Numerical study of mixed convection within porous square cavities using Bejan’s heatlines: Effects of thermal aspect ratio and thermal boundary conditions

The present numerical study deals with mixed convection flows within square enclosures filled with porous media. The influence of various thermal boundary conditions on bottom and side walls based on thermal aspect ratio (A) is investigated for a wide range of parameters (1 ? Re ? 100, 0.015 ? Pr ? 7.2, 10^?5 ? Da ? 10^?3 and 10³ ? Gr ? 10⁵). A penalty finite element method with bi-quadratic elements has been used to investigate the results in terms of streamlines, isotherms and heatlines and average Nusselt numbers. Lid driven effect is dominant at low Darcy number (Da = 10^?5), whereas buoyancy driven effect is dominant at high Darcy numbers (Da = 10^?4 and Da = 10^?3) for Re = 1. Asymmetric pattern is observed in isotherms and heatlines for Re = 100. It is found that thermal gradient is high at the center of the bottom wall for A = 0.1 due to large dense heatlines at that zone and that is low for A = 0.9 irrespective of Re, Pr and Gr. Overall heat transfer rates are higher for A = 0.1 compared to other thermal aspect ratios (A = 0.5, A = 0.9) irrespective of Darcy number, Prandtl number and Reynolds number.     

Analysis of Bejan’s heatlines on visualization of heat flow and thermal mixing in tilted square cavities

This article analyzes the detailed heat transfer phenomena during natural convection within tilted square cavities with isothermally cooled walls (BC and DA) and hot wall AB is parallel to the insulated wall CD. A penalty finite element analysis with bi-quadratic elements has been used to investigate the results in terms of streamlines, isotherms and heatlines. The present numerical procedure is performed over a wide range of parameters (10³ ? Ra ? 10⁵,0.015 ? Pr ? 1000,0° ? φ ? 90°). Secondary circulations cells are observed near corner regions of cavity for all φ’s at Pr = 0.015 with Ra = 10⁵. Two asymmetric flow circulation cells are found to occupy the entire cavity for φ = 15° at Pr = 0.7 and Pr = 1000 with Ra = 10⁵. Heatlines indicate that the cavity with inclination angle φ = 15° corresponds to large convective heat transfer from the wall AB to wall DA whereas the heat transfer to wall BC is maximum for φ = 75°. Heat transfer rates along the walls are obtained in terms of local and average Nusselt numbers and they are explained based on gradients of heatfunctions. Average Nusselt number distributions show that heat transfer rate along wall DA is larger for lower inclination angle (φ = 15°) whereas maximum heat transfer rate along wall BC occur for higher inclination angle (φ = 75°).     

Non-Newtonian power-law flow and heat transfer across a pair of side-by-side circular cylinders

Flow and heat transfer of non-Newtonian power-law fluids across a pair of identical circular cylinders in side-by-side arrangement are investigated numerically by solving the continuity, momentum and energy equations along with the appropriate boundary conditions. The numerical calculations are performed in an unconfined computational domain for the following range of physical parameters: Reynolds number, Re = 1–40 and power-law index, n = 0.4–1.8 (covering shear-thinning, n < 1; Newtonian, n = 1 and shear-thickening, n > 1 behaviors) for gap ratio, T/D = 1.5–4.0 at a constant Prandtl number of 50. The global characteristics such as drag coefficients and average Nusselt number, etc. are calculated and the representative streamline and isotherm contours are presented for the above range of conditions. It has been found that the individual and overall drag coefficients decrease and the average Nusselt number increases with Reynolds number for all T/D and n considered here. The heat transfer is found higher in shear-thinning fluids than Newtonian fluids and followed by shear-thickening fluids for 1.5 ? T/D ? 4.0 and 1 ? Re ? 40.     

Numerical study of heat transfer by natural convection and surface thermal radiation in an open cavity receiver

In this work the numerical results of natural convection and surface thermal radiation in an open cavity receiver considering large temperature differences and variable fluid properties are presented. Numerical calculations were conducted for Rayleigh number (Ra) values in the range of 10⁴–10⁶. The temperature difference between the hot wall and the bulk fluid (ΔT) was varied between 100 and 400 K, and was represented as a dimensionless temperature difference (φ) for the purpose of generalization of the trends observed. Noticeable differences are observed between the streamlines and temperature fields obtained for φ = 1.333 (ΔT = 400 K) and φ = 0.333 (ΔT = 100 K). The total average Nusselt number in the cavity increased by 79.8% (Ra = 10⁶) and 88.0% (Ra = 10⁴) as φ was varied from 0.333 to 1.333. Furthermore the results indicate that for large temperature differences (0.667 ? φ ? 1.333) the radiative heat transfer is more important that convective heat transfer.     

A porous model for the square pin-fin heat sink situated in a rectangular channel with laminar side-bypass flow

This work illustrates the compact heat sink simulations in forced convection flow with side-bypass effect. Conventionally, the numerical study of the fluid flow and heat transfer in finned heat sinks employs the detailed model that spends a lot of computational time. Therefore, some investigators begin to numerically study such problem by using the compact model (i.e. the porous approach) since the regularly arranged fin array can be set as a porous medium. The computations of the porous approach model will be faster than those of the detailed mode due to the assumption of the volume-averaging technique. This work uses the Brinkman–Forchheimer model for fluid flow and two-equation model for heat transfer. A configuration of in-line square pin-fin heat sink situated in a rectangular channel with fixed height (H = 23.7 mm), various width and two equal-spacing bypass passages beside the heat sink is successfully studied. The pin-fin arrays with various porosities (ε = 0.358–0.750) and numbers of pin-fins (n = 25–81), confined within a square spreader whose side length (L) is 67 mm, are employed. The numerical results suggest that, within the range of present studied parameters (0.358 ? ε ? 0.750, 25 ? n ? 81 and 1 ? W/L ? 5), the pin-fin heat sink with ε = 0.750 and n = 25 is the optimal cooling configuration based on the maximum ratio of Nusselt number to dimensionless pumping power (Nu/(ΔP × Re³)). Besides, based on medium Nu/(ΔP × Re³) value and suitable channel size, W/L = 2–3 is suggested as the better size ratio of channel to heat sink.     

Unsteady heat transfer from an oblate/prolate spheroid

Numerical methods are used to investigate the transient heat transfer from an oblate/prolate spheroid to a steady stream of viscous, incompressible fluid. The temperature of the spheroid is considered spatially uniform but not constant in time. The momentum and heat balance equations were solved numerically in oblate/prolate spheroidal coordinates system. The solutions span the parameter ranges 10 ? Re ? 100 (for the oblate spheroid), 10 ? Re ? 200 (for the prolate spheroid), Pr = 1, 10 and axis ratio ε, 0.1 ? ε ? 0.9. The computations were focused on the influence of the axis ratio and volume heat capacity ratio on the heat transfer rate.     

Effects of dilution with carbon dioxide on the laminar burning velocity and flame stability of H2–CO mixtures at atmospheric condition

The objective of this investigation was to study the effect of dilution with CO₂ on the laminar burning velocity and flame stability of syngas fuel (50% H₂–50% CO by volume). Constant pressure spherically expanding flames generated in a 40 l chamber were used for determining unstretched burning velocity. Experimental and numerical studies were carried out at 0.1 MPa, 302 ± 3 K and ? = 0.6–3.0 using fuel-diluent and mixture-diluent approaches. For H₂–CO–CO₂–O₂–N₂ mixtures, the peak burning velocity shifts from ? = 2.0 for 0% CO₂ in fuel to ? = 1.6 for 30% CO₂ in fuel. For H₂–CO–O₂–CO₂ mixtures, the peak burning velocity occurred at ? = 1.0 unaffected by proportion of CO₂ in the mixture. If the mole fraction of combustibles in H₂–CO–O₂–CO₂ mixtures is less than 32%, then such mixtures are supporting unstable flames with respect to preferential diffusion. The analysis of measured unstretched laminar burning velocities of H₂–CO–O₂–CO₂ and H₂–CO–O₂–N₂ mixtures suggested that CO₂ has a stronger inhibiting effect on the laminar burning velocity than nitrogen. The enhanced dilution effect of CO₂ could be due to the active participation of CO₂ in the chemical reactions through the following intermediate reaction CO + OH ? CO₂ + H.     

Confined,milliscale unsteady laminar impinging slot jets and surface Nusselt numbers

Different modes of unsteadiness which develop within confined, laminar impinging slot jets of millimeter-scale are considered, including experimental measurements and numerical predictions of different flow characteristics, including spatially-resolved distributions of local Nusselt numbers measured on a constant heat flux surface. The effects of Reynolds number, and nozzle-to-plate distance on the local Nusselt number are investigated for a slot nozzle width B of 1.0 mm, Reynolds numbers Re from 120 to 200, nozzle-to-plate distances H/B from 0.75 to 12.5, and a nozzle aspect ratio y/B of 50. Observed are several different types of unsteady slot jet behavior, including: (i) a flow fluctuations/flapping motion mode of unsteadiness which is present for B = 1.0 mm, 4.75 ? H/B ? 5.5, and 120 ? Re ? 140, (ii) an intermittent flapping motion of the jet column which is present for B = 1.0 mm, 9 ? H/B ? 11.25, and 120 ? Re ? 200, and (iii) a continuous sinusoidal oscillation state, which is observed to be present for Re = 160 and H/B = 10. The flow fluctuations/flapping motion mode of unsteadiness, and the intermittent flapping motion of the jet column are both associated with local maxima in local, stagnation point Nusselt number distributions. The variations of these stagnation point Nusselt numbers associated with these two modes of unsteadiness are characterized by correlations which provide the dependence upon Reynolds number and normalized nozzle-to-plate distance ratio, H/B. Also described is the lateral variation of local Nusselt numbers for five nozzle-to-plate distances H/B of 2, 6, 8, 10, and 12, and Reynolds numbers from 120 to 200.     

Research on the shell-side thermal performances of heat exchangers with helical tube coils

This paper presents the results of experimental research on shell-side heat transfer coefficient concerning 3 heat exchangers with helical coils. Measurements were carried in laboratory and the following correlation was found to be adequate Nu = 0.50 ? Re^0.55 ? Pr ^1/3 ? (η/η_w)^0.14 where Re and Nu are based on shell-side hydraulic diameter.     

Determination of hematocrit using on-line conductance cell

Hematocrit has been considered as an important marker of oxygen carrying capacity of the blood associated with whole blood viscosity to assess the mortality risk of both cardiovascular, cerebral, and kidney diseases. The present study developed a new on-line conductivity cell to measure the hematocrit of whole blood using a bipolar square-wave voltage signal at a frequency of 5 kHz. By applying such a voltage signal to a blood flowing in a range of 1.2–3.0 mL/min, the electrolyte effect of blood plasma, the conductive and capacitive effects of blood cells, and the sedimentation effect of erythrocytes on the conductivity of whole blood could be minimized for an accurate hematocrit measurement. The coefficient of correlation between the present method and conventional microcentrifuge method showed an excellent linear relationship. A new equation between the specific conductance and Hct of whole blood was obtained: C = 12.561 ? 0.1527 Hct (P < 0.001).     

Biodiesel production from palm oil via heterogeneous transesterification

This paper presents the study of the transesterification of palm oil via heterogeneous process using montmorillonite KSF as heterogeneous catalyst. This study was carried out using a design of experiment (DOE), specifically response surface methodology (RSM) based on four-variable central composite design (CCD) with α (alpha) = 2. The transesterification process variables were reaction temperature, x₁ (50–190 °C), reaction period, x₂ (60–300 min), methanol/oil ratio, x₃ (4–12 mol mol^?1) and amount of catalyst, x₄ (1–5 wt%). It was found that the yield of palm oil fatty acid methyl esters (FAME) could reach up to 79.6% using the following reaction conditions: reaction temperature of 190 °C, reaction period at 180 min, ratio of methanol/oil at 8:1 mol mol^?1 and amount of catalyst at 3%.     

Finite element based heatline approach to study mixed convection in a porous square cavity with various wall thermal boundary conditions

A penalty finite element method based simulation is performed to analyze the influence of various walls thermal boundary conditions on mixed convection lid driven flows in a square cavity filled with porous medium. The relevant parameters in the present study are Darcy number (Da = 10^?5 ? 10^?3), Grashof number (Gr = 10³ ? 10⁵), Prandtl number (Pr = 0.7–7.2), and Reynolds number (Re = 1–10²). Heatline approach of visualizing heat flow is implemented to gain a complete understanding of complex heat flow patterns. Patterns of heatlines and streamlines are qualitatively similar near the core for convection dominant flow for Da = 10^?3. Symmetric distribution in heatlines, similar to streamlines is observed irrespective of Da at higher Gr in natural convection dominant regime corresponding to smaller values of Re. A single circulation cell in heatlines, similar to streamlines is observed at Da = 10^?3 for forced convection dominance and heatlines are found to emanate from a large portion on the bottom wall illustrating enhanced heat flow for Re = 100. Multiple circulation cells in heatlines are observed at higher Da and Gr for Pr = 0.7 and 7.2. The heat transfer rates along the walls are illustrated by the local Nusselt number distribution based on gradients of heatfunctions. Wavy distribution in heat transfer rates is observed with Da ? 10^?4 for non-uniformly heated walls primarily in natural convection dominant regime. In general, exponential variation of average Nusselt numbers with Grashof number is found except the cases where the side walls are linearly heated. Overall, heatlines are found to be a powerful tool to analyze heat transport within the cavity and also a suitable guideline on explaining the Nusselt number variations.     

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.     

Hydrothermal preparation and electrochemical properties of Gd3+ and Bi3+, Sm3+, La3+, and Nd3+ codoped ceria-based electrolytes for intermediate temperature-solid oxide fuel cell

The structure, the thermal expansion coefficient, electrical conductivities of Ce_0.8Gd_0.2?xM_xO_2?δ (for M: Bi, x = 0–0.1, and for M: Sm, La, and Nd, x = 0.02) solid solutions, prepared for the first time hydrothermally, are investigated. The uniformly small particle size (28–59 nm) of the materials allows sintering of the samples into highly dense ceramic pellets at 1300–1400 °C. The maximum conductivity, σ_700 °C around 4.46 × 10^?2 S cm^?1 with E_a = 0.52 eV, is found at x = 0.1 for Bi-co-doping. Among various metal-co-dopings, for x = 0.02, the maximum conductivity, σ_700 °C around 2.88 × 10^?2 S cm^?1 with E_a = 0.67 eV, is found for Sm-co-doping. The electrolytic domain boundary (EDB) of Ce_0.8Gd_0.1Bi_0.1O_2?δ is found to be 1.2 × 10^?19 atm, which is relatively lower than that of the singly doped samples. The thermal expansion coefficients, determined from high-temperature X-ray data are 11.6 × 10^?6 K^?1 for the CeO₂, 12.1 × 10^?6 K^?1 for Ce_0.8Gd_0.2O_2?δ, and increase with co-doping to 14.2 × 10^?6 K^?1 for Ce_0.8Gd_0.18Bi_0.02O_2?δ. The maximum power densities for the single cell based on the codoped samples are higher than that of the singly doped sample. These results suggest that co-doping can further improve the electrical performance of ceria-based electrolytes.     

Experimental and kinetic modeling study of methyl butanoate and methyl butanoate/methanol flames at different equivalence ratios and C/O ratios

Premixed laminar methyl butanoate/oxygen/argon and methyl butanoate/methanol/oxygen/argon flames were studied with tunable synchrotron vacuum ultraviolet (VUV) photoionization and molecular-beam sampling mass spectrometry at 30 torr (4.0 kPa). Three flames were investigated in the experiment: MB (methyl butanoate) flame F1.54 (? = 1.54, C/O = 0.479), MB flame F1.67 (? = 1.67, C/O = 0.511) and MB/methanol flame F1.67M (? = 1.67, C/O = 0.479). By measuring the signal intensities at different distances from the burner surface, the mole fraction profiles of intermediates are derived. Experimental results show that the flame front shifts downstream and peak mole fractions of intermediates increase remarkably with the increase of equivalence ratio for pure MB fuel. When methanol is added, the peak mole fractions of most intermediates including those of soot precursors decrease remarkably at the same equivalence ratio, while peaks of soot precursors vary little (only slightly decreasing) at same C/O ratio. It is concluded that the formation of soot precursors is more sensitive to C/O ratio than to equivalence ratio. Besides, more CO₂ is produced near the burner surface in MB flame than that in MB/methanol flame, and this validates an early production of CO₂ in methyl ester oxidation. In addition, a modified MB detailed mechanism is used to model flame structure, and improved agreements between the experimental and predicted results are realized. Based on the simulation results, reaction flux and sensitivity are analyzed for CO₂ and C₃H₃, respectively.     

Convective diffusion from strip-like micro-probes into colloidal suspensions

Full equations of convective diffusion are solved numerically for a strip-like (2D) electrodiffusion friction probe in a stream of microdisperse liquid, assuming a non-linear near-to-wall velocity profile ranging from simple shear flow (p = 1) to ideal slip (p = 0). The range of generalized Peclet number H from H = 0.01 (almost pure spatial diffusion) to H = 100 (diffusion layer with negligible longitudinal diffusion) covers all cases of possible experimental relevance. The main result is expressed as a relative deviation of actual total diffusion flux N from its diffusion-layer approximation N_DLA, Ψ = N/N_DLA ? 1.     

The effect of different inlet geometries on laminar flow combined convection heat transfer inside a horizontal circular pipe

The effect of different inlet geometries on laminar air flow combined convection heat transfer inside a horizontal circular pipe has been experimentally investigated for Reynolds number range of 400–1600, and the Grashof number range from 3.12 × 10⁵ to 1.72 × 10⁶. The experimental setup consists of an aluminum circular pipe as a heated section with 30 mm inside diameter and 900 mm heated length (L/D = 30) with different inlet geometries. A wall boundary heating condition of a uniform heat flux was imposed. The inlet configurations used in this paper are calming sections having the same inside diameter as the heated pipe but with variable lengths of L_calm. = 600 mm (L/D = 20), L_calm. = 1200 mm (L/D = 40), L_calm. = 1800 mm (L/D = 60), L_calm. = 2400 mm (L/D = 80), sharp-edged and bell-mouth. It was found that the surface temperature values for calming section length corresponding to (L/D = 80) were higher than other inlet geometries due to the lower mass flow rate and higher flow resistance. It was also observed that the Nusselt number values for bell-mouth inlet geometry were higher than other inlet geometries due to the differences in the average temperatures and densities of the air. The average heat transfer results were correlated with an empirical correlation in terms of dependent parameters of Grashof, Prandtl and Reynolds numbers. The proposed correlation was compared with available literature and it shows reasonable agreement.     

Unsteady fluid mechanics and heat transfer study in a double-tube air–combustor heat exchanger with porous medium

Fluid mechanics and heat transfer are studied in a double-tube heat exchanger that uses the combustion gases from natural gas in a porous medium located in a cylindrical tube to warm up air that flows through a cylindrical annular space. The mathematical model is constructed based on the equations of continuity, linear momentum, energy and chemical species. Unsteady fluid mechanics and heat transfer by forced gas convection in the porous media, with combustion in the inner tube, coupled to the forced convection of air in the annular cylindrical space are predicted by use of finite volumes method. Numerical simulations are made for four values of the annular air flow Reynolds number in the range 100 ? Re ? 2000, keeping constant the excess air ψ = 4.88, the porosity ε = 0.4, and the air–fuel mixture inlet speed Uo = 0.43 m/s. The results obtained allow the characterization of the velocity and temperature distributions in the inner tube and in the annular space, and at the same time to describe the displacement of the moving combustion zone and the annular porous media heat exchanger thermal efficiency. It is concluded that the temperature increase is directly related to the outer Reynolds number.     

Biomass production and allocation in Jatropha curcas L. seedlings under different levels of drought stress

In a greenhouse experiment we applied three levels of drought stress and monitored growth variables and biomass production of Jatropha curcas seedlings propagated from three seed accessions. We determined biomass allocation, allometric relationships and plant traits. Well-watered J. curcas seedlings grew 0.81 ± 0.15 cm day^?1 in length and produced 1.49 ± 0.31 g dry biomass day^?1. Under medium stress (40% plant available water) the plants maintained a similar stem shape, although they grew at lower rate (stem length: 0.28 ± 0.11 cm day^?1; dry biomass production: 0.64 ± 0.18 g day^?1). Seedlings under extreme drought stress (no irrigation) stopped growing, started shedding leaves and showed shrinking stem diameter from the 12th day after the start of the drought treatment. The drought treatment did not influence the wood density (0.26 g cm^?3). The root/shoot ratio of the wet treatment was 0.27, which is low compared to other tropical trees. Both the biomass allocation and root/shoot were significantly influenced by drought. Plants of the different accessions were uniform in biomass production and plant traits. The allometric relationship predicting total aboveground biomass (B) with the stem diameter (D) (B = 0.029 × D^2.33; R² = 0.89) fits well in universal scaling models in which the exponent is expected to converge to ～2.67 at plant maturity. Based on a small validation data set from mature J. curcas individuals this hypothesis could be confirmed. A second regression model predicts the total leaf area (LA) as a function of stem diameter (LA = 2.03 × D^2.41; R² = 0.95). The estimated transpiration crop coefficient K_cb ranged from 0.51 to 0.60 for the well-watered plants.     

Laminar free convection from a horizontal semi-circular cylinder to power-law fluids

Extensive numerical results on the flow and thermal fields are presented for free convection from a semi-circular cylinder (flat base upward) immersed in quiescent power-law fluids for the following ranges of conditions: Grashof number, 10 ? Gr ? 10⁵, Prandtl number, 0.72 ? Pr ? 100, and power-law index, 0.2 ? n ? 1.8. The heat transfer characteristics are analyzed in terms of the isotherm patterns, local and average Nusselt number as functions of the pertinent dimensionless parameters. The flow field is visualized in terms of the streamline patterns adjacent to the surface of the cylinder for a range of values of the Grashof number, Prandtl number and power-law index. A separated flow region forms at as low values of the Prandtl number as Pr = 0.72 for n ? 1 (Newtonian and shear-thickening fluids); whereas for shear-thinning fluids (n < 1), the flow remains attached to the cylinder surface over the range of conditions encompassed here. The bubble size grows with Grashof number and it shrinks with Prandtl number. In order to quantify the deviation from the Newtonian behaviour, the normalized values of average Nusselt number are analyzed as a function of the power-law index. In addition, a correlation is proposed for average Nusselt number as a function of the Grashof number, Prandtl number and power-law index. In general terms, shear-thinning fluid behaviour enhances heat transfer whereas shear-thickening has adverse influence on it.