Vertical Plane Surface Research Articles

Experimental investigation of condensation heat transfer on vertically inclined grooved aluminium surfaces

This study details the experimental investigation of surface condensation heat transfer on vertically inclined aluminium surfaces with simple modifications. A bespoke experimental apparatus was constructed to control the saturation conditions inside the condensation chamber where the test surface is located. The degree of subcooling of the test surface was precisely controlled by an external heat exchanger. The meter bar technique was used to evaluate the condensation heat flux. Using distilled water as the working fluid and a plane aluminium test surface as the baseline case, the experimental apparatus was validated by comparison of the determined heat transfer coefficient with Nusselt’s model of filmwise condensation on a vertical plane surface, where an excellent agreement was obtained. 7 different aluminium test surfaces were subsequently investigated, each one modified with grooves measuring 0.5mm by 0.5mm (height and width), with a consistent spacing of 0.5mm between them. Groove angles relative to the vertical axis of 0° (180°), 30°, 45°, 60°, 90°, 120°, and 150° were investigated, where grooves were symmetrically mirrored at the centre of each test surface. Results highlighted a significant influence of groove angle on the heat transfer coefficient, with the best-performing sample (150˚) producing a maximum enhancement of 45% and an average enhancement of 34% compared to the baseline test surface over the respective range of subcooling.

Numerical Predictions of Laminar Free and Mixed Convection Heat Transfer to Supercritical Water from a Non-Isothermal Vertical Plate

Numerical predictions of heat transfer have been made for laminar free and mixed convective heat transfer from non-isothermal vertical plane surface to supercritical water. Variation of all the thermo-physical properties of the supercritical fluid under investigation have been considered. The numerical scheme employed in the present investigation is first validated with respect to experimental data for isothermal wall conditions and good agreement is achieved with maximum deviation not exceeding 15 %. Linear and parabolic variation of wall temperatures are considered for the present investigation. Computations are made for two pressures of 225 Bar and 235 Bar, for wide range of temperature difference from 4K to 20K. The values of temperature difference are chosen. Based on the results obtained, correlations have been proposed to evaluate the Nusselt numbers for both free and mixed convection with pressure ratios of P/Pc = 1.02 (p = 225 bar) and P/Pc = 1.065 (p = 235 bar). The correlations cover a range of Rayleigh numbers, Rax from 106 to 109 for Free Convection and grashoff Number/Reynolds Number2 ranging from 0.4 to 8 for Mixed convection. The proposed correlations for local Nusselt numbers do not exceed maximum deviation of 15% from the predicted values. It has been found that the maximum deviation occurs for those cases for which the pseudo-critical temperature, T* is within the boundary layer. It is further observed that for these cases both the velocity and temperature profiles are distorted at locations where the temperature is close to the pseudo-critical temperature thereby affecting the gradients at the wall, which in turn influences the heat transfer coefficient.

Flame morphologic characteristics of horizontally oriented jet fires impinging on a vertical plate: Experiments and theoretical analysis

Flame morphological characteristics of horizontal impinging jet fires are of practical importance in predicting and controlling the undesirable energy transfer to the nearby obstacle, which usually results in an escalating accident accompanied by severe consequences. But up to now, the relevant research is still very limited. The length of flame spread on the obstacle's surface for various nozzle diameters as well as the lift-off distance restricted by a vertical plane surface downstream the flame has not been quantified yet. In this work, the evolutions of flame spread length and lift-off distance of horizontal jet fires impinging on a vertical plate for different nozzle diameters at various energy (heat) release rates and nozzle-plate spacings have been quantified comprehensively. Experiments were conducted with three nozzles with different inner diameters of 2.0, 3.0 and 4.2 mm. The heat release rates of the fire source ranged between 5.7 and 32.2 kW, and the nozzle-plate spacings were varied from 0.20 to 0.40 m with a corresponding free condition. The results showed that the length of flame spread along the vertical plate increased with increasing the heat release rate and decreasing the nozzle-plate spacing for a given nozzle diameter. In addition, the large nozzle had a relatively greater increase in the flame spread length than the small one. A new correlation was proposed on physically the coupling effects of the flux ratio of buoyancy-induced air entrainment and jet momentum and the dimensionless heat release rate, showing good agreement with the experimental results. It was also found that the normalized lift-off distance under impingement can be correlated with the modified dimensionless flow number, and the correlation can well collapse all the lift-off data of this work. The present findings contribute to a better understanding of horizontal impinging jet fires, allowing predictions to be made regarding the possible threat and the establishment of the necessary safety distance for the pipeline to reduce the potential risk of such fire disasters.

Hall current impacts on unsteady MHD free convective flow past an infinite vertical porous surface

AbstractIn this paper, the magnetohydrodynamic free convective flow of an incompressible electrically conducting fluid over a vertical plate embedded in a porous medium is considered. A homogeneous transverse magnetic field is applied in the presence of a heat source and chemical reaction in a rotating frame, taking Hall current effects into account. The momentum equations for the fluid flow in a porous medium were determined by Brinkman modeling. At the undisturbed state, both the plate and fluid have an rigid body rotation due to the constant angular velocity, perpendicular to the infinite vertical plane surface. The vertical surface is subject to the homogeneous constant suction and the heat on the surface vary by time about a nonzero constant rate whereas the temperature of free stream is engaged to be constant. The accurate solutions for the velocity, temperature, and concentration distributions were acquired systematically using the perturbation method. The consequences of an assortment of governing flow parameters on the velocity, temperature, and concentration were analyzed through graphical profiles. The computational results for the skin friction, Nusselt number, and Sherwood number in a tabular format were also examined.

English

In this paper, unsteady two-dimensional convective heat and mass transfer flow of a viscous, incompressible, electrically conducting optically thin fluid which is bounded by a vertical infinite plane surface was considered. A uniform applied homogeneous magnetic field is considered in the transverse direction with first order chemical reaction. An analytical solution for two-dimensional oscillatory flow on unsteady mixed convection of an incompressible viscous fluid, through a porous medium bounded by an infinite vertical plate in the presence of chemical reaction and thermal radiation are presented. The surface absorbs the fluid with a constant suction and the free stream velocity oscillates about a constant mean value. The resulting nonlinear partial differential equations were transformed into a set of ordinary differential equations using two-term series. The closed form solutions for velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number have been obtained, using the regular perturbation technique. Numerical evaluation of the analytical solutions was performed and the results are presented in tabular and graphical form. This illustrates the influence of the various parameters involved in the problem on the solutions. Key words: Magnetohydrodynamics (MHD) flow, heat and mass transfer, oscillatory flow, thermal radiation, chemical reaction.

The Solar Ultraviolet Environment at the Ocean.

Atmospheric and oceanic radiative transfer models were used to compute spectral radiances between 285 and 400 nm onto horizontal and vertical plane surfaces over water. The calculations kept track of the contributions by the sun's direct beam, by diffuse-sky radiance, by radiance reflected from the sea surface and by water-leaving radiance. Clear, hazy and cloudy sky conditions were simulated for a range of solar zenith angles, wind speeds and atmospheric ozone concentrations. The radiances were used to estimate erythemal exposures due to the sun and sky, as well as from radiation reflected by the sea surface and backscattered from the water column. Diffuse-sky irradiance is usually greater than direct-sun irradiance at wavelengths below 330 nm, and reflected and water-leaving irradiance accounts for <20% of the UV exposure on a vertical surface. Total exposure depends strongly on solar zenith angle and azimuth angle relative to the sun. Sea surface roughness affects the UV exposures by only a few percent. For very clear waters and the sun high in the sky, the UV index within the water can be >10 at depths down to two meters and >6 down to 5 m.

A variational method in the problem of convective heat transfer near the vertical plane of the outer building fence in terms of free air movement

An unconventional method for solving the heat transfer problem for free convection near the vertical surfaces of the enclosing structures is proposed. It is based on the laws of thermodynamics of irreversible processes. A variational principle is used to find the unknown functions that analytically express the velocity fields and other flow quantities in the boundary layer near the vertical walls. A variational formulation of the hydrodynamic and thermal boundary layer near a vertical plane surface in conditions of free convection is given. It is given an analytical solution of the problem of the distribution of the vertical component of velocity and temperature in the wall boundary layer in the laminar flow. Theoretical formulas for the thickness of the boundary layer are obtained, as well as for the local and mean values of convective heat transfer coefficient.

Observation and description of the shape of water bridge retaining between vertical plane surfaces

As the shape of water bridge retaining between vertical fins affects the performance of fin-and-tube heat exchangers, it is necessary to investigate water bridge shape and to develop description methods for water bridge, including those for contact line and contact angles. In this study, a visual experimental apparatus for observing the shapes of water bridges between vertical plane surfaces was designed, and the contact lines and the contact angles for water bridges on 7 types of plane surfaces made of aluminum, copper, stainless steel, quartz glass, acrylic plastics, Teflon and hydrophobic modified copper were measured. The test conditions cover water bridge volumes of 3–21 µL, and plane surface separations of 0.5–2.0 mm. The description method of water bridge shape is presented and compared with experimental data, including the description method of contact line with mean deviation of 2.2%, and the description method of contact angles with mean deviation of 6.1%.

Qualitative and quantitative assessment of outdoor daylight on vertical surfaces for six climate specific Indian cities

AbstractThis article deals with experimental validation of solar illuminance model for vertical plane surfaces against measured solar global illuminance at New Delhi. The paper also deals with computation of solar illuminance (daylight), both quantitatively and qualitatively, on four cardinal vertical surfaces at six Indian stations. The stations identified for the study are: New Delhi, Jodhpur, Pune, Kolkata, Shillong and Leh. Quantitative analysis of daily average solar illuminance shows that most of the stations under study receive maximum illuminance on north, east and west surfaces, during summer months of April–July, whereas the south surface receives maximum illuminance during winter months of November–February. Higher range of daily average solar illuminance on four vertical surfaces is evaluated as follows: 45–55 klx on south surface, 20–35 klx on west surface (all the stations except Pune), 20–30 klx on east (Pune) and 14–15 klx on north surface. Qualitative analysis shows that for the global il...

State space approach to magnetohydrodynamic flow of perfectly conducting micropolar fluid with stretch

SUMMARYIn this work we introduce a model of the boundary layer equations for a perfect conducting micropolar fluid with stretch, bounded by an infinite vertical flat plane surface of a constant temperature. This model is applied to study the effects of free convection currents on the flow of the fluid in the presence of a constant magnetic field. The state space technique is adopted for the solution of a one‐dimensional problem for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Freeform surface design for a light-emitting diode–based collimating lens

A freeform collimating lens is designed to project light rays emitted from an LED light source to a far target plane. Generally, the projection distance is assumed to be more than 100 m, and the light beam to have negligible divergence. The lens consists of a total internal reflection (TIR) side surface, a spherical surface in the rear, a vertical plane surface in the outer part of the front, and a freeform refractive surface in the central part of the front. Light rays emitted from the LED source with large spread angles hit the TIR surface and are redirected parallel to the light axis, and those having small spread angles will be collimated by the freeform refractive surface, which is designed with a simple approximation method, and then travel parallel to the light axis. Computer simulation results show that an optical efficiency of 81.5% is achieved under a view angle of ±5 deg and for a 1 mm×1 mm LED source.

Hydromagnetic Oscillatory Flow and Heat Transfer of a Viscous Liquid Past a Vertical Porous Plate in a Rotating Medium

Unsteady oscillatory flow of an incompressible, electrically conducting viscous liquid through a porous medium past an infinite vertical porous plate with constant suction has been studied. A transverse uniform magnetic field has been applied in a rotating frame of reference. The porous medium is bounded by a vertical plane surface. The temperature on the vertical surface fluctuates in time about a non-zero constant mean. The analytical expressions for the velocity, temperature, skin friction and Nusselt number are presented showing the effects of pertinent parameters. It is observed that steady part of the velocity field has two layers character viz thermal layer and suction layer, while the oscillatory part exhibits a multilayer character.

Space approach to the hydro-magnetic flow of a dusty fluid through a porous medium

The technique of the state space approach and the inversion of the Laplace transformation method are applied to the non-dimensional equations of an unsteady laminar free convection flow of an incompressible, viscous, electrically conducting dusty fluid through a porous medium, which is bounded by an infinite vertical plane surface of constant temperature, in the presence of a constant magnetic field. The technique is applied to the thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. The numerical results of the dimensionless temperature, velocity, and induced magnetic and electric field distributions are given and illustrated graphically. The effects of the material’s parameters such as the Grashof number, the Prandtl number, the permeability parameter, the mass concentration of the particle phase, the Alfven velocity, the thermal relaxation time and the relaxation time of the particle phase on the temperature, velocity and the induced magnetic and electric fields are discussed.

Effects of Vapor Pressure on Marangoni Condensation of Steam-Ethanol Mixtures

Reported herein are the experimental data for Marangoni condensation of steam-ethanol on a vertical plane surface. To clarify the effect of vapor pressure on Marangoni condensation, the heat flux and the vapor-to-surface temperature difference (surface subcooling) were measured for steam-ethanol mixtures over a wide range of compositions at vapor pressures of 84.5, 47.36, and 31.16 kPa. Seven condensation modes, smooth film, drop, film-drop, streak, drop-streak, wavy-streak, and drop with tail, were observed in this experiment The experimental results showed that heat transfer coefficients of vapor mixtures of different compositions increased with vapor pressure. The effect of vapor pressure in enhancing the condensation heat transfer coefficient was less for pure steam and extremely high compositions (22 and 51%) than for low and middle compositions (0.5,1, 5, and 10%). The maximum heat flux and heat transfer coefficient in the condensation characteristic curves were 2.37 MW/m 2 and 0.15 MW/(m 2 K), respectively, for a vapor velocity of 2.0 m/s, and appeared at an ethanol vapor mass fraction of approximately 1% and a pressure of 84.53 kPa. The condensation heat transfer was enhanced approximately 7.5 times compared with pure steam.

Marangoni condensation of steam–ethanol mixtures on a horizontal tube

For condensation of binary mixtures where the less volatile constituent has the higher surface tension the condensate film is potentially unstable and various “modes” of condensation are seen depending primarily on composition and vapour-to-surface temperature difference. Of particular interest is the so-called “pseudo-dropwise” mode of condensation where the appearance of the condensate closely resembles that of dropwise condensation of a pure fluid on a hydrophobic surface. In recent years the so-called Marangoni condensation problem has been studied experimentally in great detail by Utaka and co-workers [4–8,11] for condensation of steam–ethanol mixtures on small vertical plane surfaces. It has been found that very small concentrations of ethanol in the liquid phase can give rise to significantly larger heat-transfer coefficients than found with pure steam. In the present investigation the problem has been studied using a horizontal condenser tube. Heat flux and vapour-to-surface temperature difference have been measured for steam–ethanol mixtures over a wide range of composition at atmospheric pressure. The results show the same trends as those found by Utaka for vertical surfaces. Differences in detail can be explained by geometry considerations and strong dependence of heat-transfer coefficient on vapour-to-surface temperature difference and vapour velocity, both of which vary around the perimeter of the horizontal tube.

Influence of the Wetted Surface Curvature on the Laminar Liquid Film Thickness

Liquid films flowing down vertical surfaces under the influence of gravity are encountered in many types of heat and mass transfer equipment consisting of vertical tubes and vertical plane surfaces. Therefore, a complete understanding of liquid film flow on vertical surfaces from the entrance to the exit should be of interest industrially and academically. The main reason for that is the influence exerted by the surface cross curvature and the film itself on heat transfer characteristics on the surface, transverse shear stress distribution, and correspondingly the thickness of the liquid film. This paper presents the evaluation of the surface cross curvature on the hydromechanical parameters of a laminar liquid film. The cross curvature of a wetted surface and the film alter the hydromechanical parameters of the liquid film. Simultaneously, the intensity of heat exchange between the wetted surface and liquid film is altered. Calculations evaluating velocity distribution across water and transformer oil film and correspondingly the thickness of the film were performed.

Computational treatment of free convection effects on perfectly conducting viscoelastic fluid

We introduced a magnetohydrodynamic model of boundary-layer equations for a perfectly conducting viscoelastic fluid. This model is applied to study the effects of free convection currents with one relaxation time on the flow of a perfectly conducting viscoelastic fluid through a porous medium, which is bounded by a vertical plane surface. The state space approach is adopted for the solution of one-dimensional problems. The resulting formulation together with the Laplace transform technique is applied to a thermal shock problem and a problem for the flow between two parallel fixed plates, both without heat sources. Also a problem for the semi-infinite space in the presence of heat sources is considered. A discussion of the effects of cooling and heating on a perfectly conducting viscoelastic fluid is given. Numerical results are illustrated graphically for each problem considered.

Free convection flow of conducting micropolar fluid with thermal relaxation including heat sources

The present work is concerned with unsteady free convection flow of an incompressible electrically conducting micropolar fluid, bounded by an infinite vertical plane surface of constant temperature. A uniform magnetic field acts perpendicularly to the plane. The state space technique is adopted for the one‐dimensional problems including heat sources with one relaxation time. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. The reflection method together with the solution obtained for the whole space is applied to a semispace problem with a plane distribution of heat sources located inside the fluid. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the temperature, the velocity, and the angular velocity distributions are given and illustrated graphically for the problems considered.

Free convection effects on the oscillatory flow of a viscoelastic fluid with thermal relaxation in the presence of a transverse magnetic field

Effects of free convection currents on the oscillatory flow of a viscoelastic fluid with thermal relaxation in the presence of a transverse magnetic field, which is bounded by a vertical plane surface, have been studied. The surface absorbs the fluid with a constant suction and the free stream velocity oscillates about a constant mean value. Analytical expressions for velocity, induced magnetic and electric fields and the electric current density have been obtained, using the regular perturbation technique. The effects of Grashof number G r , Prandtl number P r , Alfven velocity α, elastic parameter k 0 and frequency parameter n on the velocity are discussed. The effects of cooling and heating of a viscoelastic fluid compared to the Newtonian fluid have also been discussed.

MHD oscillatory flow on free convection–radiation through a porous medium with constant suction velocity

Unsteady two-dimensional hydromagnetic free convection and thermal radiation flow of an electrically conducting viscous-incompressible fluid, through a highly porous medium bounded by a vertical plane surface of constant temperature are presented. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. Expressions for the velocity and temperature are obtained. The free-stream velocity of the fluid vibrates about a mean constant value and the surface absorbs the fluid with constant velocity. Effects of varying R (radiative parameter), G (Grashof number), k′ (permeability of the porous medium) and M (magnetic parameter upon the velocity field and the effect of varying R and Pr (Prandtl number) on the temperature are discussed.