Laminar free convection inside an inclined L-shaped enclosure

We have numerically reported the buoyancy induced flow and heat transfer characteristics inside an inclined L-shaped enclosure. A control volume based Finite-Volume method is applied to discretize the governing equations with collocated variable arrangement. SIMPLE algorithm is used and the system of equations is solved by Stone's SIP solver with full multigrid acceleration. Results are presented in the form of the average Nusselt number for a range of inclination angle, θ = 0°–360°; Rayleigh number, Ra = 1–10⁵; and aspect ratio, A = 0.1–0.5.     

Heat transfer by free convection from the inside surface of the vertical and inclined elliptic tube

Free convection from the inside surface of vertical and inclined elliptic tubes of axis ratio (a:b) 2:1 with a uniformly heated surface (constant heat flux) is investigated experimentally. The effects of orientation angle (α) and inclination angle (ϕ) on the heat transfer coefficient were studied. The orientation angle (α) is varied from 0° (when the major axis is horizontal) to 90° (when the major axis is vertical) with steps of 15°. The inclination angle (ϕ) is measured from the horizontal and varied from 15° to 75° with steps of 15°. The vertical position is considered as a special case of the inclined case when ϕ = 90. The experiments covered a range of Rayleigh number, Ra from 2.6 × 10⁶ to 3.6 × 10⁷. The local and average Nusselt numbers are estimated for different orientation angles and inclination angles at different Rayleigh numbers. The results obtained showed that the local Nu increased with the increase of axial distance from the lower end of the elliptic tube until a maximum value near the upper end, and then, it gradually decreased. The average Nu increases with the increase of α or ϕ at the same Ra. The results obtained are correlated by dimensionless groups and with the available data of the inclined and vertical elliptic tubes.     

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.     

3-D Numerical study on the correlation between variable inclined fin angles and thermal behavior in plate fin-tube heat exchanger

In this study, the heat transfer enhancement and pressure drop values of seven different fin angles with plain fin-tube heat exchangers were investigated. The numerical simulation of the fin-tube heat exchanger was performed by using a three dimensional (3-D) numerical computation technique. Therefore, a CFD computer code, the FLUENT was used to solve the equation for the heat transfer and pressure drop analyses in the fin-tube heat exchanger. The model drawing was created and meshed by using GAMBIT software. The heat transfer and pressure drop values of the vertical fin angle (θ = 0°) were provided to compare with variable inclined fin angles (θ = 5°, 10°, 15°, 20°, 25°, 30°). The heat transfer values were normalized to compare all cases. For inclined fin angle θ = 30°, which is the optimum angle, the maximum heat transfer enhancement per segment was obtained 1.42 W (the normalized value 105.24%), the maximum loss power associated with pressure drop per segment was only 0.54 mW.     

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).     

Effects of duct inclination angle on thermal entrance region of laminar and transition mixed convection

Experimental investigation was performed on the mixed convection heat transfer of thermal entrance region in an inclined rectangular duct for laminar and transition flow. Air flowed upwardly and downwardly with inclination angles from ?90° to 90°. The duct was made of duralumin plate and heated with uniform heat flux axially. The experiment was designed for determining the effects of inclination angles on the heat transfer coefficients and friction factors at seven orientations (θ = ? 90°, ?60°, ?30°, 0°, 30°, 60° and 90°), six Reynolds numbers (Re ≈ 420, 840, 1290, 1720, 2190 and 2630) within the range of Grashof numbers from 6.8 × 10³ to 4.1 × 10⁴. The optimum inclination angles that yielded the maximum heat transfer coefficients decreased from 30° to ?30° with the increase of Reynolds numbers from 420 to 1720. The heat transfer coefficients first increased with inclination angles up to a maximum value and then decreased. With further increase in Reynolds numbers, the heat transfer coefficients were nearly independent of inclination angles. The friction factors decreased with the increase of inclination angles from ?90° to 90° when Reynolds numbers ranged from 420 to 1290, and independent of inclination angles with higher Reynolds numbers.     

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.     

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.     

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.     

Natural convective flow in an inclined lid-driven enclosure with a heated thin plate in the middle

Natural convection heat transfer from a heated thin plate located in the middle of a lid-driven inclined square enclosure has been analyzed numerically. Left and right of the cavity are adiabatic, the two horizontal walls have constant temperature lower than the plate’s temperature. The study is formulated in terms of the vorticity-stream function procedure and numerical solution was performed using a fully higher-order compact (FHOC) finite difference scheme on the 9-point 2D stencil. Air was chosen as a working fluid (Pr = 0.71). Two cases are considered depending on the position of heated thin plate (Case I, horizontal position; Case II, vertical position). Governing parameters, which are effective on flow field and temperature distribution, are Rayleigh number values (Ra) ranging from 10³ to 10⁵ and inclination angles γ (0° ? γ < 360°). The fluid flow, heat transfer and heat transport characteristics were illustrated by streamlines, isotherms and Nusselt number (Nu). It is found that fluid flow and temperature fields strongly depend on Rayleigh numbers and inclination angles. Further, for the vertical located position of thin plate heat transfer becomes more enhanced with lower γ at various Rayleigh numbers.     

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.     

Computational analysis of natural convection in a parallelogrammic cavity with a hot concentric circular cylinder moving at different vertical locations

A finite volume numerical simulation of natural convection in a parallelogrammic air-filled cavity having a heated concentric circular cylinder is performed. The left and right sidewalls of the cavity are maintained at a uniform cold temperature, while both upper and lower walls of it are considered thermally insulated. A wide range of significant parameters such as Rayleigh number, inclination angle and cylinder vertical locations are considered in the present study. Comparison with previously published works is made and found to be an excellent agreement. The results show that the strength of the flow circulation and the thickness of thermal boundary layer around the hot circular cylinder are increased dramatically when the Rayleigh number increases. Also, to increase the flow circulation inside the parallelogrammic cavity, it is recommended to make the inner cylinder moves downward until it reaches to [δ = − 0.2] and the parallelogrammic cavity sidewalls inclined to [Φ = 15°]. Moreover, it is found that for various values of the inclination angle, the average Nusselt numbers at inner cylinder surface and at both cavity sidewalls, decrease when the cylinder moves upward, while they increase when the cylinder moves downward.     

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.     

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.     

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.     

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.     

Optical and thermal optimization of stationary non-evacuated CPC solar concentrator with fully illuminated wedge receivers

Stationary low concentrator collectors (C < 2), of the CPC type, are of great interest for thermal energy supply of industrial processes, at temperatures below or equal to 100 °C. In particular, concentrators with fully illuminated V inverted absorbers have attractive properties for thermal energy conversion.Numerical analysis of the geometric and optical characteristics of different low concentration CPC’s (C between 1 and 2) with fully inverted wedge absorbers, shows that the cavities with the minimal relationship between the length and height of the reflector surface and the aperture, (L/A) and (H/A), and the lower average number of reflections 〈n〉 correspond to the lowest angular acceptance concentrator. If a concentration of 1.2 is desired, the smallest ratios of (L/A) and (H/A) and mean number of reflections 〈n〉 occur for C = 2 (θ_a = 30°). However, when the annual generated thermal energy is also considered (for example, for Recife, tilt equals latitude, fluid temperature equals 50 °C, East–West orientation), a very large maximum value in the concentration region between 1.4 and 1.6 (acceptance angles of 38.68° e 45.58°) occurs. The simulation results indicate, that while the operational temperature rises, the ratio between the annual generated thermal energy by the CPC and a good quality flat-plate collector becomes greater than 1: for CPC with 1.2 concentration these ratios become 1.0 at 50 °C and 1.35 at 80 °C. The improvement in the reflectivity of the reflector surface of the CPC rises significantly this relation, i.e., if the reflectivity exceeds from 0.86 to 0.96 the CPC of the concentration relation 1.2, operating at 80 °C may generate 55% more thermal energy than flat-plate collector.     

Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium

A numerical investigation of the steady magnetohydrodynamics free convection in a rectangular cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. A uniform magnetic field, inclined at an angle γ with respect to the horizontal plane, is externally imposed. The values of the governing parameters are the inclined angle γ = 0, π/6, π/4 and π/2, Hartmann number Ha = 0, 1, 5, 10 and 50, Rayleigh number Ra = 10, 100, 10³ and 10⁵, and the aspect ratio a = 0.01, 0.2, 0.5 and 1 (square cavity). It is shown that the intensity of the core convection is considerably affected by the considered parameters. It is also found that the local Nusselt number Nu_Y decreases on the bottom wall as γ increases (magnetic field changes its direction from the horizontal to the vertical direction) and vice versa for the top wall of the cavity. The reported results are in good agreement with the available published work in the literature.     

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.     

Investigation of natural circulation in cavities with uniform heat generation for different Prandtl number fluids

Natural convection in enclosures with uniform heat generation and isothermal side walls is studied here. For the rectangular enclosure, two-dimensional conservation equations are solved using SIMPLE algorithm. Parametric studies are conducted to examine the effects of orientation of the cavity, fluid properties (Pr number), and aspect ratio for Rayleigh numbers up to 10⁶. For a horizontal square cavity, the flow becomes periodically oscillating at Ra = 5 × 10⁴ and chaotic at Ra = 8 × 10⁵. With a slight increase in the inclination angle, the oscillations die and for inclination angles greater than 15⁰, the flow attain a steady state over a range of Ra. It is found that for tall cavities (aspect ratio > 1), the steady-state solution is obtained for all values of Ra considered here. However, for wide cavities (aspect ratio < 1), an oscillatory flow regime is observed. The maximum temperature within the cavity is calculated for the range of Ra, aspect ratio and Pr number. Correlations for the maximum cavity temperature is presented here. The values of critical Rayleigh number at which the convection sets in the rectangular cavity are also studied and two distinct criteria are determined to evaluate the critical Rayleigh number. Further, a three-dimensional simulation is performed for a cubic cavity. It is found that the steady state solutions are obtained for all Rayleigh number, except at Ra = 10⁶. This is in contrast to the predictions for a two-dimensional square cavity, which has an oscillatory zone from Ra = 5 × 10⁴ onwards.