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.     

Investigation of a large top wall temperature on the natural convection plume along a heated vertical wall in a square cavity

The characteristics of the laminar natural convection in an air-filled square cavity heated and cooled on the side walls was studied for cases where the temperature of the top wall was significantly larger than the heated vertical wall. Experiments were performed for a horizontal Grashof number of 1.3 × 10⁸, and non-dimensional top wall temperatures from 1.4 to 2.3. The results show that the plume formed on the heated vertical wall separated from this wall before reaching the top wall. As a result, three different regions were observed in the cavity: a stratified core region, a buoyant plume region, and a highly stratified region above the plume after it had separated from the vertical wall. The highly stratified region above the plume became larger and more stable with an increase of the top wall temperature, stabilizing the motion of the plume across the cavity. The similarity solutions developed by Kulkarni et al. [A.K. Kulkarni, H.R. Jacobs, J.J. Hwang, Similarity solution for natural convection flow over an isothermal vertical wall immersed in thermally stratified medium, Int. J. Heat Mass Transfer 30 (1987) 691–698] to characterize the natural convection heat transfer along an isothermal single vertical plate did not agree with the results for the current measurements; however, the non-similarity model of Chen and Eichhorn [C.C. Chen, R. Eichhorn, Natural convection from a vertical surface to thermally stratified fluid, J. Heat Transfer 98 (1976) 446–451] was in good agreement over most of the wall. There were some discrepancies in the temperature distributions and the heat transfer characteristics, especially at y/H ? 0.8 due to the separated flow in this region.     

Average heat transfer rates measured in two different temperature ranges for magnetic convection of horizontal water layer heated from below

The average heat transfer rates of gravitational and magnetic convection of water heated from below and cooled from above are measured for two cases of cold wall temperature θ_c at 10 °C and 30 °C. The height of the cylindrical enclosure is 2 mm with 40 mm in diameter. The magnetic field is imposed in a vertical direction to increase or decrease 29% of the gravitational acceleration in a bore space of a super-conducting magnet of 10 T at the solenoid center. The group of data at θ_c = 30 °C gives a better agreement with the classical heat transfer rate of Silveston than that at θ_c = 10 °C. This is probably due to the almost constant value in the volumetric magnetic susceptibility of water at about 10 °C.     

Transport phenomena and performance of a plate methanol steam micro-reformer with serpentine flow field design

A numerical investigation of the transport phenomena and performance of a plate methanol steam micro-reformer with serpentine flow field as a function of wall temperature, fuel ratio and Reynolds number are presented. The fuel Reynolds number and H₂O/CH₃OH molar ratio (S/C) that influence the transport phenomena and methanol conversion are explored in detail. In addition, the effects of various wall temperatures on the plates that heat the channel are also investigated. The predictions show that conduction through the wall plays a significant effect on the temperature distribution and must be considered in the modeling. The predictions also indicate that a higher wall temperature enhances the chemical reaction rate which, in turn, significantly increases the methanol conversion. The methanol conversion is also improved by decreasing the Reynolds number or increasing the S/C molar ratio. When the serpentine flow field of the channel is heated either through top plate (Y = 1) or the bottom plate (Y = 0), we observe a higher degree of methanol conversion for the case with top plate heating. This is due to the stronger chemical reaction for the case with top plate heating.     

Numerical study of assisting and opposing mixed convective nanofluid flows in an inclined circular pipe

A numerical investigation of mixed convection is carried out to study the heat transfer and fluid flow characteristics in an inclined circular pipe using the finite volume method. The pipe has L/D of 500 and it was subjected to a uniform heat flux boundary condition. Four types of nanofluids (Al₂O₃, CuO, SiO₂, and TiO₂ with H₂O) with nanoparticles concentration in the range of 0 ≤ φ ≤ 5% and nanoparticles diameter in the range of 20 ≤ dp ≤ 60 nm were used. The pipe inclination angle was in the range of 30^∘ ≤ θ ≤ 75^∘ using assisting and opposing flow. The influences of Reynolds number in the range of 100 ≤ Re ≤ 2000, and Grashof numbers in the range of 6.3 × 10² ≤ Gr ≤ 8.37 × 10³ were examined. It is found that the velocity and wall shear stress are increased as Re number increases, while the surface temperature decreases. There is no significant effect of increasing Gr number on thermal and flow fields. The velocity and wall shear stress are increased and the surface temperature is decreased as φ and dp are decreased. It is concluded that the surface temperature is increased as the pipe inclination angle increases from the horizontal position (θ = 0^°) to the inclined position (θ = 75^°). In addition, it is inferred that the heat transfer is enhanced using SiO₂ nanofluid compared with other nanofluids types. Furtheremore, it is enhanced using assisting flow compared to opposing flow.     

Steady natural convection flow in a square cavity filled with a porous medium for linearly heated side wall(s)

In this paper natural convection flows in a square cavity filled with a porous matrix has been investigated numerically when the bottom wall is uniformly heated and vertical wall(s) are linearly heated whereas the top wall is well insulated. Darcy–Forchheimer model without the inertia term is used to simulate the momentum transfer in the porous medium. Penalty finite element method with bi-quadratic rectangular elements is used to solve the non-dimensional governing equations. Numerical results are presented for a range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁶, Darcy number Da, 10⁻⁵ ⩽ Da ⩽ 10⁻³, and Prandtl number Pr, 0.2 ⩽ Pr ⩽ 100) in terms of stream functions and isotherm contours, and local and average Nusselt numbers.     

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.     

Numerical investigation of several physical and geometric parameters in the natural convection into trapezoidal cavities

Natural convection in trapezoidal cavities, especially those with two internal baffles in conjunction with an insulated floor, inclined top surface, and isothermal left-heated and isothermal right-cooled vertical walls, has been investigated numerically using the Element based Finite Volume Method (EbFVM). In numerical simulations, the effect of three inclination angles of the upper surface as well as the effect of the Rayleigh number (Ra), the Prandtl number (Pr), and the baffle’s height (H_b) on the stream functions, temperature profiles, and local and average Nusselt numbers has been investigated. A parametric study was performed for a wide range of Ra numbers (10³ ? Ra ? 10⁶) H_b heights (H_b = H¹/3, 2H¹/3, and H¹), Pr numbers (Pr = 0.7, 10 and 130), and top angle (θ) ranges from 10 to 20. A correlation for the average Nusselt number in terms of Pr and Ra numbers, and the inclination of the upper surface of the cavity is proposed for each baffle height investigated.     

Radiative effects on natural convection in vertical convergent channels

Natural convection in air, in a convergent channel, uniformly heated at the principal walls, is experimentally investigated, in order to analyze the effects of the radiative heat transfer. Results in terms of wall temperature profiles as a function of the walls inclination angle, the spacing between the walls, the heat flux, are given for two values of the wall emissivity. Flow visualization is carried out to show the peculiar pattern of the flow between the plates in several configurations. The comparison between two wall emissivity values, 0.10 and 0.90, shows that the effect of thermal radiation is more pronounced for larger convergence angles. For a wall emissivity equal to 0.90 and for small values of the minimum channel spacing, heat transfer in slightly convergent vertical channels is stronger than in a vertical parallel channel. Flow visualization points out a recirculating zone in the upper part of the channel for small values of the minimum channel spacing and for converging angles equal to 5° and 10°. Nusselt numbers and dimensionless maximum temperatures are then evaluated and correlated to the Rayleigh number, in the investigated range from 5 to 5 × 10⁸ and 0° ? θ ? 10°. A very good agreement between experimental data and correlations is observed for the dimensionless parameters based on the maximum channel spacing. Comparisons between experimental and numerical data are also performed and a good relationship is observed.     

Measurement of local heat/mass transfer coefficients on a dimple using naphthalene sublimation

Local and average heat/mass transfer characteristics on a single dimple were investigated using a naphthalene sublimation technique. The dimple depth in this study ranged from 20% to 40% of the channel height. The experimental conditions covered the range from laminar to low-velocity turbulent flow regimes, 500 ? Re_H ? 5000. Secondary flows from the dimple were clearly observed in the transient flow regime of Re_H = 2000–3000. The velocity fluctuation in the mixing layer over the dimple increased with the dimple depth and the Reynolds number. The impingement of the mixing layer and the induced secondary flows augmented the Sherwood number around the rear rim of the dimple and in the rear plateau region, respectively. For a Reynolds number of 3000, the Sherwood number increased significantly due to the increased fluctuation in the mixing layer and the intensified secondary flows from the dimple. The heat/mass transfer augmentation factors increased as the Reynolds number increased, reaching 1.5 at a Reynolds number of 5000.     

Mixed convective transport in a lid-driven cavity containing a nanofluid and a rotating circular cylinder at the center

The mixed convective transport of Cu-H₂O nanofluid in a differentially heated and lid-driven square enclosure in the presence of a rotating circular cylinder is investigated numerically. The top wall of the enclosure is sliding from left to right at a uniform speed while all other walls are stationary. A thermally insulated circular cylinder is placed centrally within the enclosure. The cylinder can rotate about its centroidal axis. The top and bottom walls are kept isothermal at different temperatures while the side walls are assumed adiabatic. Simulations are performed for, Richardson number 1 ≤ Ri ≤ 10, dimensionless rotational speed 0 ≤ Ω ≤ 5 and nanoparticle concentration 0 ≤ ϕ ≤ 0.20 keeping the Grashof number fixed as Gr = 10⁴. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ω and Ri. Furthermore, the drag coefficient of the moving lid and Nusselt number of the hot wall are also computed to understand the effects of Ω and Ri on them. It is observed that the heat transfer greatly depends on the rotational speed of the cylinder, mixed convective strength and the nanoparticle concentration.     

Steady natural convection flows in a square cavity with linearly heated side wall(s)

The present numerical study deals with natural convection flow in a closed square cavity when the bottom wall is uniformly heated and vertical wall(s) are linearly heated whereas the top wall is well insulated. Non-linear coupled PDEs governing the flow have been solved by penalty finite element method with bi-quadratic rectangular elements. Numerical results are obtained for various values of Rayleigh number (Ra) (10³ ⩽ Ra ⩽ 10⁵) and Prandtl number (Pr) (0.7 ⩽ Pr ⩽ 10). Results are presented in the form of streamlines, isotherm contours, local Nusselt number and the average Nusselt as a function of Rayleigh number.     

Jet impingement interaction with cross flow in horizontal porous layer under thermal non-equilibrium conditions

In the present article the jet impingement cooling of heated portion of a horizontal surface immersed in a thermally non-equilibrium porous layer is considered for investigation numerically with the presence of a cross flow. The mathematical model is derived for steady, two-dimensional laminar flow based on Darcy model and two-energy equation for fluid and solid phases. A parametric study is carried out by varying the following parameters: cross flow to jet flow velocity ratio parameter (0 ⩽ M ⩽ 1); porosity scaled thermal conductivity ratio parameter (0.1 ⩽ K_r ⩽ 1000); heat transfer coefficient parameter (0.1 ⩽ H ⩽ 1000); Péclet number (1 ⩽ Pe ⩽ 1000) and Rayleigh number (10 ⩽ Ra ⩽ 100). The total average Nusselt number is defined based on the overall thermal conductivity, which is assumed to be the arithmetic mean of the porosity scaled thermal conductivity of the fluid and solid phases. The total average Nusselt number as well as the average Nusselt number for both fluid and solid phases is presented for different governing parameters. It is found that the presence of a weak cross flow in a jet impinging jet may degrade the heat transfer. The results show that the average Nusselt number calculated from the thermal equilibrium model are the maximum possible values and these values can be reproduced by large values of H × K_r.     

Jet impingement cooling of a horizontal surface in an unconfined porous medium: Mixed convection regime

Two-dimensional slot jet impingement cooling of an isothermal horizontal surface immersed in an unconfined porous medium is simulated numerically to gain insight into thermal characteristics under mixed convection conditions with the limitation of the Darcy model. The jet direction is considered to be perpendicular from the top to the horizontal heated element; therefore, the jet flow and the buoyancy driven flow are in opposite directions. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Péclet number (1 ? Pe ? 1000), Rayleigh number (10 ? Ra ? 100), half jet width (0.1 ? D ? 0.5), and the distance between the jet and the heated portion (0.1 ? H ? 1.0). It is found that the average Nusselt number increases with increase in either Rayleigh number or jet width for high values of Péclet number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. It is shown that mixed convection mode can cause minimum average Nusselt number at two values of Péclet number and a maximum average Nusselt number occurs in between theses two Péclet numbers at higher Rayleigh number due to counteraction of jet flow against buoyancy driven flow. Hence careful consideration must be given while designing a system of jet impingement cooling through porous medium.     

Vortex formation and heat transfer in turbulent flow past a transverse cavity with inclined frontal and rear walls

The process of vortex formation, distributions of pressure coefficients, and convective heat transfer in a turbulent flow past a cavity with a low aspect ratio and inclined frontal and rear walls were experimentally studied. The angle of wall inclination φ was varied in the interval from 30° to 90°. Visualization techniques were applied to trace the evolution of the flow with the angle φ as the transverse cavity became more open. Pressure fields in the longitudinal and transverse sections on the bottom wall of the cavity, and on its frontal and rear walls, were measured. The measured distributions of temperature in the longitudinal and transverse sections on the three heated walls, and the obtained thermographic fields over the whole heated surface, were used to calculate local and average heat-transfer coefficients. It is found that in the interval of wall inclination angles φ = 60–70° the flow in the cavity becomes unstable, with the primary vortex changing its structure from single-cellular to double-cellular. As a result, the distributions of static pressure and surface temperature across and along the cavity suffer dramatic changes. At smallest angles φ the flow re-attachment point gets displaced into the cavity to cause an abrupt growth of pressure and heat-transfer coefficients on the rear wall, which leads to a slight increase of the surface-mean pressure and heat transfer inside the cavity. At the angle of instability, φ = 60°, the local heat-transfer coefficient decreases markedly over the cavity span from the end faces of the cavity toward its center, and a most pronounced intensification of heat transfer is observed.     

Numerical study of hydrodynamic and heat transfer of nanofluid flow in microchannels containing micromixer

In this study heat transfer and fluid flow of Al₂O₃/water nanofluid in two dimensional parallel plate microchannel without and with micromixers have been investigated for nanoparticle volume fractions of ϕ = 0, ϕ = 4%  and base fluid Reynolds numbers of Re_f = 5, 20, 50. One baffle on the bottom wall and another on the top wall work as a micromixer and heat transfer enhancement device. A single-phase finite difference FORTRAN code using Projection method has been written to solve governing equations with constant wall temperature boundary condition. The effect of various parameters such as nanoparticle volume fraction, base fluid Reynolds number, baffle distance, height and order of arrangement have been studied. Results showed that the presence of baffles and also increasing the Re number and nanoparticle volume fraction increase the local and averaged heat transfer and friction coefficients. Also, the effect of nanoparticle volume fraction on heat transfer coefficient is more than the friction coefficient in most of the cases. It was found that the main mechanism of enhancing heat transfer or mixing is the recirculation zones that are created behind the baffles. The size of these zones increases with Reynolds number and baffle height. The fluid pushing toward the wall by the opposed wall baffle and reattaching of separated flow are the locations of local maximum heat transfer and friction coefficients.     

Turbulent separated convection flow adjacent to backward-facing step—effects of step height

Simulations of turbulent convection flow adjacent to a two-dimensional backward-facing step are presented to explore the effects of step height on turbulent separated flow and heat transfer. Reynolds number and duct’s height downstream from the step are kept constant at Re₀ = 28,000 and H = 0.19 m, respectively. Uniform and constant heat flux of q_w = 270 W/m² is specified at the stepped wall downstream from the step, while other walls are treated as adiabatic. The selection of the values for these parameters is motivated by the fact that measurements are available for this geometry and they can be used to validate the flow and heat transfer simulation code. Two-equation low-Reynolds-number model is employed to achieve the turbulent Prandtl number. The primary and secondary recirculation regions increase in size as the step height increases. The bulk temperature increases more rapidly as the step height increases. Increasing the step height causes the magnitude of the maximum turbulent kinetic energy to increase. Near the step and below the step height, the turbulent kinetic energy becomes smaller as the step height increases. Inside the recirculation region, magnitude of the peak friction coefficient does not significantly change with the increase of step height. The friction coefficient becomes smaller in magnitude with the increase of the step height. The peak Stanton number becomes smaller as the step height increases.     

The effect of nanofluids flow on mixed convection heat transfer over microscale backward-facing step

Laminar mixed convection flow over a 2D horizontal microscale backward-facing step (MBFS) placed in a duct is numerically investigated. The governing equations along with the boundary conditions are solved using the finite volume method (FVM). The upstream wall and the step wall are considered adiabatic, while the downstream wall is heated by uniform heat flux. The straight wall of the duct is maintained at a constant temperature that is higher than the inlet fluid temperature. Different types of nanoparticles such as Al₂O₃, CuO, SiO₂ and ZnO, with volume fractions in the range of 1–4% are used. The nanoparticles diameter was in the range of 25 nm ? d_p ? 70 nm. The expansion ratio was 2 and the step height was 0.96 μm. The Reynolds number was in the range of 0.05 ? Re ? 0.5. The results revealed that the Nusselt number increases with increasing the volume fraction and Reynolds number. The nanofluid of SiO₂ nanoparticles is observed to have the highest Nusselt number value. It is also found that the Nusselt number increases with the decrease of nanoparticle diameter. However, there is no recirculation region was observed at the step and along the duct.     

Experimental investigation of mixed convection heat transfer from longitudinal fins in a horizontal rectangular channel

Mixed convection heat transfer from longitudinal fins inside a horizontal channel has been investigated for a wide range of modified Rayleigh numbers and different fin heights and spacings. An experimental parametric study was made to investigate effects of fin spacing, fin height and magnitude of heat flux on mixed convection heat transfer from rectangular fin arrays heated from below in a horizontal channel. The optimum fin spacing to obtain maximum heat transfer has also been investigated. During the experiments constant heat flux boundary condition was realized and air was used as the working fluid. The velocity of fluid entering channel was kept nearly constant (0.15 ? w_in ? 0.16 m/s) using a flow rate control valve so that Reynolds number was always about Re = 1500. Experiments were conducted for modified Rayleigh numbers 3 × 10⁷ < Ra¹ < 8 × 10⁸ and Richardson number 0.4 < Ri < 5. Dimensionless fin spacing was varied from S/H = 0.04 to S/H = 0.018 and fin height was varied from H_f/H = 0.25 to H_f/H = 0.80. For mixed convection heat transfer, the results obtained from experimental study show that the optimum fin spacing which yields the maximum heat transfer is S = 8–9 mm and optimum fin spacing depends on the value of Ra¹.     

Experimental investigations on heat transfer and frictional characteristics of a turbulator roughened solar air heater duct

An experimental investigation has been carried out to study the heat transfer coefficient and friction factor by using artificial roughness in the form of specially prepared inverted U-shaped turbulators on the absorber surface of an air heater duct. The roughened wall is uniformly heated while the remaining three walls are insulated. These boundary conditions correspond closely to those found in solar air heaters.The experiments encompassed the Reynolds number range from 3800 to 18000; ratio of turbulator height to duct hydraulic mean diameter is varied from, e/D_h = 0.0186 to 0.03986 (D_h = 37.63 mm and e = 0.7 to 1.5 mm) and turbulator pitch to height ratio is varied from, p/e = 6.67 to 57.14 (p = 10 to 40 mm). The angle of attack of flow on turbulators, α = 90° kept constant during the whole experimentation. The heat transfer and friction factor data obtained is compared with the data obtained from smooth duct under similar geometrical and flow conditions. As compared to the smooth duct, the turbulator roughened duct enhances the heat transfer and friction factor by 2.82 and 3.72 times, respectively. The correlations have been developed for area averaged Nusselt number and friction factor for turbulator roughened duct.