Horizontal Flat Plate Research Articles

Analytical solution to boundary layer flow and convective heat transfer for low Prandtl number fluids under the magnetic field effect over a flat plate

AbstractThe present study aims to quantify the flow field, flow velocity, and heat transfer features over a horizontal flat plate under the influence of an applied magnetic field, with a particular emphasis on low Prandtl number fluids. Nonlinear partial differential expressions can be incorporated into the ordinary differential framework with the use of appropriate transformations. This research utilizes the variational iteration method (VIM) to approximate solutions for the system of nonlinear differential equations that define the problem. The objective is to demonstrate superior flexibility and broader application of the VIM in addressing heat transfer issues, compared to alternative approaches. The results obtained from the VIM are compared with numerical solutions, revealing a significant level of accuracy in the approximation. The numerical findings strongly suggest that the VIM is effective in providing precise numerical solutions for nonlinear differential equations. The analysis includes an examination of the flow field, velocity, and temperature distribution across various parameters. The study found that improving temperature patterns, velocity distribution, and flow dynamics were all positively impacted by increasing the Prandtl numbers. As a result, this leads to the thickness of the boundary layer to decrease and improves heat transfer at the moving surface. Thus, the convection process becomes more efficient. When the strength of the magnetic field is increased, the velocity of the fluid decreases. This observation aligns with expectations since the magnetic field hampers the natural flow of convection. Notably, the convection process can be precisely controlled by carefully applying magnetic force.

Dimensionless correlation of mass transfer on a frosted flat plate with thickness, mass, heat flux measurements

The aim of the study is to investigate frosting on the horizontal flat plate which has uniform air velocity distribution upstream. While the air temperature is 21.9 °C, the relative humidity is 80% and the air velocity is 0.7 m/s; frost is formed on the flat plate at surface temperatures of −15.1, −11.2, −7.1 °C, then under these conditions frost thickness, frost mass are measured. Continuous heat flux measurements under frosting which is very rare in literature are performed, too. Considering only the initial part of the frosting process at high plate temperature first an increase in heat flux then a continuous decrease is observed. A new dimensionless mass transfer correlation that does not require frost surface temperature and additionally includes dimensionless plate length is presented. The mass transfer correlation is based on dimensionless numbers of Reynolds, Fourier, specific humidity, dimensionless temperature, and dimensionless plate length which are derived from air temperature, air velocity, air relative humidity, plate temperature, plate length, plate width, and time information. In obtaining the correlation, frost mass measurements from previous researchers were added to the presented experimental results to develop a correlation valid over a wide range. As a result of the broad data set, the ranges at which the correlation is valid; air velocity of 0.7–2.5 m/s, air temperature of 5–22 °C, plate temperature of −5 to −25 °C, air relative humidity of 50%–83.73% and plate length of 85.6–300 mm. Nondimensionalizing the plate length has increased the prediction capability of the correlation.

NUMERICAL STUDY FOR A THREE DIMENSIONAL LAMINAR NATURAL CONVECTION HEAT TRANSFER FROM AN ISOTHERMAL HEATED HORIZONTAL AND INCLINED SQUARE PLATE AND WITH A CIRCULAR HOLE

A theoretical study for a three-dimensional natural convection heat transfer from an isothermal horizontal , vertical and inclined heated square flat plates (with and without circular hole) has been done in the present work. The study involved the numerical solution of the transient Navier-Stokes and energy equations by using finite deference method (F.D.M.). The complete Navier-Stokes equation are transformed and expressed in terms of vorticity-vector potential. The Energy and Vorticity equations were solved by using an Alternating Direction Implicit (ADI) method because they are transient equations of parabolic portion, and the Vector potential is solved by using an equations Successive Over-Relaxation (S.O.R) method because it is from elliptic portion. The numerical solution is capable of calculating the Vector potential, three components of Vorticity and temperature field of the calculation domain. The numerical results were obtained in rang of Grashof number (103≤Gr≤5x104 ) with Prandtl number of (0.72) for square flat plate and the other consist a circle hole with ratio 0.6 and 0.8 diameter of the hole to main square side length. The numerical results showed that the main process of heat transfer is conduction for Grashof number less than 103 and convection for Grashof number larger than 103 and the results of local Nusselt number show fairly large dependence on inclination angle. For horizontal plate facing upward and downward, average Nusselt number is proportional to one-fifth power of Rayleigh number, and there is a significant difference in heat transfer rates between the upward and downward cases. For horizontal plate with circle hole facing upward for Grashof number 104 , the effect of core portion caused a limited increment in the heat transfer rate, where as for the facing downward case, the effect was larger and the maximum value of heat transfer rates is be for square flat plate with circle hole by ratio 0.6 for all inclination angles. With the increase of Grashof number to 5x104 heat transfer rates decrease except the square horizontal flat plate with circle hole by ratio 0.6 . The average Nusselt number increases with the increase of inclination of plates facing upward to reach to the higher average Nusselt number at vertical position then decrease with increase of inclination of plates. And the maximum value of average Nusselt number is depended on the ratio of diameter of the hole to main square side length, showed that the maximum temperature gradient occurs at the external edge of the horizontal plate (with and without circle hole) facing upward and at the lower external edge in inclined case. The numerical results was made through comparison with a previous numerical and experimental work, the agreement was good.

COMBINED EFFECT OF LOCAL THERMAL NONEQUILIBRIUM AND GRAVITY MODULATION ON THERMAL INSTABILITY IN MICROPOLAR NANOFLUID SATURATED POROUS MEDIA

In the present paper an effect of gravity modulation in a horizontal parallel flat plate having micropolar nanofluid saturated by a porous medium is examined. Local thermal nonequilibrium (LTNE) has been observed for the problem, i.e., the fluid, particle, and solid matrix are at different temperatures. Onset of convection and heat and mass transfer for both the cases, i.e., linear stability and nonlinear stability, is analyzed. We conclude that rate of convection in the LTNE case is faster than in the LTE case. Effect of porosity is observed in the LTNE region, which is opposite to the effect observed in the LTE region. Increase in value of A, K<sub>1</sub>, and δ delay the rate of convection. Small value of frequency of gravity modulation forms a greater number of small periods which delay the rate of convection. On increasing the value, heat transfer increases. At higher frequency of modulation we obtain the case similar to unmodulated case.

Droplet generation by the oscillation of two spark-generated bubbles near a confined opening

Cavitation bubbles can be both beneficial and detrimental. One of their beneficial applications is to produce droplets as they oscillate near a confined free surface. In this paper, the oscillation of two spark-generated bubbles beneath a confined free surface and the resultant droplet generation are studied numerically using boundary element method. Three different configurations are considered: (i) a vertical cylinder (θ = 0°), (ii) a vertical nozzle (θ = 45°) and (iii) a perforated horizontal flat plate (θ = 90°). The influences of the effective parameters, including the initial pressure and locations of the bubbles, and the configuration geometry on the dynamics of the bubbles, the free surface and the resultant droplet are studied. It was found that by decreasing the inter-bubble distance, the droplet size increases and its pinch-off occurs earlier. In general, the effect of the distance of the upper bubble from the free surface on the droplet behavior is much more significant than that of the inter-bubble distance. Furthermore, through the augmentation of the upper bubble's strength parameter, the droplet size is reduced and the moment of droplet pinch-off is postponed. Finally, the droplet size and its pinch-off time increase from the vertical cylinder to the flat plate case.

Flow and Heat Transfer of Micropolar Ferrofluid at Stagnation Point on a Horizontal Flat Plate in the Presence of Magnetic Field and Thermal Radiation

Ferrofluid demonstrates Newtonian or non-Newtonian fluid behaviour depending on the characteristics of ferrofluid. Generally, ferrofluid consists of a stable colloidal suspension of single-domain magnetic particles in a base fluid that can assume non-Newtonian fluid behaviour involving a spin vector and microinertia tensor in flow motion. These two properties possess the theory of micropolar fluid which exhibits microrotational motions and spin inertia in microscopic behaviour. Therefore, this theoretical study is focused to investigate the boundary layer of micropolar ferrofluid flow and heat transfer at the stagnation point on the horizontal flat plate. Magnetite (Fe3O4) nanoparticles and water (H2O) compose in ferrofluid exposed to the magnetic field and thermal radiation is considered. The influences of ferroparticles volume fraction and micropolar parameter on the ferrofluid flow and heat transfer are evaluated mathematically. The partial differential equations have been formulated based on purposed assumptions using Tiwari and Das model and are simplified into ordinary differential equations, which are then solved numerically by Runge-Kutta Fehlberg (RFK45) method. The numerical results of the velocity profile, temperature profile, angular velocity profile, reduced skin friction and reduced Nusselt number are scrutinised in different values of ferroparticles volume fraction and micropolar parameter to estimate the ferrofluid flow and heat transfer. It is found the velocity profile of micropolar ferrofluid flow increases when elevates the ferroparticles volume fraction but decreases when increasing the micropolar parameter. Meanwhile, enlarging ferroparticles volume fraction of micropolar ferrofluid also enhances the temperature profile, reduced skin friction and reduced Nusselt number in the presence of magnetic field and thermal radiation parameter.

An experimental study on the plate edge effect of frosting characteristics for horizontal flat cold plates with surface wettability considered

Frosting happens frequently in nature and industry and the accumulated frost layer always plays negative effects on a variety of applications. To clarify the frosting characteristics of cold plates with different surface wettability considering the plate edge effect, the frosting experiments of horizontal flat cold plates with hydrophilic, hydrophobic and superhydrophobic surfaces were carried out under forced convection. The results show that, different from the large condensed droplets in the edge-affected regions of the hydrophilic and hydrophobic surfaces, which are small and few on the superhydrophobic surface. The area-average equivalent contact diameter and coverage area ratio of condensed droplets decrease with the increase of surface wettability. The average freezing propagation velocity in the edge-affected region of the superhydrophobic surface is 166.4 × 10−6 m/s, which is 81.8% and 54.5% lower than those on hydrophilic and hydrophobic ones, respectively. And the maximum frost layer growth rate of the superhydrophobic surface is 3.36 × 10−6 m/s, which is 2.78 and 2.30 times the two other ones. The frost layer surface roughness of the superhydrophobic surface is 85.1 × 10−6 m, which is 27.8% and 74.7% higher than those on hydrophilic and hydrophobic ones, respectively. This study can reveal the time–space frosting characteristics in the edge region of horizontal cold plates and provide a reference for anti-frosting in practical applications.

A steady flow of MHD Maxwell viscoelastic fluid on a flat porous plate with the outcome of radiation and heat generation

Maxwell fluids display viscous flow on a long timescale but exhibit additional elastic resistance during rapid deformations. Among various types of rate-type fluids, the Maxwell fluid has achieved prominence in numerous study fields. This viscoelastic fluid has viscous and elastic properties. Due to their reduced complexity, this Maxwell fluid is utilized used in the polymeric industries. We have established a mathematical model based on the applications. This article examines the mathematical and graphical analysis for steady-state magnetohydrodynamic flow in a horizontal flat plate of Maxwell viscoelastic fluid for a permeable medium with heat and thermal radiation. The non-dimensional and similarity transformation used to frame the partial differential equations with restored ordinary differential equations. The shooting technique is originated to find solutions to nonlinear boundary value problems with the help of MATLAB software via the Runge-Kutta Fehlberg method. The primary idea behind this strategy is to change the boundary conditions of boundary value problems into initial value problems. Several plots illustrate the leading parameters such as Prandtl number (Pr), Deborah number (De), Eckert number (Ec), heat generation (Q), radiation (Rd), Lewis number (Le), magnetic parameter (M), and thermal slip condition (β) on the velocity profile and energy transfer behaviour. We validated our results with published work. The most significant impact of this study is that the Nusselt number drops as the Eckert number rises and climbs when heat radiation increases. The skin friction coefficient increases as Deborah number increases.

Heat and mass transmission in a boundary layer flow due to swimming of motile gyrotactic microorganisms with variable wall temperature over a flat plate

Nanotechnology can significantly revolutionize several industries and technology domains, such as homeland security, food safety, information technology, healthcare, energy, transportation, and environmental research. Thus, a numerical study of boundary layer flow on a moving horizontal flat plate filled with nanofluid with variable temperature at the wall and viscous dissipation in the presence of gyrotactic microorganisms is presented. The partial differential equations governing flow phenomena are transformed into ordinary differential equations with the aid of appropriate similarity transformations. The transformed ordinary differential equations are solved numerically with the help of the built-in BVP4C scheme of MATLAB. After the validation of the scheme, numerical solutions are determined for the temperature, nanoparticle concentration, and motile microorganism profiles, along with physical quantities of interest. The outcomes of physical factors such as the variable temperature index, Prandtl number, Eckert number, Lewis number, Peclet number, plate moving parameter, thermophoresis motion, and Brownian parameters are examined and reported through graphs and tables. From the tables, it is clear that skin friction = 0 when the velocity parameter = 1, which shows that there is no resistance at the fluid-solid surface. It is concluded that by increasing the variable temperature, the temperature gradient rises, because of which the thickness of the thermal boundary layer reduces. Finally, more innovations are inevitable with the advancement of this interdisciplinary science. Moreover, the current investigation may help to efficiently enhance the viscosity, thermal conductivity, thermal diffusivity, and convective heat transmission linked to those base fluids, such as water and oil.

Viscoelastic fluid flow over a horizontal flat plate with various boundary slip conditions and suction effects

This study examines the numerical representation of fluid flow on the Maxwell model in a double-diffusive boundary layer over a horizontal plate.

Resin infusion in porous preform in the presence of HPM considering complex geometry and gravity: Flow simulation and experimental validation

Present work demonstrates the complete numerical modeling and experimental validation of transient incompressible two-phase flow during vacuum infusion (VI) in the presence and absence of high permeability media (HPM) considering gravity effects. Coupled flow modeling based on continuity equations, Darcy’s law for porous media flow, including gravity effects with level set front tracking algorithm, has been developed on the multiblock-structured grid with higher-order finite-difference framework to predict the spatio-temporal preform saturation during infusion with/without HPM on the complex mold configurations. The model-predicted instantaneous change in pressure, thickness elevation, fill time, flow front positions, and influence of gravity have been validated with experiments for horizontal and vertical flat plates using pressure sensors and digital cameras. For the first time, the complete modeling and experimentation of transient VI in the presence or absence of HPM, including gravity, shows the ability to predict realistic preform saturation during VI in different mold geometry.

Analysis of second grade hybrid nanofluid flow over a stretching flat plate in the presence of activation energy

The research of fluid containing nanoparticles for the heat transport characteristics is very famous because of its variety of real-life applications in various thermal systems. Although the thermal efficiency of the nanofluid was effective but still the nano scientists were trying to introduce some new advance class of fluid. Therefore, an advance class of fluid is developed by the dispersion of two different nano sized particles in the conventional base fluid known as “Hybrid nanofluid” which is more effective compared to simple nanofluids in many engineering and industrial applications. Therefore, motivated from the hybrid type of nanofluids in the current research we have taken two-dimensional laminar and steady flow of second grade fluid passing through porous plate. The engine oil base fluid is widely used fluid in the engineering and industrial problems. Keeping these applications in mind the engine oil is considered and two different nanoparticles Copper and aluminum oxide are added in ordered to get the required thermal characteristics. In addition to this the thermal radiation, chemical reaction, activation energy, Brownian motion and thermophoresis are also addressed during the current research. The present proposed higher-order PDE’s is transformed to the non-linear system of ODE’s. For the solution of the proposed high non-linear model HAM method is employed. As the hybrid nanofluid are highlighted on the second-grade fluid flow over a horizontal porous flat plate. During the present analysis and experimental study, it has been proved that the performance of hybrid nanofluid is efficient in many situations compared to nanofluid and regular fluid. For physical interpretation all the flow parameters are discussed through graphs. The impact of volume fraction is also addressed through graphs. Moreover, the comparative analysis between hybrid and nanofluid is carried out and found that hybrid nanofluid performed well as compared to nanofluid and regular fluid. The engineering quantities obtained from the present research have been presented in tables.

Nonlinear approximation for buoyancy-driven mixed convection heat and mass transfer flow over an inclined porous plate with Joule heating, nonlinear thermal radiation, viscous dissipation and thermophoresis effects

This study considered a classical magnetohydrodynamics (MHD) mixed convection heat and mass transfer flow over an inclined porous plate with thermophoresis, Joule heating, viscous dissipation, and nonlinear thermal radiation. The impact of nonlinear density variation with temperature and concentration (NDTC) in the buoyancy term is also taken into consideration. The mathematical model is first transformed into ordinary differential equations (ODEs) by similarity variables. The reduced ODEs are solved through the classical Runge–Kutta algorithm after utilizing the shooting technique. Some major findings of the analysis include; the heat transfer rate increases with the fluid injection but it decreases the rate of particle deposition and skin friction. Regarding the fluid suction, the heat transfer rate is observed to decrease as the fluid suction intensifies whereas increases the particle deposition and shear stress at the plate surface. As (a classical horizontal flat plate), the rate of heat transfer enhances but decreases the particle deposition rate and plate shear stress. With blowing/suction and in the presence of the magnetic parameter, the plate shear stress and heat transfer increase with nonlinear thermal radiation propagation whereas decreases the particle deposition. The species concentration near the porous plate, velocity, and temperature curves is enhanced by escalating the dissipation parameter. The radiative heat flux boosts the fluid temperature that consequently enhanced the velocity and the species concentration near the porous plate. The fluid velocity past the porous plate is higher in the case of a vertical plate () compared to the classical flow over a horizontal porous plate ().

Long-time solutions for some mixed boundary value problems depicting motions of a class of Maxwell fluids with pressure dependent viscosity

Closed-form expressions are established for dimensionless long-tome solutions of some mixed initial-boundary value problems. They correspond to three isothermal unsteady motions of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure. The fluid motion, between infinite horizontal parallel flat plates, is induced by the lower plate that applies time-dependent shear stresses to the fluid. As a check of the obtained results, the similar solutions corresponding to the classical incompressible Maxwell fluids performing same motions are recovered as limiting cases of present solutions. Finally, some characteristics of fluid motion as well as the influence of pressure-viscosity coefficient on the fluid motion are graphically presented and discussed.

Computational Analysis of Nanoparticle Shapes on Hybrid Nanofluid Flow Due to Flat Horizontal Plate via Solar Collector.

The present work discusses the 2D unsteady flow of second grade hybrid nanofluid in terms of heat transfer and MHD effects over a stretchable moving flat horizontal porous plate. The entropy of system is taken into account. The magnetic field and the Joule heating effects are also considered. Tiny-sized nanoparticles of silicon carbide and titanium oxide dispersed in a base fluid, kerosene oil. Furthermore, the shape factors of tiny-sized particles (sphere, bricks, tetrahedron, and platelets) are explored and discussed in detail. The mathematical representation in expressions of PDEs is built by considering the heat transfer mechanism owing to the effects of Joule heating and viscous dissipation. The present set of PDEs (partial differential equations) are converted into ODEs (ordinary differential equations) by introducing suitable transformations, which are then resolved with the bvp4c (shooting) scheme in MATLAB. Graphical expressions and numerical data are obtained to scrutinize the variations of momentum and temperature fields versus different physical constraints.

Optimum Solar Panel Orientation and Performance: A Climatic Data-Driven Metaheuristic Approach

This study presents an optimization platform based on the climatic data provided by the National Renewable Energy Laboratory (NREL) to determine the optimum solar panel orientation. Our optimization model is simpler to use than the clearness index model since there is no need to calculate the extraterrestrial insolation on a horizontal flat plate and the shape factor. This optimization approach is based on the hourly climatic data. It determines the optimum tilt angle and azimuth angle of a solar panel for the maximum power generation, considering the diurnal variation of climatic conditions. The hourly evaluation of insolation allows setting up a solar panel azimuth angle that responds to the peak power demand. The main data that impacts the solar panel performance consists of the solar direct normal incident (DNI), direct horizontal incident (DHI), global horizontal incident (GHI), ambient temperature, wind speed, and ground albedo, all of which were obtained from the NREL database for over twenty years. The accuracy of the optimization platform introduced in this study is scrutinized by investigating the three locations in the United States with different climatic conditions. The results based on the present optimization model show higher PV power than the general rule of thumb for south-facing panels with title angles the same as the latitude of the location. Moreover, the effect of deviations from optimum panel orientation is discussed to show the versatility of our technique. Our optimization model is easy-to-use, computationally efficient, and capable of being applied to other locations worldwide.

Experimental study on burning rates of large-scale hydrocarbon pool fires under controlled wind conditions

Open square fuel pools with areas of 50 m2, 100 m2, 200 m2, 380 m2, and 400 m2 were used to burn RP-5 aviation fuel and diesel oil, under a well-controlled and regulated horizontal wind field with speeds ranging from 0 to 17 m/s by a large-scale open jet wind tunnel. The mean mass burning rate of the fuel in the quasi-steady period was taken as the representative value. Under the calm condition, the burning rates of the two fuels were proportional to the ratios of the ideal heat of combustion to the effective heat of gasification. The burning rates of different size pool fires were little affected by various wind conditions. With the increase of wind speed, all pool fires exhibited a common pattern in the burning rate, a steady growth followed by a level-off constant value. The traditional Froude number (Fr) was unable to predict the behavior of large-scale pool fires under various wind speeds. A modified Froude number (Fr* = Fr·Re0.2) was developed based on the heat transfer correlation for turbulent mixed convection on a horizontal flat plate and successfully correlated a total of nine different large-scale pool fire experimental data under wind conditions.

Parametric Effects of Heater Size, Contact Angle, and Surrounding Vessel Size on Pool Boiling Critical Heat Flux From Horizontal Surfaces

Abstract Saturated water at one-atmosphere pressure was boiled on horizontal flat copper disks of diameters 1.0, 1.5, and 2.0 cm, respectively. The contact angle was varied from about 10 to 80 deg by controlling thermal oxidation of the disks, while the surrounding vessel size was changed by placing glass tubes of different inner diameters around the disks. Nucleate boiling heat transfer data were obtained up to critical heat flux (CHF), where vapor removal pattern was photographed. Vapor jet diameter and the dominant wavelength at water–steam interface were measured from the photographs for the well wetted disks. For well wetted surfaces, the magnitude of CHF increased when the heater size was reduced from 2.0 to 1.0 cm. Improving the wettability enhanced the CHF substantially, whereas the increased size of the liquid-holding vessel had a smaller effect. The highest measured CHF is 233 W/cm2 or 2.11 times Zuber's CHF prediction for infinite horizontal flat plates. It was obtained on a 1.0-cm-diameter disk of contact angle about 10 deg surrounded by a large vessel. The CHF for this surface was increased from 203 to 233 W/cm2 when the ratio of heater size to surrounding vessel size was decreased from 1 to about 0.

Numerical analysis of porous flat plate solar collector under thermal radiation and hybrid nanoparticles using two-phase model

Solar collectors will play a very important role in absorbing solar renewable energy for use in various industries in the future of the world. This study looks at the resulting combination of using porous medium and hybrid nanofluids, in the presence of thermal radiation, on the thermo-hydrodynamic features, heat transfer, supply temperature, and hybrid nanoparticles’ distribution within a horizontal flat plate solar collector. The two-phase approach is considered for modelling. The migration of Ag-Al2O3 hybrid nanoparticles due to the Brownian motion and thermophoresis effects was also taken into account. The set of governing equation was numerically solved employing the finite element method. The investigation is performed by reporting the roles of hybrid nanofluid concentration, porosity coefficient, Darcy number, Reynolds number, porous media to hybrid nanofluid thermal conductivity ratio, Brownian motion parameter, thermophoretic parameter, radiation parameter, and Schmidt number. The results indicate that The high values of porosity coefficient, radiation parameter, conductivity ratio, and thermophoretic parameter ameliorate thermophoresis effects, and therefore, a high concentration of nanoparticles was observed near the bottom part of the collector, especially at low Reynolds. Also, Employing hybrid nanofluid lead to a decrease in the heat transfer rate and slightly raised the supply temperature at low Re.

Uniform suction or blowing control influence on double diffusion mechanism effectiveness in confined wall jet

Natural vortex development in double diffusive confined wall jet flow is firstly analyzed as a basic state. A consecutive vortices production and shedding processes are observed at moderated Reynolds numbers. The influence of these phenomena on combined transfers is then discussed. Strouhal number evolution was determined by spectral analysis conducted in the near-field region of the laminar wall jet. Accordingly, two critical values were found indicating the transitions between stationary, non stationary and quasi-periodic states. Uniform amounts of water are then added or extracted through a thin slot placed on the horizontal flat plate in order to control large structures creation and growth. The main purpose is to assess the effectiveness of uniform suction or blowing on each flow state and to establish the appropriate conditions under which the natural instability disappears. An Average Nusselt and Sherwood numbers as well as skin friction coefficient dependent behavior were observed which implies that vortex dynamic directly affects thermo-solutal transfer.