An opaque cloud cover model of sky short wavelength radiance

The average angular distribution of short wavelength sky radiance for clear, partly cloudy, and overcast sky conditions has been measured for the range of solar zenith angle 31° to 80°. Detailed analysis of this sky radiance data shows that the normalized sky radiance is given analytically by N(θ, φ) = CN₀(θ, φ) + [1−C]N_C(θ, φ) where N₀(θ, φ) = 0.45 +0.12 θ^* + 0.43 cosθ + 0.72e^−1.88ψ N_c(θ, φ) = [1.63 + 53.7e^−5.49ψ + 2.04 cos² ψ cosθ^*] [1− e^−0.19Secθ][1minus; e^−0.53Secθ], and θ^* is the solar zenith angle (radians), (θ, φ) is the sky radiance direction, Ψ is the scattering angle (radians) between sky and sun directions, and C is the prevailing opaque cloud cover.     

Maximization of heat transfer density rate from a single row of rhombic tubes cooled by forced convection based on constructal design

The heat transfer density rate from a row of rhombic tubes cooled by forced convection is maximized based on constructal design. A row of parallel rhombic tubes are placed in a fixed volume, the horizontal axis of the tubes is kept constant while the vertical axis of the tubes and the spacing between the tubes are changed to facilitate the heat flow from the tubes to the coolant. The tubes are kept at constant temperature and the incoming free‐stream flow is induced by constant pressure drop. For steady, two‐dimensional, incompressible, and laminar forced convection, the governing equations are solved numerically by finite volume method with SIMPLE algorithm. The dimensionless pressure drop (Bejan number, Be) ranging from 10 ³ to 10 ⁵, the range of the vertical axis of the tube is 0.2 ≤ B ≤ 2, and the working fluid is air ( Pr = 0.71). The results show that the optimal spacing decreases and the maximum heat transfer density increases as the Bejan number increases for all vertical axes of the tube. Bejan number and the bluntness of the tube have a significant effect of the flow structure (separation and vortex formation) around the tubes at the optimal spacings.     

Angular distribution of overcast sky short wavelength radiance

A detailed analysis of 1438 all-sky scans of shortwave radiance (95 skypoints per scan) for overcast skies shows that angular dependence of the (suitably normalized) diffuse sky radiance can be represented by the analytical expression. N_C2(ψ)= 0.45 + 1.12θ^* + 0.43 cos θ + 0.72 exp[−1.88ψ] where Cosψ = Cos θ^*cos θ + sin θ^*cos φθ = sky zenith angle, Φ = sky azimuth angle (relative to the sun), θ^* = solar zenith angle. Both θ^* and ψ are in radians.     

Angular distribution of clear sky short wavelength radiance

Over 3000 scans of the clear sky short wavelength (0.3–3.0 μm) radiance were used to produce sky radiance contour maps for solar zenith angles 32° to 80°. The radiance contours are symmetrical about the solar meridian with minimum radiance in the solar meridian at approximately 90° to 110° from the sun. There is no significant change in contour for a change in aerosol optical depth from 0.1 to 0.5. The clear sky radiance is given analytically by N(ψ) = (1.63 + 53.7e−5.49ψ + 2.04 cos² ψ cos θ^*) (1 − e^{−1.90 sec θ}) (1 − e^{−0.53 sec θ}*) where θ^* is the solar zenith angle, θ the zenith angle of the sky radiance direction, and Ψ is the scattering angle between sky and sun directions.     

Maximization of heat transfer density from a vertical array of flat tubes in cross flow under fixed pressure drop using constructal design

The density of heat transfer rate from a vertical array of flat tubes in cross flow is maximized under fixed pressure drop using constructal design. With the constructal design, the tube arrangement is found such that the heat currents from the tubes to the coolant flow easily. The constraint in the present constructal design is the volume where the tubes are arranged inside it. The two degrees of freedom available inside the volume are the tube‐to‐tube spacing and the length of the flat part of the tubes (tube flatness). The tubes are heated with constant surface temperature. The equations of continuity, momentums, and energy for steady, two‐dimensional, and laminar forced convection are solved by means of a finite‐volume method. The ranges of the present study are Bejan number (dimensionless pressure drop) (10³ ≤ Be ≤ 10⁵) and tube flatness (dimensionless length of the tube flat part) (0 ≤ F ≤ 0.8). The coolant used is air with Prandtl number (Pr = 0.72). The results reveal that the maximum heat transfer density decreases when the tube flatness decreases at constant Bejan number. At constant tube flatness, the heat transfer density increases as the dimensionless pressure drop (Bejan number) increases. Also, the optimal tube‐to‐tube spacing is constant, irrespective of the tube flatness at constant Bejan number.     

Local resistance of fluid flow across sudden contraction in small channels

The pressure drop caused by flow area contraction in microchannels has been experimentally studied in this paper using the tiny gap pressure measurement method. The working fluid was deionized water at room temperature at near-atmospheric pressure. Three test sections with area ratios of 0.284 and 0.274 and at different tube diameter sizes were used. The experimental results show that the abrupt contraction coefficient K _c decreases with the Reynolds number increasing, and it is much higher than that of conventional tubes in laminar flow. The widely-applied correlation K _c= 0.5(1 − σ)^0.75 could not predict the contraction coefficient of turbulent flow in the micro tubes. The K _c decreases as the tube diameter increases. The transition from laminar to turbulent flow is not obvious when the diameter of the small tube is 0.32 mm.     

Spectrally selective solar absorbers in different non-black colours

Silicon paints were prepared from yellow, ochre, dark ochre, green and blue pigments. To improve the solar absorptance, a_s, of these coatings, an existing black paint was admixed in different ratios. The optical properties of the mixed paints thus formed are expressed in terms of the Kubelka–Munk absorption and scattering coefficients in the spectral region 400–17000 nm. The scattering coefficient obtained for all paints was essentially equal. In the visible region the absorption coefficient follows the spectral characteristics of each respective colour. In the infrared absorption at 9000 nm and above 12000 nm are seen in all cases which result in a thickness-dependent increase of the thermal emittance, e_T, of the coating. The metric chroma (C_ab^*) and lightness (L^*) in CIELAB colour space were calculated for wide-angle observer in average daylight conditions. A range of non-black spectrally selective solar absorber surfaces with a_s>0.8 and e_T<0.3 have been prepared with L^*<45 and C_ab^*<10.     

Simultaneously developing laminar flow in an isothermal circular tube

An accurate numerical solution for simultaneously developing laminar flow in an isothermal circular tube is presented for Pr = 0.01, 0.70, 5.0 and 50.0 for 10⁻⁶ < x⁺ < 0.10. Local and average Nusselt numbers are tabulated. very large number of radial nodes is required to achieve grid independence and accuracy. Previous results are inaccurate at small nondimensional axial distances from the tube entrance because of an insufficient number of radial nodes and simplifying assumptions.     

Experimental study of laminar forced convective mass transfer and pressure drop in microtubes

The investigation of laminar convective mass transfer and friction factor was performed experimentally for the circular tubes with the diameter of 0.20 mm and the L/d values in the range of 100–500 for a Reynolds number range of 40–1400. The pressure drop experiments were conducted with distilled water, and the mass transfer experiments were carried out with an electrochemical solution by using the electrochemical limiting diffusion current technique. The friction factor results showed good agreement with the classical Poiseuille flow theory, while Sherwood numbers are smaller than those obtained by conventional correlations.     

The effects of turbulence on molten pool transport during melting and solidification processes in continuous conduction mode laser welding of copper–nickel dissimilar couple

The melting and solidification stages of a continuous copper–nickel dissimilar metal conduction mode laser welding have been simulated numerically in this study. The heat, mass and momentum transports in molten metal pool have been analysed using both laminar and turbulent flow models separately for the same process parameters. The phase change aspects related to solidification and melting are accounted for by a modified enthalpy–porosity technique while the turbulent transport is modelled by a high Reynolds number k–ε model. It has been observed that temperature fields obtained from both laminar and turbulent transport simulations are qualitatively similar to each other. The molecular thermal diffusivity of the molten metal mixture is found to be in the same order of magnitude as eddy thermal diffusivity, as a result of which the thermal field gets marginally affected by fluid turbulence. By contrast, eddy viscosity remains much greater than molecular viscosity, which leads to greater amount of momentum diffusion in the case of a turbulent molten metal pool, in comparison to that obtained from the corresponding laminar simulation. This is reflected in the reduction in maximum velocity magnitude in the turbulent simulation in comparison to the maximum velocity obtained from laminar simulation. In the case of species transport, the turbulent mass diffusivity is found to be about 10⁷–10⁸ times greater than molecular mass diffusivity. As a result, the species field in turbulent simulation shows characteristics of better mixing between two dissimilar molten metals than the species field obtained using the laminar transport model. The species distribution obtained from turbulent transport is shown to be in better agreement with experimental data reported in literature than the corresponding mass fraction distribution obtained from laminar simulation. It is also found that species distribution in the molten pool is principally determined by advective and diffusive transport during the melting stage and species transport by advection and eddy diffusion in turbulent pool increasingly weakens with decreasing temperature during the cooling following the laser melting stage.     

Constructal design of flat tubes cooled by natural convection

A set of vertical flat tubes cooled by natural convection and placed in a finite size space is designed based on the constructal law. The constraint in this design is the size of the space where the tubes are placed. The freedom inside the space is the distance between the tubes. When the constructal law is applied, the optimal distance between the tubes is determined. Rayleigh numbers are taken as (Ra = 10³, 10⁴, and 10⁵). The dimensionless tube diameter (tube diameter/tube height) is changed from (D* = 0.2) to (D* = 1) (circular tube). All the tubes are heated to the same wall temperature. The air used to cool the tubes has a Prandtl number (Pr = 0.72). The equations of conservation of mass, momentum, and energy for steady, two-dimensional, and incompressible flow are solved by the finite volume method. The result showed that the best or optimal distance at a given Rayleigh number remains constant for all tube diameters. The result also showed that the number of the small diameter tubes must be more than the number of the large-diameter tubes for the same Rayleigh number and the same size of the space to make the heat flow from the tubes to the coolant easier.     

Measurement and prediction of pressure drop in a two-phase micro-pin-fin heat sink

This study concerns pressure drop in a two-phase heat sink containing an array of staggered square micro-pin-fins having a 200 × 200 μm² pin cross-section by a 670 μm pin height. Three inlet temperatures of 30, 60 and 90 °C, and six maximum mass velocities for each inlet temperature, ranging from 183 to 420 kg/m² s, were tested. Frictional pressure drop in the boiling region is deemed the dominant pressure drop component. The Lockhart–Martinelli correlation for laminar liquid–laminar vapor combination in conjunction with a previous single-phase friction factor correlation can adequately predict the data. Micro-pin-fins offer better flow stability than parallel micro-channels.     

The effect of surface blocking on mass transfer from a stagnant cap drop

Numerical results for single-drop exterior mass transport of a solute from a surfactant covered drop to the continuous phase are presented. In particular the effect of physicochemical surface blocking is determined by considering the case in which the adsorbed surfactant accumulates at the rear of the translating drop. The stagnant cap velocity profiles are used to describe convective transport. Surface blocking is incorporated through the choice of a zero flux boundary condition on those portions of the drop where surfactant is present. Finite element numerical results for the Sherwood numbers as a function of Peclet number (Pe 10⁴) and stagnant cap angle, φ, show that for surface coverages greater than 0.1π, the effect of surface blocking cannot be ignored. For a Peclet number equal to 10⁴ and φ = 0.5π, the mass transfer coefficients calculated under the assumption that the presence of surfactant reduced convection in the vicinity of the drop without inhibiting the interfacial transport of solute, are found to overestimate the rate of solute mass transfer by as much as 20%.     

Numerical computation of thermocapillary-driven convection in an open cylindrical cavity with different aspect ratios

The surface tension gradient driven fluid flow that occurs during laser melting has been studied. The steady laminar thermocapillary motion in a cylindrical cavity has been analyzed numerically for 0.01 Pr 20, 50 Re_σ 35000, 0.01 A 10 without the inclusion of buoyancy effects. The study consists of scale analysis and numerical simulations. For a fixed Prandtl number the average free surface Nusselt number, side wall Nusselt number, bottom Nusselt number and maximum stream function are proportional to Re^2/7_σ, Re^4/9_σ, Re^4/9_σ, and Re^−2/7_σ, respectively. The numerical results are qualitatively verified by the scale analysis. The convection in the melt modifies the isotherms in the melt at high surface tension Reynolds number and Marangoni number. In addition, surface deflections are computed using a domain perturbation for small capillary number. It is shown that the degree of the free-surface deformation for the leading-order solution varies strongly with the surface tension Reynolds number.     

A numerical study on developing laminar forced convection and entropy generation in half- and double-sine ducts

In the present paper, the developing laminar forced convection and entropy generation in both double- and half-sine ducts are investigated with numerical methods. The studied cases cover Re ranging from 86 to 2000. The duct aspect ratio (Λ/a) and the external heat flux (q^*) are varied as Λ/a=2, 4 and 8, and the values of q^* are varied as 0.0405, 0.0811 and 0.1622, respectively. The comparisons of the flow features, including the distributions of axial velocity, temperature, Nusselt number and the local entropy generation, in the double- and half-sine ducts are provided in detail in the paper. Particularly, the optimal analysis of the two-type ducts based on the minimal entropy generation principle is the major concern. Through the evaluations of the overall entropy generation in the whole flow domain, the optimal option between the double- and half-sine duct is found to be dependent on the duct aspect-ratio, external heat flux and Re. Among all the cases studied, the half-sine duct with Λ/a=2 is found to have the minimal entropy generation, and therefore is concluded as the optimal option for achieving the least irreversibility and best exergy utilization in the thermal system.     

Performance rating method of thermosyphon solar water heaters

A rating method for the thermal performance of thermosyphon solar water heaters was developed. Except that the outdoor test procedure still follows the Taiwan Standard CNS B7277, a system characteristic efficiency η_s^* which is defined as the α₀ value corrected at , was derived so that η_s^* is independent of the ratio. Here, η_s^* can be evaluated by linear regression analysis of the test data. It is found from a series of tests for 31 systems that η_s^* is independent of indeed, and thus can be used to rate the thermal performance of different thermosyphon solar water heaters during the energy-collecting period. The cooling loss during the no-radiation period is rated by the system cooling time constant τ_c. The present rating method associated with the Taiwan Standard CNS B7277 has been implemented for more than three years and is accepted by the Taiwan solar industry.     

Experimental study on friction factor and numerical simulation on flow and heat transfer in an alternating elliptical axis tube

This paper focuses on the experimental study on friction factor and the numerical simulation on the periodic fully developed fluid flow and heat transfer in an alternating elliptical axis tube (AEAT). The experimental results show that in the laminar flow regime fRe = 84.7, and the transition from laminar to turbulent flow occurs at an earlier Reynolds number about 1000. The predicted cycle average Nusselt numbers from the standard k–ε model and RNG k–ε model are quite close to each other, which are appreciably higher than that of elliptic tube and round tube. Heat transfer performance comparisons are made under identical pumping power constraint, showing the obvious superiority of AEAT over a round tubes. In addition, the complicated multi-longitudinal vortex structure of the flow is detected in detail from the numerical simulation results, which improves the synergy between velocity field and temperature gradient in a large extent, hence, greatly enhancing the convective heat transfer.     

Heat transfer and fluid flow in shrouded pin fin arrays with and without tip clearance

Shrouded pin fin arrays with tip clearances (Cg) up to 25% of pin height were experimentally evaluated. Pressure loss was measured (2 × 10² < Re_D < 2 × 10⁴) and liquid crystal thermography was employed to obtain temperature distributions from which the impact of Cg on the mean heat transfer rate was determined for 2 × 10² < Re_D < 1 × 10⁴. Cg was found to influence pressure drop performance to the greatest extent at low Re_D, (<5 × 10³), with the effect being significantly diminished by Re_D = 1.5 × 10⁴. On a per unit pumping power basis, higher heat transfer rates were observed for dimensionless clearances (Cg/D) less than 0.2 as compared to the non-clearance case.     

Heat transfer characteristics of gaseous flows in microtube with constant heat flux

Heat transfer characteristics of gaseous flows in a microtube with constant heat flux whose value is positive or negative are investigated on two-dimensional compressible laminar flow for no-slip regime. The numerical methodology is based on the Arbitrary–Lagrangian–Eulerian (ALE) method. The computations are performed for tubes with constant heat flux ranging from −10⁴ to 10⁴ W m⁻². The tube diameter ranges from 10 to 100 μm and the aspect ratio of the length and diameter is 200. The stagnation pressure, p_stg is chosen in such away that the Mach number at the exit ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in microtubes with positive heat flux are compared with those of negative heat flux case and also compared with those of the incompressible flow in a conventional sized tube. In the case of fast flow, temperature profiles normalized by heat flux have different trends whether heat flux is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the microtube is proposed. Supplementary runs with slip boundary conditions for the case of D = 10 μm conducted and rarefaction effect is discussed. With increasing Ma number, the compressibility effect is more dominant and the rarefaction effect is relative insignificant where Kn number is less than Kn = 0.0096. And, the magnitudes of viscous dissipation term and compressibility term are investigated along the tube length.     

Experimental investigation of thermal resistance of a heat sink with hexagonal fins

In the present work, the effects of the heights, widths of the hexagonal fins, streamwise and spanwise distances between fins and flow velocity on thermal resistance and pressure drop characteristics were investigated using Taguchi experimental design method. Also the temperature distribution within the selected pin fins was determined. Thermal resistance and dimensionless pressure drop were considered as performance statistics. L₁₈(2¹*3⁷) orthogonal array was selected as an experimental plan for the five parameters mentioned above. While the optimum parameters were determined, due to the goals (above aims) more than one being, the trade-off among goals was considered. First of all, each goal was optimized, separately. Then, all the goals were optimized together, considering the priority of the goals, and the optimum results were found to be fin width of 14 mm, fin height of 150 mm, spanwise distance between fins of 20 mm, streamwise distance between fins of 10 mm and flow velocity of 4 m/s.