₂ nanoparticles. The fluid enters from the left and exits from the right with initial velocity U_i and temperature T_i. Governing equations are discretized using the penalty finite element method. The simulation is carried out for a wide range of Reynolds number Re (= 10–500) and Darcy number Da (= 10^?5–∞). Results are presented in the form of streamlines, isothermal lines, local and average Nusselt numbers, average temperatures of the fluid, horizontal and vertical velocities at mid‐height of the channel and mean velocity fields for various Re and Da. The enhancement of heat transfer rate is caused by the increasing Re and falling Da. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21046     

Study of turbulent natural convection coupled with thermal radiation in a vertical cavity having a large form factor

In this study, a numerical simulation study of turbulent natural convection coupled with thermal radiation in a vertical cavity differentially heated and filled with air assumed as a transparent fluid was carried out. The cavity has a variable form factor which can reach large values. The vertical walls are subjected to constant temperatures (T_c and T_f), whereas the horizontal walls are assumed adiabatic. The flow inside the cavity is turbulent and turbulence was modeled by using the $K?\epsilon$ model, and to take into account of the radiative transfer, the discrete ordinate model (DO) was introduced. To solve the different equations, Ansys‐Fluent software based on the finite volume method was used. Some numerical results obtained for the Rayleigh number value of 10¹¹ have been validated by some existing results in the theory. It is found that the thermal radiation has a significant influence on the flow structure and temperature variation where the flow becomes reinforced. It accelerates the airflow inside the cavity and gives the formation of significant velocity and temperature gradients along the walls of the cavity. Taking into account of the surface, thermal radiation is essential in the correct evaluation of temperature in the cavity.     

Heat transfer in porous cavity under the influence of radiation and viscous dissipation

Heat transfer under the influence of radiation and viscous dissipation in a square cavity filled with saturated porous medium is analysed. The flow is assumed to follow Darcy law. The governing equations are non-dimensionalised and solved numerically using finite element method. Left vertical surface of the square cavity is maintained at isothermal temperature T_h and right vertical surface at T_c. Results are presented in terms of Nusselt number at hot and cold wall of the cavity for various values of viscous dissipation parameter and radiation parameter. It is seen that the average Nusselt number at hot as well as cold wall increases with increase in radiation parameter.     

Magnetohydrodynamic mixed convection in a horizontal channel with an open cavity

The development of magnetic field effect on mixed convective flow in a horizontal channel with a bottom heated open enclosure has been numerically studied. The enclosure considered has rectangular horizontal lower surface and vertical side surfaces. The lower surface is at a uniform temperature T_h while other sides of the cavity along with the channel walls are adiabatic. The governing two-dimensional flow equations have been solved by using Galarkin weighted residual finite element technique. The investigations are conducted for different values of Rayleigh number (Ra), Reynolds number (Re) and Hartmann number (Ha). Various characteristics such as streamlines, isotherms and heat transfer rate in terms of the average Nusselt number (Nu), the Drag force (D) and average bulk temperature (θ_av) are presented. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the cavity whereas in the channel these effects are less significant.     

Natural convection near 4°C in a water saturated porous layer heated from below

This paper reports a numerical study of two-dimensional natural convection in a horizontal porous layer heated from below and saturated with cold water. The density maximum of water at 3.98°C and atmospheric pressure occurs inside the layer, as the top surface is maintained at 0°C and the bottom surface is varied from 4 to 8°C. Three separate series of numerical simulations document the effect of Rayleigh number, bottom surface temperature, and horizontal length of the porous layer on the overall heat transfer rate vertically through the layer. The range of these numerical experiments is 200 < Ra_p < 10000, 0.167 < H/L < 1 and °C < T_H < 8°C, where Ra_p, H/L and T_H are the Darcy-modified Rayleigh number for a fluid with density maximum, the geometric ratio height/length, and the bottom wall temperature. The numerical results agree with published linear stability results regarding the onset of convection.     

Magnetoconvection in an enclosure of water near its density maximum with Soret and Dufour effects

In this paper, unsteady double-diffusive magnetoconvection of water in an enclosure with Soret and Dufour effects around the density maximum has been numerically investigated. The right vertical wall has constant temperature, θ_c, while left vertical wall is θ_h, with θ_h > θ_c. The concentration in right wall is maintained lower than left wall (c_h > c_c). The remaining horizontal walls are adiabatic. The governing equations are solved by control volume method using SIMPLE algorithm with QUICK scheme. Representative results illustrating the effects of the thermal Rayleigh number, Hartmann number, the direction of magnetic field, density inversion parameter, buoyancy ratio, Schmidt number, and Soret and Dufour parameters on the contour maps of the fluid flow, temperature and concentration as well as the profile of velocity at mid-section of the enclosure are reported. In addition, numerical results for the average Nusselt and Sherwood numbers are presented for various parametric conditions and discussed.     

Finite element simulation of hydromagnetic convective flow in an obstructed cavity

The hydromagnetic natural convective flow and heat transfer characteristics in a square cavity with a solid circular heated obstacle located at the center have been investigated numerically. The left vertical surface of the cavity is uniformly heated of temperature T_c and other three surfaces are adiabatic. The obstacle consists of constant heat T_h. Under all circumstances the condition T_h > T_c is maintained. The physical problem is represented mathematically by sets of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual finite element simulation. The behavior of the fluid in the ranges of Prandtl number (0.073-2.73), Hartmann number (0-50) and Joule heating parameter (1-7) is explained in details. It is found that the flow and temperature fields are strongly dependent on the above stated parameters for the ranges considered. The variation of the average Nusselt number (Nu) for various Prandtl number (Pr) is also presented.     

Combined convection heat transfer in a lid driven cavity filled with nanofluids

A simulation study is performed of laminar steady combined convection heat transfer in a lid-driven cavity containing various types of nanofluid (CuO–water nanofluid and Al₂O₃–water nanofluid) at various boundary conditions. The influence of two different types of temperature distributions applied to the cavity's bottom wall is investigated. There are two types of temperature distributions: constant temperature (T_h) and a sinusoidal temperature distribution applied to the bottom wall, which has a higher temperature than the top moving wall (T_c). In both circumstances, the sidewalls are kept adiabatic. The finite element method is utilized for the current issue. The influence of the Richardson number, which ranges from 0.01 to 10, and the volume fraction of nanoparticles, which ranges from 0 to 0.1, on the heat transfer rate has been explored. The influence of the sinusoidal temperature distribution's amplitude and phase angle is also examined. The isotherm and streamline patterns within the cavity are diverse with distinct nanoparticle volume fractions, and the Richardson numbers are presented and analyzed. The numerical findings showed that lowering the Richardson number raises the average Nusselt number. Also, the existence of nanoparticles in pure water increases heat transmission. Additionally, raising the sinusoidal temperature's amplitude increases the average Nusselt number. The results show that the increase of average Nusselt number at (φ = 0, Gr = 10⁴, Pr = 1, Ɣ = 3π/2) for amplitude 0.25, 0.5, 0.75, and 1 is 0.53, 0.9, 1.3, and 1.87, respectively.     

Film boiling heat transfer from a horizontal circular plate facing downward

The two‐dimensional, steady, pool film boiling heat transfer from a horizontal circular plate facing downward to a stagnant saturated liquid is studied theoretically. It is assumed that the vapor‐liquid interface is smooth and that radiation can be disregarded. The relevant governing equations for the vapor film are solved for saturated water at atmospheric pressure using an improved two‐equation boundary‐layer integral method. It is shown that the dimensionless temperature profile is affected by the wall superheat ΔT_sat and that the ratio of Nu to X^0.2 is an increasing function of ΔT_sat. Here, Nu represents the mean Nusselt number and X the film‐boiling Rayleigh number. In addition, it is revealed that the one‐equation boundary‐layer integral method developed by Nishio and colleagues is fairly accurate in predicting the film thickness, the representative radial velocity, and the mean Nusselt number. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 72–84, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10071     

Heat transfer for flow boiling of water and critical heat flux in a half‐heated round tube under low‐pressure conditions

Heat transfer for flow boiling of water and critical heat flux (CHF) experiments in a half‐circumferentially heated round tube under low‐pressure conditions were carried out. To clarify the flow patterns in the heated section, experiments in the round tube under the same conditions were also carried out, and their results were compared. The experiments were conducted with atmospheric‐pressure water in test sections with inner diameter D = 6 mm, heated length L = 360 mm, inlet water subcooling ΔT_in = 80 K, and mass velocity G from 0 to 2000 kg/(m²·s) for the half‐circumferentially heated round tube and from 0 to 7000 kg/(m²·s) for the full‐circumferentially heated tube. The experimental data demonstrated that the wall temperature near the outlet of the half‐circumferentially heated tube remained almost the same until CHF. It was found that burnout occurred when the flow regime changed from churn flow to annular flow, and the liquid film on the heated wall dried out although liquid film on the unheated wall remained. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(3): 149–164, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10022     

Influence of nanofluids on mixed convective heat transfer over a horizontal backward‐facing step

Predictions are reported for laminar mixed convection using various types of nanofluids over a horizontal backward‐facing step in a duct, in which the upstream wall and the step are considered adiabatic surfaces, while the downstream wall from the step is heated to a uniform temperature that is higher than the inlet fluid temperature. The straight wall that forms the other side of the duct is maintained at constant temperature equivalent to the inlet fluid temperature. Eight different types of nanoparticles, Au, Ag, Al₂O₃, Cu, CuO, diamond, SiO₂, and TiO₂, with 5% volume fraction are used. The conservation equations along with the boundary conditions are solved using the finite volume method. Results presented in this paper are for a step height of 4.9 mm and an expansion ratio of 1.942, while the total length in the downstream of the step is 0.5 m. The Reynolds number is in the range of 75 ≤ Re ≤ 225. The downstream wall was fixed at a uniform wall temperature in the range of 0 ≤ ΔT ≤ 30 °C which is higher than the inlet flow temperature. Results reveal that there is a primary recirculation region for all nanofluids behind the step. It is noticed that nanofluids without secondary recirculation region have a higher Nusselt number and it increases with Prandtl number decrement. On the other hand, nanofluids with secondary recirculation regions are found to have a lower Nusselt number. Diamond nanofluid has the highest Nusselt number in the primary recirculation region, while SiO₂ nanofluid has the highest Nusselt number downstream of the primary recirculation region. The skin friction coefficient increases as the temperature difference increases and the Reynolds number decreases. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20344     

Mixed convective heat and mass transfer on a peristaltic flow of a non‐Newtonian fluid in a vertical asymmetric channel

In the present analysis we discuss the effects of mixed convective heat and mass transfer on the peristaltic flow of a non‐Newtonian fluid in a vertical asymmetric channel. The flow is investigated in a wave frame of reference moving with the velocity c away from the fixed frame. The governing equations for the present flow problem are first modeled and then discussed. The analytical solution of the present flow problem is discussed using regular perturbation technique. The graphical results are discussed to see the effects of various physical parameters of interest. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21020     

Simulation of mixed convection heat transfer in a horizontal channel with an open cavity containing a heated hollow cylinder

The objective of this paper is to numerically investigate the mixed convective flow and heat transfer controlled by a heated hollow cylinder inside an open cavity attached with a horizontal channel. All the boundaries of the channel and cavity are perfectly insulated while the inner surface of the cylinder is heated uniformly by heat flux q. The equations of conservation of mass, momentum, and energy were solved using adequate boundary conditions by Galarkin's weighted residual finite element technique. The solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been conducted for Ra = 10³–10⁵, Prandtl number Pr varying from 0.7 to 7 and ratio of solid to fluid thermal conductivities from 0.2 to 50. Results are presented in terms of streamlines, isotherms, heat transfer rate in terms of the average Nusselt number (Nu_av), drag force (D), and maximum bulk temperature (θ_max). © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21002     

Effects of diameter ratio of adiabatic circular cylinder and tilt angle on natural convection from a square open tilted cavity

A numerical analysis is carried out to study the performance of natural convection inside a square open tilted cavity filled with air. An adiabatic circular solid cylinder is placed at the center of the cavity and the sidewall in front of the breathing space is heated by a constant heat flux. The top and bottom walls are kept at the ambient constant temperature. Two‐dimensional forms of Navier–Stokes equations along with the energy equations are solved using the Galerkin finite element method. Results are obtained for a range of Grashof numbers from 10³ to 10⁶ at Pr = 0.71 while the tilt angle varies from 0 to 45° and the diameter ratio of the cylinder is considered to be 0.2, 0.3, and 0.4 with constant physical properties. The parametric studies for a wide range of cylinder diameter ratios and cavity tilt angles show significant features of the present problem in terms of stream functions and temperature profiles. The computational results indicate that the heat transfer coefficient is strongly influenced by the above governing parameters. It is also found that the average Nusselt number decreases when the diameter ratio increases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21001     

Lattice Boltzmann simulation of natural convection and heat transfer from multiple heated blocks

This study is aimed to investigate the natural convection heat transfer from discrete heat sources (similar to heated microchips) using Bhatnagar‐Gross‐Krook lattice Boltzmann method via graphics process unit computing. The simulation is carried out separately for three and six heated blocks model for different Rayleigh numbers and fixed Prandtl number, $Pr=0.71$ (air). The uniformly heated blocks are placed at the bottom wall inside a rectangular enclosure. The enclosure is maintained by the cold temperature at its left and right walls. The top and bottom surface is maintained by adiabatic conditions apart from the regions where blocks are attached to the bottom wall. The numerical code is validated with the benchmark heat transfer problem of side‐heated square cavity as well as with an experimental study for one discrete heat source. The rate of heat transfer is presented in terms of the local Nusselt and average Nusselt number for each block. It is found that the heat transfer rate becomes maximized in the leftmost and rightmost blocks due to the adjacent cold walls. It is found that the number of blocks and their positions play a substantial role in determining their collective performance on the heat transfer rate.     

Effects of aspect ratio on mixed convection in a horizontal rectangular duct with heated and cooled side walls

This paper describes the effect of aspect ratio on mixed convection in a horizontal rectangular duct with heated and cooled side walls numerically and experimentally. In the numerical analysis, fluid flow and temperature distributions for Ri=1.61, Pr=6.99, Re=100 and aspect ratio, Ar=0.2–10, were obtained by solving dimensionless governing equations using the SIMPLE procedure. The QUICK scheme was applied to the convective term of these equations. In the experimental analysis, the flow behavior for A_r=0.5–2 was visualized by the dye‐injection method. Numerical results showed that the swirl flow was generated along the flow direction, and its pitch length was influenced by A_r. The pitch length was the shortest when A_r=0.5–1, and this tendency was the same in numerical results and experimental results. The heat transfer behavior was also discussed corresponding to the flow, and the heat transfer ratio was highest at A_r=1 in 0.2 ≤ A_r ≤ 10. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20391     

Numerical analysis of convection conduction and radiation using a non-equilibrium model in a square porous cavity

Numerical analysis of heat transfer by convection, conduction and radiation in a saturated porous medium enclosed in a square cavity is investigated using a thermal non-equilibrium model. The flow is assumed to follow Darcy law. The governing partial differential equations are non-dimensionalised and solved numerically using finite element method. The left vertical surface of the square cavity is maintained at an isothermal temperature $T_h$ and the right vertical surface at $T_c$ such that $T_c<T_h$. The top and bottom surfaces of the cavity are assumed to be adiabatic. Results are presented in terms of Nusselt number for fluid, Nusselt number for solid and total Nusselt number, for various parameters such as inter-phase heat transfer coefficient, modified conductivity ratio, radiation parameter and Rayleigh number.