Performance evaluation of mixed convection in an inclined square channel with uniform temperature walls

Numerical analyses were performed for the effect of inclined angle on the mixing flow in a square channel with uniform temperature walls (T_w = 30 °C) and inlet temperature (T₀ = 10 °C). Three-dimensional governing equations were solved numerically for Re = 100, Pr = 0.72 and various inclined angles (from ?90° to 90°). Three-dimensional behavior of fluid in a channel was examined for each angle. Thermal performance was evaluated using the relationship between Nusselt number ratio and pressure loss ratio with and without buoyancy induced flow as a parameter of inclined angles. High heat transfer and low pressure loss region was from ?15° to ?60° in thermal performance using mean Nusselt number ratio.     

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°).     

Turbulent forced convection effectiveness of alumina–water nanofluid in a circular tube with elevated inlet fluid temperatures: An experimental study

The present study aims to explore experimentally the influence of elevated inlet fluid temperature on the turbulent forced convective heat transfer effectiveness of using alumina–water nanofluid over pure water in an iso-flux heated horizontal circular tube at a fixed heating power. A copper circular pipe of inner diameter 3.4 mm was used in the forced convection experiments undertaken for the pertinent parameters in the following ranges: the inlet fluid temperature, T_in = 25 °C, 37 °C and 50 °C; the Reynolds number, Re_bf = 3000–13,000; the mass fraction of the alumina nanoparticles in the water-based nanofluid formulated, ω_np = 0, 2, 5, and 10 wt.%; and the heating flux, q_o^″ = 57.8–63.1 kW/m². The experimental results clearly indicate that the turbulent forced convection heat transfer effectiveness of the alumina–water nanofluid over that of the pure water can be further uplifted by elevating its inlet temperature entering the circular tube well above the ambient, thereby manifesting its potential as an effective warm functional coolant. Specifically, an increase in the averaged heat transfer enhancement of more than 44% arises for the nanofluid of ω_np = 2 wt.% as the inlet fluid temperature is increased from 25 °C to 50 °C.     

Natural convection in tilted rectangular enclosures with a vertically situated hot plate inside

A numerical study of laminar natural convection in tilted rectangular enclosures that contain a vertically situated hot plate is performed. The plate is very thin and isothermal on both lateral ends, and it acts as a heat source within the medium. Three surfaces of the rectangular enclosure are insulated while one lateral surface is cold. Navier–Stokes equations, continuity equation and the energy equation, along with the Boussinesq approximation, are expressed in the form of vorticity-transport equations. All the pertinent equations are solved using the finite volume method with SIMPLE algorithm. The Rayleigh numbers and the tilt angle of the enclosure are ranged from 10⁵ to 10⁷ and from 0° to 90°, respectively. The aspect ratios of the rectangular enclosures that are considered in this study are A = 1 and A = 2. The isotherms and streamlines are produced for various Rayleigh numbers and geometrical conditions, and steady-state Nusselt numbers are computed. The steady-state plate-surface-averaged Nusselt numbers are computed for each case as a function of Rayleigh number and other non-dimensional geometrical parameters and a correlation useful for practical problems was derived.     

Influence of natural convection on the melting of ice block surrounded by water on all sides

The ice block at initial temperature T_is = 0 °C is fixed at the center of a long, prismatic enclosure with isothermal vertical walls and insulated horizontal walls. The enclosure is completely filled with water at initial temperature T_il = 0 °C. Six numerical simulations were performed by varying vertical wall temperatures from T_W = 2 to 12 °C (range of Rayleigh number from 4.22 × 10⁶ to 2.28 × 10⁷). In the case of T_W > 8 °C the ice melts faster from above and for T_W < 8 °C from below. In the case of T_W = 8 °C, two vortices are separated by nearly vertical 4 °C isotherm and the average Nusselt number remains constant during the convection dominated regime.     

Combined convection heat transfer for thermally developing aiding flow in an inclined circular cylinder with constant heat flux

Experiments have been conducted to study the local and average heat transfer by mixed convection for hydrodynamically fully developed, thermally developing and thermally fully developed laminar air flow in an inclined circular cylinder. The experimental setup consists of aluminum cylinder as test section with 30 mm inside diameter and 900 mm heated length (L/D = 30), is subjected to a constant wall heat flux boundary condition. The investigation covers Reynolds number range from 400 to 1600, heat flux is varied from 70 W/m² to 400 W/m² and cylinder angles of inclination including 30°, 45° and 60°. The hydrodynamically fully developed condition has been achieved by using aluminum entrance section pipes (calming sections) having the same inside diameter as test section pipe but with variable lengths. The entrance sections included two long calming sections, one with length of 180 cm (L/D = 60), another one with length of 240 cm (L/D = 80) and two short calming sections with lengths of 60 cm (L/D = 20), 120 cm (L/D = 40). The results present the surface temperature distribution along the cylinder length, the local and average Nusselt number distribution with the dimensionless axial distance Z⁺. For all entrance sections, the results showed an increase in the Nusselt number values as the heat flux increases and as the angle of cylinder inclination moves from θ = 60° inclined cylinder to θ = 0° horizontal cylinder. The mixed convection regime has been bounded by the convenient selection of Re number range and the heat flux range, so that the obtained Richardson numbers (Ri) is varied approximately from 0.13 to 7.125. The average Nusselt numbers have been correlated with the (Rayleigh numbers/Reynolds numbers) in empirical correlations.     

Experimental study of forced convection heat transfer from a cam shaped tube in cross flows

An experimental investigation has been conducted to clarify forced convection heat transfer characteristic and flow behavior of an isothermal cam shaped tube in cross flow. The range of angle of attack and Reynolds number based on an equivalent circular tube are within 0° < α < 180° and 1.5 × 10⁴ < Re_eq < 2.7 × 10⁴, respectively.The results show that the mean heat transfer coefficient is a maximum at about α = 90° over the whole range of the Reynolds numbers. It is found that thermal hydraulic performance of the cam shaped tube is larger than that of a circular tube with the same surface area except for α = 90° and 120°. Furthermore, the effect of the diameter of the cam shaped tube upon the thermal hydraulic performance is discussed.     

Generalized correlations for predicting heat transfer and pressure drop in plate heat exchanger channels of arbitrary geometry

Characteristics of the flow in chevron plate heat exchangers are investigated through visualization tests of channels with β = 28° and β = 61°. Mathematical model is then developed with the aim of deriving correlations for prediction of f and Nu for flow in channels of arbitrary geometry (β and b/l). Thermal and hydraulic characteristics are evaluated using analytical solutions for the entrance and fully developed regions of a sinusoidal duct adapted to the basic single cell. The derived correlations are finally adjusted so as to agree with experimental results from tests on channels with β = 28° and β = 65°. f and Nu calculated by the presented correlations are shown to be consistent with experimental data from the literature at Re = 2–10,000, β = (15–67)° and b/l = 0.26–0.4.     

Wide-optical bandgap with improved conductivity p-μc-Si:Ox:H films prepared by Cat-CVD

Boron-doped hydrogenated microcrystalline silicon oxide (p-μc-Si:O_x:H) films have been deposited using catalytic chemical vapor deposition (Cat-CVD). The single-coiled tungsten catalyst temperature (T_fil) was varied from 1850 to 2100 °C and films were deposited on glass substrates at the temperatures (T_sub) of 100–300 °C. Different catalyst-to-substrate distances of 3–5 cm and deposition pressures from 0.1 to 0.6 Torr were considered.Optical and electrical characterizations have been made for the deposited samples. The sample transmittance measurement shows an optical-bandgap (Eg_opt) variation from 1.74 to 2.10 eV as a function of the catalyst and substrate temperatures. One of the best window materials was obtained at T_sub=100 °C and T_fil=2050 °C, with Eg_opt=2.10 eV, dark conductivity of 3.0×10^?3 S cm^?1 and 0.3 nm s^?1 deposition rate.     

Natural convection of water-based nanofluids in an inclined enclosure with a heat source

This study investigates natural convection heat transfer of water-based nanofluids in an inclined square enclosure where the left vertical side is heated with a constant heat flux, the right side is cooled, and the other sides are kept adiabatic. The governing equations are solved using polynomial differential quadrature (PDQ) method. Calculations were performed for inclination angles from 0° to 90°, solid volume fractions ranging from 0% to 20%, constant heat flux heaters of lengths 0.25, 0.50 and 1.0, and a Rayleigh number varying from 10⁴ to 10⁶. The ratio of the nanolayer thickness to the original particle radius is kept at a constant value of 0.1. The heat source is placed at the center of the left wall. Five types of nanoparticles are taken into consideration: Cu, Ag, CuO, Al₂O₃, and TiO₂. The results show that the average heat transfer rate increases significantly as particle volume fraction and Rayleigh number increase. The results also show that the length of the heater is also an important parameter affecting the flow and temperature fields. The average heat transfer decreases with an increase in the length of the heater. As the heater length is increased, the average heat transfer rate starts to decrease for a smaller inclination angle (it starts to decrease with inclination at 90° for ? = 0.25, 60° for ? = 0.50, 45° for ? = 1.0, respectively).     

Heat flow visualization for natural convection in rhombic enclosures due to isothermal and non-isothermal heating at the bottom wall

Analysis has been carried out for the energy distribution and thermal mixing in steady laminar natural convective flow through the rhombic enclosures with various inclination angles, φ for various industrial applications. Simulations are carried out for various regimes of Prandtl (Pr) and Rayleigh (Ra) numbers. Dimensionless streamfunctions and heatfunctions are used to visualize the flow and energy distribution, respectively. Multiple flow circulations are observed at Pr = 0.015 and 0.7 for all φs at Ra = 10⁵. On the other hand, two asymmetric flow circulation cells are found to occupy the entire cavity for φ = 75° at higher Pr (Pr = 7.2 and 1000) and Ra (Ra = 10⁵). Heatlines are found to be parallel circular arcs connecting the cold and hot walls for the conduction dominant heat transfer at Ra = 10³. The enhanced convective heat transfer is explained with dense heatlines and convective loop of heatlines at Ra = 10⁵. Heatlines clearly demonstrate that the left wall receives heat from the bottom wall as heatlines directly connect both the walls whereas the convective heat circulation cells play lead role to distribute the heat along the right wall, especially for smaller φs. On the other hand, the heat flow is evenly distributed to both side walls at higher φs via convection as well as direct conductive transport. Significant convective heat transfer from the bottom hot wall to the left cold wall occurs for φ = 30° cavity whereas the heat transfer to the right cold wall is maximum for φ = 75° irrespective of Pr. Average Nusselt number studies also show that φ = 30° cavity gives maximum heat transfer rate from the bottom to left wall irrespective of Pr in isothermal heating case. On the other hand, enhanced thermal mixing occurs at φ = 75° for both isothermal and non-isothermal heating strategies except at Pr = 0.015 in isothermal heating case.     

Heat transfer and pressure drop properties of high viscous solutions in plate heat exchangers

Heat transfer and pressure drop characteristics of an absorbent salt solution in a commercial plate heat exchanger serving as a solution sub-cooler in the high loop of triple-effect absorption refrigeration cycle was investigated. The main objectives of this research were to establish the correlation equations to predict the heat transfer and pressure drop and to analyze and optimize the operating parameters for use in the design of absorption systems.In order to conduct above studies, a single-pass cross-corrugated ALFA-LAVAL plate heat exchanger, Model PO1-VG, with capacity of 14,650 W (50,000 Btu/h) was used. In order to evaluate the performance, hot solution inlet temperatures from 55 °C (130 °F) to 77 °C (170 °F), and inlet temperature differences from 14 °C (25 °F) to 20 °C (35 °F) were used. The cold side of the heat exchanger was operated to match the equal heat capacity rate of hot side.Based on the empirical models proposed in the literature, a program was developed and experimental data were curve fitted. From the best-fitted curves, the power-law equations for heat transfer and pressure losses were established and the performance was evaluated.In the hot salt solution side, the Reynolds number was varied from 250 to 1100 and the resulting Nusselt number varied from 7.4 to 15.8. The measured overall heat transfer coefficient U_overall varied from 970 W/m² °C (170 Btu/h ft² °F) to 2270 W/m² °C (400 Btu/h ft² °F) and the Fanning friction factor in the absorbent side of the heat exchanger varied from 5.7 to 7.6. The correlation equations developed to predict the heat transfer and friction factor perfectly agree with the experimental results. Those equations can be used to predict the performance of any solution with Prandtl numbers between 82 and 174, for heat exchangers with similar geometry.     

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.     

Natural convection and fluid flow in inclined enclosure with a corner heater

The phenomena of natural convection in an inclined square enclosure heated via corner heater have been studied numerically. Finite difference method is used for solving momentum and energy equations in the form of stream function–vorticity. One wall of the enclosure is isothermal but its temperature is colder than that of heaters while the remaining walls are adiabatic. The numerical procedure adopted in this analysis yields consistent performance over a wide range of parameters; Rayleigh number, Ra (10³ ? Ra ? 10⁶); Prandtl number, Pr (0.07 ? Pr ? 70); dimensionless lengths of heater in x and y directions (0.25 ? hx ? 0.75, 0.25 ? hy ? 0.75); and inclination angle, ? (0° ? ? ? 270°). It is observed that heat transfer is maximum or minimum depending on the inclination angle and depending on the length of the corner heaters. The effect of Prandtl number on mean Nusselt number is more significant for Pr < 1.     

New approach relevant to total heat transfer coefficient including the effect of radiation and convection at the ceiling in a cooled ceiling room

In this study, radiative and convective heat transfer coefficients at the ceiling are determined for a cooled ceiling room. Firstly, convective heat transfer is simulated numerically neglecting the radiative heat transfer at the surfaces (ε_f = ε_w = ε_c = 0), then, radiative heat transfer is calculated theoretically for different surface emissivities (ε_f = ε_w = ε_c = 0.5, 0.6, 0.7, 0.8 and 0.9) for different room dimensions (3 × 3 × 3, 4 × 3 × 4 and 6 × 3 × 4 m) and thermal conditions (T_f = 25 °C, T_w = 28–36 °C and T_c = 0–25 °C). Numerical data is compared with the results of correlations based on experimental data given in literature. New equations related to convective and total (including the effect of convection and radiation) heat transfer coefficients for ceiling are found in the current study.     

Numerical investigation for natural convection of a nanofluid in an inclined L-shaped cavity in the presence of an inclined magnetic field

The problem of natural convection in an inclined L-shaped enclosure filled with Cu/water nanofluid that operates under differentially heated walls in the presence of an inclined magnetic field is presented in this paper. The fully implicit finite difference method is used to solve the governing equations. A comparison with previously published results in special case of the present study is performed and a very good agreement is found. Heat transfer and fluid flow are examined for parameters of the Hartmann number (0 ≤ Ha ≤ 100), the nanoparticles volume fraction (0% ≤ ϕ ≤ 20%), the cavity inclination angle (0° ≤ ϑ ≤ 300°), the magnetic field inclination angle (0° ≤ γ ≤ 270°), the cavity aspect ratio (0.25 ≤ AR ≤ 0.6) and the Rayleigh number (10³ ≤ Ra ≤ 10⁶). It is found that, the presence of the magnetic field in the fluid region causes a significant reduction in the fluid flow and heat transfer characteristics. Also, a good enhancement in the heat transfer rate can be obtained by adding the copper nanoparticles to the base fluid.     

Pool boiling of R-123/oil mixtures on enhanced tubes having different pore sizes

The effect of enhanced geometry (pore diameter, gap width) is investigated on the pool boiling of R-123/oil mixture for the enhanced tubes having pores with connecting gaps. Tubes having different pore diameters (and corresponding gap widths) are specially made. Significant heat transfer degradation by oil is observed for the present enhanced tubes. At 5% oil concentration, the degradation is 26–49% for T_sat = 4.4 °C. The degradation increases 50–67% for T_sat = 26.7 °C. The heat transfer degradation is significant even with small amount of oil (20–38% degradation at 1% oil concentration for T_sat = 4.4 °C), probably due to the accumulation of oil in sub-tunnels. The pore size (or gap width) has a significant effect on the heat transfer degradation. The maximum degradation is observed for d_p = 0.20 mm tube at T_sat = 4.4 °C, and d_p = 0.23 mm tube at T_sat = 26.7 °C. The minimum degradation is observed for d_p = 0.27 mm tube for both saturation temperatures. It appears that the oil removal is facilitated for the larger pore diameter (along with larger gap) tube. The highest heat transfer coefficient with oil is obtained for d_p = 0.23 mm tube, which yielded the highest heat transfer coefficient for pure R-123. The optimum tube significantly (more than 3 times) outperforms the smooth tube even with oil. The heat transfer degradation increases as the heat flux decreases.     

Numerical simulation of turbulent natural convection in a rectangular enclosure having finite thickness walls

Turbulent natural convection in a rectangular enclosure having finite thickness heat-conducting walls at local heating at the bottom of the cavity provided that convective-radiative heat exchange with an environment on one of the external borders has been numerically studied. Mathematical simulation has been carried out in terms of the dimensionless Reynolds averaged Navier–Stokes (RANS) equations in stream function–vorticity formulations. The formulation comprises the standard two equation k–ε turbulence model with wall functions, along with the Boussinesq approximation, for the flow and heat transfer. The special attention was paid to the effects of the Grashof number 10⁸ ? Gr < 10¹⁰, the transient factor 0 < τ < 1000 and the thermal conductivity ratio k_2,1 = 5.7 × 10^?4, 6.8 × 10^?5 both on local and on integral problem parameters. Detailed results including stream lines, temperature profiles and correlation for the average Nusselt number in terms of Grashof number have been obtained.     

Experiments on impingement heat transfer with film extraction flow on the leading edge of rotating blades

A transient liquid crystal experiment was performed to study the heat transfer characteristic of impingement cooling with outflow film on the leading edge of turbine blades under rotating conditions. In the experiments, the angles between the jet direction and rotating shaft were 0°, 30°, and 45°, respectively. The impinging jet Reynolds number, based on the diameter of the impingement hole, ranged from 2000 to 12,000. The rotation number Ro (Ωd/u) ranged from 0 to 0.278. The relative impingement distance was fixed at 2. The results showed that, due to the effect of rotation, the spreading rate of the jet flow was enhanced and the heat transfer was weakened for all Reynolds numbers. For the condition of Re = 4000 and Ro = 0.139 with corresponding angles θ = 0°, 30°, 45°, the Nusselt number of the stagnation point decreased by 33%, 30%, and 35%, respectively, compared to the stationary results. Furthermore, for the corresponding angles θ = 30° and 45°, the location of the stagnation point is offset 0.6d (jet impingement hole diameter) and 0.9d down, respectively, when Ro = 0.139. The average Nusselt numbers on the suction surface and the pressure surface both decreased with increased rotating speed. Moreover, the reduction of the average Nusselt number on the pressure surface was larger than that on the suction surface. At Ro = 0.139, the average Nusselt number on the suction surface decreased less than 10% for all three angles, while on the pressure surface, the decrease was almost 20% compared to the result for Ro = 0.     

Experimental investigation of opposing mixed convection hear transfer in the vertical flat channel in a laminar–turbulent transition region

In this paper we present the results on experimental investigation of the local opposing mixed convection heat transfer in the vertical flat channel with symmetrical heating in a laminar–turbulent transition region. The experiments were performed in airflow (p = 0.1–1.0 MPa) in the range of Re from 1.5 × 10³ to 6.6 × 10⁴ and Gr_q up to 1 × 10¹¹ at the limiting condition q_w1 = q_w2 = const. The analysis of the results revealed significant increase in the heat transfer with increasing of air pressure (Gr number). Also sharp increase in heat transfer was noticed in the region with vortex flow in comparison with the turbulent flow region.