Vertical Flat Plate Research Articles

Heat and Mass Transfer Characteristics of Nanofluids in a Rotating System: A Convective Boundary Layer Flow

Introduction: Convective heat and mass transfer in nanofluids is a topic of major contemporary interest in both science and technology. In view of this, an unsteady MHD free convective flow of nanofluids through a porous medium bound by a moving vertical semi-infinite permeable flat plate with a constant heat source and convective boundary condition in a rotating frame of reference is studied theoretically. Experimental: The novelty is the consideration of constant heat source and convective boundary condition in a rotating frame. The velocity along the plate i.e., slip velocity is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are of the same oscillatory type. The dimensionless governing equations for this investigation are solved analytically using small perturbation approximation. Two types of nanofluids, namely Cu-water and Al2O3-water are used. Results: The effects of various parameters on the flow, heat and mass transfer characteristics are discussed through graphs and tables. Conclusion: An increase in the convective parameter and nanoparticle volume fraction leads to increase the thermal boundary layer thickness but opposite effect occurs for heat generation.

Elliptic tube free convection augmentation: An experimental and ANN numerical approach

Experimental results of free convection thermal performance on the elliptical-tube outer surface at various inclination angles (θ) and heat fluxes (q) with artificial neural network modelling (ANN) and 3D ANSYS numerical evaluations are presented. The considered parameters include: axial distance (0.1 ≤ X/L ≤ 0.9), (0° ≤ θ ≤ 90°), and Rayleigh number (2.6 × 106 ≤ Ra ≤ 2.05 × 108). Bayesian regularization algorithm as a method of back-propagation technique is used for selecting the optimal ANN size. Results revealed that Nu increases with the increase in θ at constant Ra. Furthermore, θ = 90° gives higher values of Nu compared to all other elliptical-tube inclination angles at the considered Ra range. The elliptical-tube shape with major to minor diameter of (≈1.8) and at θ = 90° can be approximated as a vertical flat plate case. So, the elliptical-tube with θ = 90° is equivalent to two vertical-plates. The recapitulation of the ANN results indicates that, the highest Nu values exist at the tube two peripheral ends with (405 W/m2 ≤ q ≤ 885 W/m2) and Nu achieves the highest values at 555 W/m2. The current experimental data is correlated and compared with the ANN model output and other reported work in the literature.

Analysis of Natural Convection Bionanofluid Between Two Vertical Parallel Plates

In this paper, natural convection flow of non-Newtonian bionanofluid flow between two vertical flat plates is considered. Sodium alginate (SA) is considered the base non-Newtonian fluid, and nanoparticles such as titania (TiO2) and alumina (Al2O3) were added to them. Analytical solutions for temperature and velocity field are determined by means of integral transform (Laplace transform) method. The influences of some physical parameters non-dimensional velocity and temperature profiles are graphically underlined.

Overlapping Multi-Domain Spectral Method for Conjugate Problems of Conduction and MHD Free Convection Flow of Nanofluids over Flat Plates

An efficient overlapping multi-domain spectral method is used in the analysis of conjugate problems of heat conduction in solid walls coupled with laminar magnetohydrodynamic (MHD) free convective boundary layer flow of copper (Cu) water and silver (Ag) water nanofluids over vertical and horizontal flat plates. The combined effects of heat generation and thermal radiation on the flow has been analyzed by imposing a magnetic field along the direction of the flow to control the motion of electrically conducting fluid in nanoscale systems. We have assumed that the nanoparticle volume fraction at the wall may be actively controlled. The dimensionless flow equations are solved numerically using an overlapping multi-domain bivariate spectral quasilinearisation method. The effects of relevant parameters on the fluid properties are shown graphically and discussed in detail. Furthermore, the variations of the skin friction coefficient, surface temperature and the rate of heat transfer are shown in graphs and tables. The findings show that the surface temperature is enhanced due to the presence of nanoparticles in the base fluid and the inclusion of the thermal radiation, heat generation and transverse magnetic field in the system. An increase in the nanoparticle volume fraction, heat generation, thermal radiation, and magnetic field parameter enhances the nanofluid velocity and temperature while reducing the heat transfer rate. The results also indicate that the Ag–water nanofluid has higher skin friction and surface temperature than the Cu–water nanofluid, while the opposite behaviour is observed in the case of the rate of heat transfer. The computed numerical results are compared with previously published results and found to be in good agreement.

Mixed convection boundary layer flow and heat transfer over a vertical plate embedded in a porous medium filled with a suspension of nano-encapsulated phase change materials

The flow and thermal behavior of nano-encapsulated phase change materials (NEPCMs) dispersed in a liquid is investigated over a vertical flat plate. The NEPCM particles are consist of an encapsulation shell and a core made of phase change materials (PCMs). When the temperature of the liquid around the NEPCM particle is higher than the fusion temperature of the PCM core, the PCM core absorbs a notable amount of heat (the latent heat of the phase change) from the host fluid and melts. The vertical plate is embedded in a porous medium, and the porous medium is saturated with the suspension of NEPCM. There is a uniform flow over the plate, which can aid or oppose the natural convection flow over the plate. The partial differential governing equations for the flow and heat transfer of NEPCM suspension are introduced and transformed into a high order boundary value ordinary differential equation. The finite difference method with a colocation technique as the grid adaptation and automatic error control is utilized to integrate the governing equations. Validations are performed by comparing the results with the literature. It is found that there are two solution branches in the case of high opposing flows. The results indicate that the presence of NEPCM particles enhances the heat transfer over the plate. The decrease in the fusion temperature of NEPCM cores enhances the heat transfer.

MHD mixed convection boundary layer stagnation-point flow on a vertical surface with induced magnetic field

Purpose This study aims to perform a stability analysis on a steady magnetohydrodynamic (MHD) mixed convection boundary-layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a vertical flat plate. The effect of induced magnetic field is also considered. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB. Findings Dual solutions are found to exist for a certain range of the buoyancy parameter for both the assisting and opposing flows. The results from the stability analysis showed that the first solution (upper branch) is stable and valid physically, while the second solution (lower branch) is unstable. Practical implications This problem is important in many metallurgical processes, namely, drawing, annealing and tinning of copper wires. The results obtained are very useful for researchers to determine which solution is physically stable, whereby mathematically more than one solution exists for the skin friction coefficient and the heat transfer characteristics. Originality/value The present results of the stability analysis are original and new for the problem of MHD mixed convection stagnation-point flow of viscous conducting fluid over a vertical flat plate, with the effect of induced magnetic field.

Unsteady Magnetohydrodynamic Convective Fluid Flow of Oldroyd-B Model Considering Ramped Wall Temperature and Ramped Wall Velocity

This paper examines unsteady magnetohydrodynamic (MHD) convective fluid flow described by the Oldroyd-B model using ramped wall temperature and velocity simultaneously. The fluid flow is closed to an infinite vertical flat plate immersed through a porous medium. Laplace transformation is used to find solutions of momentum and energy equations. Afterwards, the Nusselt number and skin friction coefficient are obtained. A parametric study is performed to investigate the effects of ramped velocity and temperature (at wall) on the considered fluid flow model.

Measurement of unsteady wind loads in a wind tunnel: Scaling of turbulence spectra

Mismatch of turbulence spectra from the corresponding full-scale conditions is a common challenge in wind tunnel modelling of unsteady wind loads on small-scale structures, such as solar panels, heliostats and low-rise buildings. Understanding the effect of this mismatch on the unsteady wind loads is necessary for providing an accurate estimation of wind loads on full-scale structures. The correlation between the turbulence spectra and the unsteady wind loads in wind tunnel measurements is investigated in this study through measurement of unsteady lift and drag forces on horizontal and vertical flat plates. It was found through spectral analysis that the turbulent eddies in the range of reduced frequencies between 0.01 and 1 contributed the most to the unsteady wind loads. An approach for wind tunnel modelling was proposed in which the geometric scaling ratio of each model is determined based on the analysis of the turbulence power spectrum as a function of reduced frequency. The suitable geometric scaling ratio should be then chosen such that the turbulence spectrum as a function of reduced frequency is the closest match to that at full-scale for reduced frequencies between approximately 0.01 and 1.

Effect of Internal Heat Generation and Concentration Change on Free Convection Boundary Layer from Vertical Flat Plate Embedded in Porous Medium

The effects of exponentially decaying internal heat generation (IHG) and internal mass generation (IMG) over specific components are presented numerically on coupled heat and mass transfer by a free convection boundary layer over a vertical flat plate embedded in a fluid-saturated porous medium. Corresponding similarity solutions are used to reduce the governing partial nonlinear differential equations to three ordinary differential equations for the dimensionless stream function, temperature, and concentration with the following parameters: buoyancy force N, exponent of x, λ, and Lewis number Le. Media with and without IHG and IMG are compared in context with the help of graphs and tables. Computations are performed with a system of parameters using built-in codes in Maple. The influences of these parameters on velocity, temperature and concentration profiles, and Sherwood and Nusselt numbers are thoroughly compared and graphically illustrated.

Efficient Multi-Domain Bivariate Spectral Collocation Solution for MHD Laminar Natural Convection Flow from a Vertical Permeable Flat Plate with Uniform Surface Temperature and Thermal Radiation

A recently developed numerical method, multidomain quasilinearization, is applied on a steady laminar, natural convection boundary layer flow of MHD viscous and incompressible fluid from a vertical permeable flat plate with uniform temperature in this paper. Nondimensionless variables are used to transform the governing equations to a system of nondimensional nonlinear partial differential equations. Then the resulting equations are solved numerically by using multidomain quasilinearization method. The numerical results for tangential velocity, transverse velocity, and temperature, skin friction are calculated and shown in various tables and graphs.

Investigation of cross-diffusion effects on Casson fluid flow in existence of variable fluid properties

A numerical investigation has been carried out for coupled partial differential equations which describe varying fluid properties on unsteady, free convective chemically reacting fluid flow on a moving vertical cone and flat plate. The computations for flow, heat, and mass transport in presence of thermal radiation, viscous dissipation, Soret and Dufour effects are carried out using Crank-Nicolson scheme. The influence of active parameters on transport properties of the fluid is displayed in form of graphs and tables. The results elucidate that the consideration of variable fluid properties has a significant influence on the flow, heat and mass transfer characteristics. Strengthening the Casson fluid parameter tends to decelerate the fluid velocity and escalate the local skin friction.

Flow and natural convection heat transfer characteristics of non-Newtonian nanofluid flow bounded by two infinite vertical flat plates in presence of magnetic field and thermal radiation using Galerkin method

The main goal of this paper is to investigate natural convective heat transfer and flow characteristics of non-Newtonian nanofluid streaming between two infinite vertical flat plates in the presence of magnetic field and thermal radiation. Initially, a similarity transformation is used to convert momentum and energy conservation equations in partial differential forms into non-linear ordinary differential equations (ODE) applying meaningful boundary conditions. In order to obtain the non-linear ODEs analytically, Galerkin method (GM) is employed. Subsequently, the ODEs are also solved by a reliable numerical solution. In order to test the accuracy, precision and reliability of the analytical method, results of the analytical analysis are compared with the numerical results. With respect to the comparisons, fairly good compatibilities with insignificant errors are observed. Eventually, the impacts of effective parameters including magnetic and radiation parameters and nanofluid volume fraction on the velocity, skin friction coefficient and Nusselt number distributions are comprehensively described. Based on the results, it is revealed that with increasing the role of magnetic force, velocity profile, skin friction coefficient and thermal performance descend. Radiation parameter has insignificant influence on velocity profile while it obviously has augmentative and decreasing effects on skin friction and Nusselt number, respectively.

A comparative study of heat transfer analysis of fractional Maxwell fluid by using Caputo and Caputo–Fabrizio derivatives

A comparative analysis is carried out to study the unsteady flow of a Maxwell fluid in the presence of Newtonian heating near a vertical flat plate. The fractional derivatives presented by Caputo and Caputo–Fabrizio are applied to make a physical model for a Maxwell fluid. Exact solutions of the non-dimensional temperature and velocity fields for Caputo and Caputo–Fabrizio time-fractional derivatives are determined via the Laplace transform technique. Numerical solutions of partial differential equations are obtained by employing Tzou’s and Stehfest’s algorithms to compare the results of both models. Exact solutions with integer-order derivative (fractional parameter α = 1) are also obtained for both temperature and velocity distributions as a special case. A graphical illustration is made to discuss the effect of Prandtl number Pr and time t on the temperature field. Similarly, the effects of Maxwell fluid parameter λ and other flow parameters on the velocity field are presented graphically, as well as in tabular form.

Natural convection flows due to evaporation of heavier-than-air fluids: Flow direction and validity of using similarity of temperature and vapor density fields

Natural convection driven by evaporation of heavier-than-air fluids from the surface of the heated horizontal and vertical flat plates is studied both experimentally and numerically. The combined buoyancy effects of temperature and vapor density are shown to result in either downward or upward flow depending on the plate temperature and evaporating substance volatility and molar mass. For some substances (e.g., butanol) flow reversals are observed: solutal buoyancy is dominant for low and high temperatures of the heated plate leading to downward flow, whereas at moderate temperatures thermal buoyancy prevails resulting in upward convection. Refractive index fields are measured using Background Oriented Schlieren (BOS). Similarity between the temperature and vapor density fields associated with heat and mass transfer analogy is used to obtain temperature and vapor density fields from experimental data. The validity of this approach is analyzed. Good agreement between experimental temperature and vapor density distributions and numerical simulations is obtained for ethanol vapor, which has Lewis number about 1.8. For butanol vapor, which has Lewis number about 2.5, similarity is violated and temperature and vapor density contributions to refractive index cannot be separated. This is also true for validity of simplified modeling using total expansion coefficient. Similarity is also shown to be violated for hot liquid evaporation from a tank with conductive walls. In this case boundary conditions are dissimilar and upward convective flow of warm clean air near the outer surface of the tank walls is observed, which entrains the heavy vapor.

Experimental investigation of heat transfer by unsteady natural convection at a vertical flat plate

The present study considers the influence of unsteady flow structures in natural convection on the heat transfer from a vertical flat plate to air. The mean and momentary intensity of convective heat transfer were determined experimentally for specific variations of the boundary conditions. For cyclic and step-like changing operation modes of a direct-electrically heated, 2 m-high copper plate, laminar, transitional and turbulent flow regimes were considered. Compared to a quasi-stationary approach, mean deviations of up to 22.0% for cyclic variations and up to 30.2% for step-like changes occur during an unsteady phase. The extent of the deviations shows a dependence on the mean Grashof number, as well as further influencing factors. Phenomenological observations of the unsteady convection flow in the form of visualizations show a temporarily increased mixing of the boundary layer, which also deviates distinctly from a quasi-stationary development. In particular, a temporary occurrence of Kelvin-Helmholtz vortices can be observed.

Sinc-collocation method for solving sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates

This paper seeks to develop an efficient method for solving natural convection of a non-Newtonian nanofluid flow between two vertical flat plates. Sodium alginate is considered as the non-Newtonian fluid, and then two distinct types of nanoparticles, namely silver and copper, are added to it. To do so, the governing boundary layer and temperature equations are reduced to a set of ordinary differential equations. This approach is based on a global collocation method using Sinc basis functions, and the resulting set of ordinary differential equations are replaced by a system of algebraic equations. It is well known that the Sinc procedure converges to the solution at an exponential rate. Numerical results are included to demonstrate the validity and applicability of the method, and a comparison is made with the existing results. Also, the effect of various parameters such as Prandtl number (Pr), dimensionless non-Newtonian viscosity number $$(\delta )$$ and nanoparticle volume fraction ( $$\phi $$ ) on non-dimensional velocity and temperature profiles are discussed. It was concluded from this study that velocity and temperature increased with increasing Pr. Moreover, our results indicate that both the velocity and temperature decrease as $$\delta $$ increases. Finally, the results demonstrated that, when $$\phi $$ increases, the velocity increases but the temperature values decrease.

Viscous and Ohmic dissipation on non-Darcy MHD nanofluid mixed convection flow in porous medium with suction/injection effects

The paper presents the influence of nanofluid flow on MHD mixed convection, incompressible and electrically conducting fluid along a vertical flat plate with viscous and ohmic dissipation effects. The plate is permeable and embedded in a fluid saturated on non-Darcy (Forchheimer flow model) porous medium with suction and injection. Dissipation parameters are described in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformation. The non linear ordinary differential equations are linearized by using Quasi-linearization technique and then solved numerically by using implicit finite difference scheme. To compute the numerical values C programming code is used. The numerical results are analyzed for the effects of various physical parameters such as magnetic parameter Ha, Reynolds number Red, Eckert number, Ec thermophoresis parameter Nt, Brownian motion parameter Nb, suction and injection parameter fw and Lewis number Le. The results obtained are discussed with the help of graphical illustrations.

Chemically reactive species of time-dependent natural convection couple stress fluid flow past an isothermal vertical flat plate

The transient two-dimensional natural convective couple stress fluid flow past a semi-infinite vertical flat plate in the presence of first-order homogenous chemical reaction is investigated. The analysis has been carried out by considering the effects of skin-friction coefficient and Nusselt and Sherwood numbers. The unsteady coupled nonlinear governing flow equations have been solved by applying the Crank–Nicolson implicit finite difference scheme. For the different set physical parameters, graphs are shown and examined. A relevant study with existing results is made in a limiting sense. The transient and steady-state velocity profiles decrease as the chemical reaction parameter, Schmidt number, and couple stress parameter increase. The deviations of concentration, temperature, and velocity contours of the couple stress fluid flow are considerably varied in comparison with the Newtonian fluid flow.

A numerical study of natural convection properties of supercritical water (H2O) using Redlich–Kwong equation of state

In this article, the Crank-Nicolson implicit finite difference method is utilized to obtain the numerical solutions of highly nonlinear coupled partial differential equations (PDEs) for the flow of supercritical fluid (SCF) over a vertical flat plate. Based on the equation of state (EOS) approach, suitable equations are derived to calculate the thermal expansion coefficient (\( \beta \)) values. Redlich–Kwong equation of state (RK-EOS), Peng-Robinson equation of state (PR-EOS), Van der Waals equation of state (VW-EOS) and Virial equation of state (Virial-EOS) are used in this study to evaluate \( \beta \) values. The calculated values of \( \beta \) based on RK-EOS is closer to the experimental values, which shows the greater accuracy of the RK-EOS over PR-EOS, VW-EOS and Virial-EOS models. Numerical simulations are performed for \( {\text{H}}_{2} {\text{O}} \) in three regions namely subcritical, supercritical and near critical regions. The unsteady velocity, temperature, average heat and momentum transport coefficients for different values of reduced pressure and reduced temperature are discussed based on the numerical results and are shown graphically across the boundary layer.

Filmwise Condensation of Steam on Pin Fin Arrays Fabricated by Selective Laser Melting

In this study, nine vertical flat plates of pin fin arrays were fabricated by selective laser melting to investigate the possible enhancements of external condensation. These specimens are cylindrical pin fins of the same fin diameter of 300 μm but are of different fin heights (l) and fin pitches (p) from 300 μm to 900 μm. Experiments were conducted in a condensation chamber with near quiescent vapor to simulate free-convection condensation. The aim is to investigate the effects of fin pitch and fin height on the condensation heat transfer performance of the surfaces. The results of this study show that the increase in fin height and the decrease in fin pitch lead to a systematic increase in the condensation heat flux (q''). At the same fin pitch, the increase in fin height from 600 μm to 900 μm resulted in a more significant increase in q'' as compared to the increase in fin height from 300 μm to 600 μm. On the other hand, at the same fin height, a larger increase in q'' is observed when the fin pitch is reduced from 900 μm to 600 μm as compared to the reduction in fin pitch from 600 μm to 300 μm. It can be deduced that increasing the fin height enables the fins to protrude out of the thick condensate film and increases the effective heat transfer area of the surfaces. However, when the fin density is large, it impedes the condensate drainage path and limits the enhancement in q''. The enhancement factor (η), which is the ratio of the average condensation heat flux of a pin fin surface to that of a plain surface, was computed for each specimen. The highest η value of 1.72 was achieved with the specimen of 900 μm fin height and 300 μm fin pitch. Finally, a relationship between η and the dimensionless fin pitch-to-height ratio (p/l) is proposed.