Free Convection Boundary Layer Research Articles

MHD Free Convection Boundary Layer Flow on a Horizontal Circular Cylinder in a Williamson Hybrid Ferrofluid with Viscous Dissipation

The present research examined the flow of a horizontal circular cylinder immersed in a Williamson hybrid ferrofluid via free convection boundary layer flow. The fluid flow is modelled by means of governing partial differential equations that incorporate viscous dissipation and magnetohydrodynamic (MHD) effects. Prior to being converted into a more practical partial differential equation, these dimensional equations are reduced to a non-dimensional form by utilising appropriate dimensionless variables. The Keller-box approach is then used to solve these equations with fewer dependent variables numerically. Graphical representations are generated, and the impacts of different interested factors are analysed using MATLAB software. According to the results, the hybrid ferrofluid outperformed ferrofluid with the same particle volume fraction in terms of skin friction and convective heat transfer capabilities.

Instability of a vertical free convection boundary layer flow: Asymptotically from a perfectly flat one to a highly curved one

Instability of a vertical free convection boundary layer flow: Asymptotically from a perfectly flat one to a highly curved one

The role of adding carbon nanoparticles to free convective boundary layer viscoelastic fluid flow past a vertical porous cone surface: application in wastewater treatment

The role of adding carbon nanoparticles to free convective boundary layer viscoelastic fluid flow past a vertical porous cone surface: application in wastewater treatment

Hall and Ion Slip Current influence on Unsteady MHD Free Convective Boundary Layer Flow Past a Vertical Porous Plate with Thermal Radiation and Chemical Reaction

The analytical reconnaissance has been effectuated to explicate the influence of Hall and ion-slip current on nonlinear MHD free convective flow near a vertical porous plate in presence of chemical reaction and Dufour effect. In this assessment the governing PDE’s are determined analytically. The impact of multifarious physical parameters has been contemplated on velocity, temperature as well as concentration which were exemplified via numerous graphs whereas quantification for the skin fiction, nusselt number and Sherwood number are demonstrated in numeric data form and are reported in table. In this examination mainly observed that velocity declined with the incremental values of Hall current as well as ion-slip current. Meanwhile velocity as well as temperature accelerated by means of the incremental values of Dufour number. However concentration diminished with the accelerated values of chemical reaction along with Schmidt number

Triple diffusive free magneto-convection of electro-conductive nanofluid from a vertical stretching sheet

In the present investigation, an analysis is carried out to study the MHD triple diffusive free thermo-solutal convection boundary layer flow of an electro-conductive nanofluid flow over a vertical stretching sheet. This problem is relevant to magnetic nanomaterials fabrication operations in which multiple species in addition to nanoparticles are present. In addition to the nanoparticle diffusion, two different salts (species) having different properties are considered. A variable magnetic field is applied transverse to the vertical sheet. It is assumed that the surface is in contact with the hot magnetic nanofluid at a temperature which provides a variable heat transfer coefficient. Buongiorno’s model is employed for the nanofluid. It is also assumed that the Oberbeck-Boussinesq approximation is valid and the mixture of nanofluid and salts is homogenous and is in local thermal equilibrium. In addition, the thermal energy equation features cross-diffusion (Soret and Dufour) terms for both components of salts having different concentration. Appropriate similarity transformations are deployed to render the model non-dimensional. The emerging transformed dimensionless non-linear non-dimensional ordinary differential boundary value problem is solved with the robust bvp4c method in MATLAB. Validation with previous studies has been included for special cases of the general model. The simulations show that the addition of nanoparticles and salts, strongly modifies Temperature and nanoparticle and salt 1 and 2 concentrations. With stronger magnetic field the velocity is suppressed as is momentum boundary layer thickness whereas temperatures are boosted.

The Newtonian heating effect on MHD free convective boundary layer flow of magnetic nanofluids past a moving inclined plate

The effect of magnetic strength on the MHD free convection flow of nanofluids over a moving inclined plate with Newtonian heating is analyzed. The governing partial differential equations with Newtonian heating boundary conditions are transformed into a system of nonlinear coupled ordinary differential equations (ODEs) by using similarity transformations. The Keller Box method was used as a solvation method for ODEs. The skin friction and Nusselt number are evaluated analytically as well as numerically in a tabular form. Numerical results for velocity and temperature are shown graphically for various parameters of interest, and the physics of the problem is well explored. The significant findings of this study are promoting an angle of an aligned magnetic field, magnetic strength parameter, the angle of inclination parameter, local Grashof number, the volume fraction of nanoparticles, and Newtonian heating parameter. The result shows that the moving inclined plate in the same direction increases the skin friction coefficient and reduces the Nusselt number. It is also observed that the velocity of moving an inclined plate with the flow is higher compared to the velocity of moving an inclined plate against the flow. The temperature of a moving inclined plate with the flow is decreased much quicker than the temperature of a moving inclined plate against the flow. The other noteworthy observation of this study demonstrates that the Nusselt number in the Newtonian heating parameter shows that Fe3O4-kerosene is better than Fe3O4-water.

Convective Flow of Water-Ethylene Glycol (50:50) Based Nanofluid Over a Spinning Down-Pointing Vertical Cone in a Darcy Porous Medium

The present work analyzes the free convective boundary layer flow of nanofluids around a heated and spinning down pointing vertical cone with the effect of magnetic field placed in a porous medium. The solutions of the partial differential equations with slip boundary conditions, which describes the flow are attained by a numerical based technique called fourth order Runge-Kutta method with shooting techniques after converting into ordinary differential equations with suitable transformations. The impact of governing parameter on velocity profile, temperature distribution is represented graphically. The range of the variables are 0 < M < 4, 0.01 < Φ < 0.04, 0 < ɛ < 4, 0 < Da < 4, 0.1 < Γ1 < 1.5 and 0.1 < Γ2 < 1.5. Increasing the value of Da noticeably promotes the F′(y) and G(y) and diminishes the H(y). Regarding tangential velocity, Fe3O4 dominates Al2O3 for every values of Magnetic parameter, spin parameter, Darcy number, velocity and thermal slip parameter. Fe3O4 possess 0.87% of high heat transfer rate than Al2O3 with respect to nanoparticle volume fraction. In case of slip parameters (velocity and thermal) Al2O3 shows good heat transfer rate than Fe3O4 with 0.93% and 0.98% respectively. It is scrutinized that the current results are in excellent compatibility with the outcomes noted as in previous works.

Magneto-convective hybrid nanofluid slip flow over a moving inclined thin needle in a Darcy-Forchheimer porous medium with viscous dissipation

PurposeThe purpose of this study is to provide that porous media and viscous dissipation are crucial considerations when working with hybrid nanofluids in various applications.Recent years have witnessed significant progress in optimizing these fluids for enhanced heat transfer within porous (Darcy–Forchheimer) structures, offering promising solutions for various industries seeking improved thermalmanagement and energy efficiency.Design/methodology/approachThe first step is to transform the original partial differential equations into a system of first-order ordinary differential equations (ODEs). The fourth-order Runge–Kutta method is chosen for its accuracy in solving ODEs. The present study investigates the free convective boundary layer flow of hybrid nanofluids over a moving thin inclined needle with the slip flow brought about by inclined Lorentz force and Darcy–Forchheimer porous matrix, viscous dissipation.FindingsIt is found that slip conditions (velocity and Thermal) exist for a range of the natural convection boundary layer flow. In the hybrid nanofluid flow, which consists of Al2O3 and Fe3O4 are nanoparticles, H2O − C2H6O2 (50:50) are considered as the base fluid. The consequence of the governing parameter on the momentum and temperature profile distribution is graphically depicted. The range of the variables is 1 ≤ M ≤ 4, 1 ≤ d ≤ 2.5, 1 ≤ δ ≤ 4, 1 ≤ Fr ≤ 7, 1 ≤ Kr ≤ 7 and 0.5≤λ ≤ 3.5. The Nusselt number and skin friction factors are used to calculate the numerical values of various parameters, which are displayed in Table 4. These analyses elucidate that upsurges in the value of the Fr noticeably diminish the momentum and temperature. It is investigated to see if the contemporary results are in outstanding promise with the outcomes reported in earlier works.Practical implicationsThe results can be very helpful to improve the energy efficiency of thermal systems.Social implicationsThe hybrid nanofluids in heat transfer have the potential to improve the energy efficiency and performance of a wide range of systems.Originality/valueThis study proposes that in the combined effects of hybrid nanofluid properties, the inclined Lorentz force, the Darcy–Forchheimer model for porous media and viscous dissipation on the boundary layer flow of a conducting fluid over a moving thin inclined needle. Assessing the potential practical applications of the hybrid nanofluids in inclined needles, this could involve areas such as biomedical engineering, drug delivery systems or microfluidic devices. In future should explore the benefits and limitations of using hybrid nanofluids in these applications.

The Departure from Mixed-Layer Similarity During the Afternoon Decay of Turbulence in the Free-Convective Boundary Layer: Results from Large-Eddy Simulations

This study analyses the departure of the velocity-variances profiles from their quasi-steady state described by the mixed-layer similarity, using large-eddy simulations with different prescribed shapes and time scales of the surface kinematic heat flux decay. Within the descriptive frames where the time is tracked solely by the forcing time scale (either constant or time-dependent) describing the surface heat flux decay, we find that the normalized velocity-variances profiles from different runs do not collapse while they depart from mixed-layer similarity. As the mixed-layer similarity relies on the assumption that the free-convective boundary layer is in a quasi-equilibrium, we consider the ratios of the forcing time scales to the convective eddy-turnover time scale. We find that the normalized velocity-variances profiles collapse in the only case where the ratio (widetilde{r}) of the time-dependent forcing time scale to the convective eddy-turnover time scale is used for tracking the time, supporting the independence of the departure from the characteristics of the surface heat flux decay. As a consequence of this result, the knowledge of widetilde{r} is sufficient to predict the departure of the velocity variances from their quasi-steady state, irrespective of the shape of the surface heat flux decay. This study highlights the importance of considering both the time-dependent forcing time scale and the convective eddy-turnover time scale for evaluating the response of the free-convective boundary layer to the surface heat flux decay.

Similarity solution for MHD nanofluid flow with heat generation in the presence of radiation and chemical reaction effects

An analysis has been carried out to study the two-dimensional free convective boundary layer MHD nanofluid flow past an inclined plate with heat generation, chemical reaction and radiation effects under convective boundary conditions. The partial differential equations describing the flow are coupled nonlinear. They have been reduced to nonlinear ordinary differential equations by utilizing a similarity transformation, which is then solved numerically with the aid of the Runge-Kutta-based shooting technique. Graphs depict the influence of different controlling factors on the velocity, temperature, and concentration profiles. Numerical findings for skin friction, Nusselt number and Sherwood number are reviewed for distinct physical parameter values. In a limited sense, there is a good correlation between the current study's results and those of the earlier published work.

Theoretical prediction of temperature difference between prefrontal cortex and forehead skin for fever screening

To improve reliability of fever screening, many studies have been conducted on the relationship between forehead skin and core temperatures. However, all studies thus far were based on only statistical analyses of temperature data, and it remains unsolved how forehead skin temperature is determined and controlled by environmental temperature as well as face details of individual. This study examined heat transfer in a free convection thermal boundary layer on the human forehead theoretically and experimentally to propose a theoretical model describing the relationship between prefrontal cortex (PFC) and forehead skin temperatures. Temperature distributions across the forehead boundary layer measured using a resistance thermometer probe showed that the convective heat flux on the forehead, including the case of wearing face mask, could be estimated similarly to that in a laminar free convection boundary layer on a heated vertical plate. It was also shown that the difference between PFC and forehead skin temperatures measured using a zero-heat-flux core-temperature monitoring probe and a thermocouple attached to the forehead was well represented by a simple formula derived from analyses of radiative and convective heat fluxes over a normal range of environmental temperature. Wearing a face mask little affected the temperature difference between PFC and forehead skin. These results provide a scientific basis for fever screening from thermo- and fluid-dynamics viewpoints.

Heat Transfer of Buoyancy and Radiation on the Free Convection Boundary Layer MHD Flow across a Stretchable Porous Sheet

Theoretical influence of the buoyancy and thermal radiation effects on the MHD (magnetohydrodynamics) flow across a stretchable porous sheet were analyzed in the present study. The Darcy–Forchheimer model and laminar flow were considered for the flow problem that was investigated. The flow was taken to incorporate a temperature-dependent heat source or sink. The study also incorporated the influences of Brownian motion and thermophoresis. The general form of the buoyancy term in the momentum equation for a free convection boundary layer is derived in this study. A favorable comparison with earlier published studies was achieved. Graphs were used to investigate and explain how different physical parameters affect the velocity, the temperature, and the concentration field. Additionally, tables are included in order to discuss the outcomes of the Sherwood number, the Nusselt number, and skin friction. The fundamental governing partial differential equations (PDEs), which are used in the modeling and analysis of the MHD flow problem, were transformed into a collection of ordinary differential equations (ODEs) by utilizing the similarity transformation. A semi-analytical approach homotopy analysis method (HAM) was applied for approximating the solutions of the modeled equations. The model finds several important applications, such as steel rolling, nuclear explosions, cooling of transmission lines, heating of the room by the use of a radiator, cooling the reactor core in nuclear power plants, design of fins, solar power technology, combustion chambers, astrophysical flow, electric transformers, and rectifiers. Among the various outcomes of the study, it was discovered that skin friction surges for 0.3 ≤F1≤ 0.6, 0.1 ≤k1≤ 0.4 and 0.3 ≤M≤ 1.0, snf declines for 1.0 ≤Gr≤ 4.0. Moreover, the Nusselt number augments for 0.5 ≤R≤ 1.5, 0.2 ≤Nt≤ 0.8 and 0.3 ≤Nb≤ 0.9, and declines for 2.5 ≤Pr≤ 5.5. The Sherwood number increases for 0.2 ≤Nt≤ 0.8 and 0.3 ≤Sc≤ 0.9, and decreases for 0.1 ≤Nb≤ 0.7.

Comparison between homotopy analysis method and homotopy renormalization method in fluid mechanics

In this paper, the homotopy renormalization method (HTR) is compared with the homotopy analysis method (HAM), an analytical approximation technique for highly nonlinear problems. Four problems in fluid mechanics, including the Blasius viscous flow, magnetohydrodynamic flow, free-convective boundary-layer flow, and Von Kármán swirling viscous flow, are used for detailed comparison. It is found that the HAM approximations are much more accurate than the HTR approximations at the same order. Furthermore, higher-order approximations with smaller errors can be obtained relatively simply by the HAM, while the HTR struggles in such scenarios. All of these confirm the superiority of the HAM for highly nonlinear problems in fluid mechanics.

Homotopy Analysis Method for Free-Convective Boundary-Layer Equation Using Pade ´Approximation

This paper is devoted to the study of a free-convective boundary layer flow modeled by a system of nonlinear ordinary differential equations. We apply Homotopy Analysis Method (HAM) along with Pade´ approximation to solve free-convective boundary-layer equation. It is observed that the combination of HAM and the Pade´ approximation improves the accuracy and enlarge the convergence domain.

MHD VISCO-ELESTIC BOUNDARY LAYER FLOW OF FLUID THROUGH POROUS MEDIUM

In the present paper the behavior of the free convective boundary layer flow of an electrically con-ducting visco-elastic,incompressible fluid through a porous medium over a continuously moving surface in the presence of uniform magnetic field with constant suction is studied. A uniform magnetic field is assumed to be applied perpendicularly to the moving surface. A similarity transformation is used which reduces the partial differential equation to ordinary differential equation. The velocity and temperature field is obtained. The effect of Reynolds number (Re), Hartmann number (H), Grashof number (Gr), viscoelastic parameter (K0) and permeability parameter (K) on velocity field and temperature field are discussed with the help of graphs.

Investigation of onset of velocity transition in free convection over an inclined flat plate by PIV

In this work, the experimental investigation of onset of velocity transition in free convection boundary layer over a 45° inclined plate has been carried out. Experiments were performed on a 150 mm long flat plate with uniform heat flux ranging from 100 W/m2 to 5000 W/m2. Particle image velocimetry (PIV) technique was used to determine the flow characteristics over an inclined plate. The impact of various hydrodynamic parameters such as shear stress and velocity boundary layer thickness for defining or identifying the onset of velocity transition has been discussed. Also, the influence of various values of the heat fluxes on the onset of transition has been examined. It has been observed that the initiation of transition is first manifested as an increase in the overall velocity boundary layer thickness. Therefore, the thickness of the velocity boundary layer has been used as a hydrodynamic measure to determine the streamwise distance from the leading edge where the transition begins. This distance decreases with an increase of heat flux. The critical Rayleigh number for the onset of the transition under various heating conditions has been reported. For example, the critical Rayleigh numbers for the beginning of transition at heat fluxes of 100 W/m2 and 5000 W/m2 are 6.07 × 108 and 2.73 × 109 respectively.

Free convection boundary layer correlations for a vertical plate with nonuniform heating

An analytical study of a free convection boundary layer (BL) for a laminar and steady flow over a vertical flat plate (VFP) having nonuniform thermal conditions has been investigated. The plate is subjected to a variable wall heat flux of where is the distance along the VFP from the leading edge and is a reference heat flux. The boundary layer equations for nonuniform wall heat flux conditions have been formulated. These equations are then solved numerically for the range of exponents and Prandtl numbers () of −0.25 to 1 and 0.01 to 1000 respectively. The effects of two physical parameters and on the characteristic of thermal boundary layer (TBL) and hydrodynamic boundary layer (VBL) are described. Moreover, correlations of TBL and VBL thicknesses have been presented as a function of Pr and The TBL and VBL thickness are more influenced by Pr as compared to These correlations are reasonably accurate for uniform heat flux (n = 0) proposed by A. Bejan using a scale analysis and no other such correlations are available for nonuniform heat flux for a wide range of Prandtl numbers (Pr). It has been found that when both the BL thicknesses decrease with the Pr till a value of is reached. For the growth of VBL and TBL thickness over the VFP increases and decreases respectively. Consequently, the local skin friction coefficient decreases and the local Nusselt number increases with the increase in and at a fixed value of modified Rayleigh number.

Free Convection Boundary Layer Flow from a Vertical Truncated Cone in a Hybrid Nanofluid

The present study investigates the mathematical model of free convection boundary layer flow from a vertical truncated cone immersed in Cu/water nanofluid and Al2O3-Cu/water hybrid nanofluid. The governing non-linear equations are first transformed to a more convenient set of partial differential equations before being solved numerically using the Keller-box method. The numerical values for the reduced Nusselt number and the reduced skin friction coefficient are obtained and illustrated graphically as well as temperature profiles and velocity profiles. Effects of the alumina Al2O3 and copper Cu nanoparticle volume fraction for hybrid nanofluid are analyzed and discussed. It is found that the high-density and highly thermal conductivity nanoparticles like copper contributed more in skin friction and convective heat transfer capabilities. The appropriate nanoparticles combination in hybrid nanofluid may reduce the friction between fluid and surface but yet still gave the heat transfer capabilities comparable to metal nanofluid.

Influence of viscous dissipation and spanwise cosinusoidally fluctuating temperature on MHD free convective boundary layer flow with radiation absorption and chemical reaction

AbstractThe current reconnaissance emphasis on spanwise cosinusoidally fluctuating temperature along with time deepened as well as radiation absorption on unsteady magneto‐hydrodynamics free convective heat and mass transfer boundary layer flow with viscous dissipation, constant suction normal to an infinite hot vertical porous plate in the existence of chemical reaction by means of heat generation. The analytical solution of nonlinear PDE's governing the flow has been accomplished by employing a second‐order multiple regular perturbation method within the stipulated boundary conditions. Velocity, temperature, concentration as well as Sherwood have been exemplified graphically; along with Skin friction, and Nusselt numbers are ascertained in tabular form. Eventually, it was found that velocity, temperature, and Skin friction accelerated with the accumulative values of Eckert number and radiation absorption, but conflicting results emerged in the case of Prandtl number. Contemporaneously Sherwood's number depreciated with the magnification of the chemical reaction parameter as well as the Schmidt number.

Newtonian Heating Effect on Heat Absorbing Unsteady MHD Radiating and Chemically Reacting Free Convection Flow Past an Oscillating Vertical Porous Plate

In this article, we have discussed in detail the effect of Newtonian heating on MHD unsteady free convection boundary layer flow past an oscillating vertical porous plate embedded in a porous medium with thermal radiation, chemical reaction and heat absorption. The governing PDEs of the model together with related initial and boundary conditions have been solved numerically by the finite element method. The dimensionless velocity, temperature and concentration profiles are analyzed graphically due to the effects of key parameters in the concerned model problem. Computed results for the skin friction coefficient, Nusselt number and Sherwood number are put in tabular form. It is observed that the thermal and mass buoyancy effects support the velocity whilst a reverse effect is noticed when the strength of the magnetic field is increased. The velocity and temperature enhances with an increase in the Newtonian heating and thermal radiation whilst a reverse effect is observed with an increase in the Prandtl number and heat absorption parameter. Increasing Schmidt number and chemical reaction parameter tends to depreciate both velocity and concentration. The Newtonian heating, thermal radiation and magnetic field tends to decrease in the skin friction. The Nusselt number increases with increasing Newtonian heating and heat absorption parameters. An increase in the Schmidt number and chemical reaction rate tends to improve the Sherwood number.