Free Convection Boundary Layer Flow Research Articles

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.

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.

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.

A note on the free convection boundary-layer flow over a vertical surface with spatial internal heat generation

A note on the free convection boundary-layer flow over a vertical surface with spatial internal heat generation

Validation of the Local Thermal Equilibrium Assumption for Free Convection Boundary Layer Flow Over a Horizontal Cylinder Embedded in an Infinite Saturated Porous Medium

Validation of the Local Thermal Equilibrium Assumption for Free Convection Boundary Layer Flow Over a Horizontal Cylinder Embedded in an Infinite Saturated Porous Medium

Validation of the Local Thermal Equilibrium Assumption for Free Convection Boundary Layer Flow Over a Horizontal Cylinder Embedded in an Infinite Saturated Porous Medium

Validation of the Local Thermal Equilibrium Assumption for Free Convection Boundary Layer Flow Over a Horizontal Cylinder Embedded in an Infinite Saturated Porous Medium

Free Convection Boundary Layer Flow over a Horizontal Circular Cylinder in Al2O3-Ag/Water Hybrid Nanofluid with Viscous Dissipation

In this paper, the mathematical model of free convection boundary layer flow of horizontal circular cylinder immersed in Ag/Water nanofluid and Al2O3-Ag/Water hybrid nanofluid are considered. The governing non-linear partial differential equations are first transformed to a more convenient way 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 Prandtl number, Eckert number and nanoparticle volume fraction are analyzed and discussed. It is found that the Nusselt number for Al2O3-Ag/Water hybrid nanofluid is comparable with Ag/Water nanofluid with a reduction in skin friction coefficient. The preliminary results reports here are important as a reference in exploring the potential of hybrid nanofluid to reduce the production cost compared to the used of metal nanofluid.

Lie Symmetry Group for Unsteady Free Convection Boundary-Layer Flow over a Vertical Surface

The Lie symmetry group transformation method was used to investigate the partial differential equations that model the motion of a natural convective unsteady flow past to a non-isothermal vertical flat surface. The one-parameter Lie group transformation was applied twice consecutively to convert the motion governing equations into a system of ordinary differential equations. The obtained system of ordinary differential equations was solved numerically using the Lobatto IIIA formula (implicit Runge–Kutta method). The effect of the Prandtl number on the temperature and velocity profiles is illustrated graphically.

Hydromagnetic Effects on Hybrid Nanofluid (Cu–Al2O3/Water) Flow with Convective Heat Transfer Due to a Stretching Sheet

In this paper, transient free convective boundary layer flow of a viscous hybrid nanofluid due to a vertical stretching sheet with MHD effects is studied numerically using the Crank Nicolson finite difference numerical technique. To explore the properties of heat transfer and the flow field due to a vertical stretching sheet in the existence of a Lorentz force, two different fluids, specifically Cu–Al2O3/water and Cu/water, are utilized. The results of different physical parameters and the practical quantities of concern that they affect are investigated. According to this article’s results, Cu–Al2O3/water has a superior heat transfer rate than Cu/water in a magnetic field setting. Various other nano mixtures can be attempted to attain the optimal heat transfer rate.

On the Numerical Analysis of Unsteady MHD Boundary Layer Flow of Williamson Fluid Over a Stretching Sheet and Heat and Mass Transfers

A thorough and detailed investigation of an unsteady free convection boundary layer flow of an incompressible electrically conducting Williamson fluid over a stretching sheet saturated with a porous medium has been numerically carried out. The partial governing equations are transferred into a system of non-linear dimensionless ordinary differential equations by employing suitable similarity transformations. The resultant equations are then numerically solved using the spectral quasi-linearization method. Numerical solutions are obtained in terms of the velocity, temperature and concentration profiles, as well as the skin friction, heat and mass transfers. These numerical results are presented graphically and in tabular forms. From the results, it is found out that the Weissenberg number, local electric parameter, the unsteadiness parameter, the magnetic, porosity and the buoyancy parameters have significant effects on the flow properties.

A Unified Treatment for Local Thermal Nonequilibrium Free, Forced, and Mixed Convective Boundary Layer Flows Over an Arbitrarily Shaped Nonisothermal Body in a Fluid Saturated Porous Medium

Abstract A unified integral solution procedure has been proposed to analyze all possible Darcian local thermal nonequilibrium (LTNE) free, forced, and mixed convective boundary layer flows, commonly encountered in porous media engineering applications. The heated body may be arbitrarily shaped, and its temperature may vary over the surface. The integral energy equation for the solid phase yields an algebraic equation between the dimensionless fluid thermal boundary layer thickness and its ratio to the solid-phase counterpart, while the integral energy equation for the fluid phase reduces to a first order ordinary differential equation in terms of the dimensionless fluid thermal boundary layer thickness. This set of the equations for determining the local Nusselt number of our primary interest proved to be valid for all possible Darcian cases of LTNE free, forced, and mixed convective boundary layer flows over an arbitrarily shaped nonisothermal body in a fluid saturated porous medium. Asymptotic expressions for the cases of arbitrary shapes were also obtained analytically for both leading edge and far downstream regions. The results are found to agree well with available direct numerical integration results. Furthermore, the regime map has been constructed to show the boundary layer transition point from the LTNE to equilibrium. The proposed unified method is found quite useful when designing thermal engineering systems associated with fluid saturated porous media.

Similarity Solution and Numerical Analysis of the Steady Nanofluid Layer Induced by Gyrotactic Microorganisms Containing Wall Temperature Variations

The problem of free convective steady boundary layer flows over a solid horizontal flat plate nested in a porous medium filled with a nanofluid containing gyrotactic microorganisms is considered. The exponent of the temperature, the nanoparticle volume fraction and the density of motile microorganisms are introduced to make the quantities dimensionless. The impacts of the considered exponent and bioconvection parameters on the dimensionless temperature, velocity, nanoparticle concentration and density of motile microorganisms along with Nusselt, Sherwood and motile microorganism numbers are tabulated and shown graphically. For a regular fluid and also for the isothermal case, the results are compared with the existing data and excellent compatibility is found.

Similarity Requirements for Mixed Convective Boundary Layer Flow over Vertical Curvilinear Porous Surfaces with Heat Generation/Absorption

Similarity requirements for three dimensional combined forced and free convective laminar boundary layer flows over the porous inclined vertical curvilinear surfaces with buoyancy effects and heat absorption/generation effects are investigated theoretically. The potential flow in the mainstream and Gabriel lame coefficients outside of the boundary layer are the function of ξ,η. Hence, the external velocity components (Ue, Ve) and Gabriel lame coefficients h1,h2,h3 are independent of ζ. Here, h3ξ,η=1 has been set such that ζ represents actual distance measured normal to the surface. Similarity requirements for an incompressible fluid are sought on the basis of detailed analyses in order to reduce the governing partial differential equations into a set of ordinary differential equations. Finally, different possible cases are exhibited in a tabular form with the inclusion of ΔT variations for onward flow study that are helpful to the future researchers for the flow over the orthogonal curvilinear surfaces.