Natural Convection Boundary Layer Flow Research Articles

Characteristics of MHD Jeffery Fluid Past an Inclined Vertical Porous Plate

This paper is concerned with the study of an unsteady, MHD natural convective boundary layer flow of a viscous, incompressible and electrically conducting, non-Newtonian Jeffery fluid over a semi-infinite vertically inclined permeable moving plate embedded in a porous medium in the presence of thermal radiation, heat absorption and thermal diffusion, heat and mass transfer. . The permeability of the porous medium and the suction velocity are considered to be an exponentially decreasing function of time. The fundamental governing equations for this investigation are solved numerically using the perturbation technique. The results are presented graphically and in tabular form for various controlling parameters. The behavior of different physical parameters is shown graphically. The numerical values of Skin friction, Nusselt number, and Sherwood number are presented in a tabular form. Obtained outcomes are compared with earlier studies in the special case and strong agreement is noted. From graphical representation, it is concluded that velocity and temperature distribution increases with the mixed convection parameter and buoyancy force parameter. An increasing value of magnetic field parameter, slip parameter, and Jeffery parameter tends to reduced velocity and also raising the values of Prandtl number, radiation parameter and heat absorption parameter tends to downfallen temperature profiles. This study may be useful in several industrial applications, for example, polymer production, manufacturing of ceramics or glassware and food processing, and so forth.

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.

Magnetohydrodynamic Effects on the Flow of Nanofluids Across a Convectively Heated Inclined Plate Through a Porous Medium with a Convective Boundary Layer

The study explores the problem of Magnetohydrodynamic natural convection boundary layer flow of a nanofluid past a convectively heated inclined porous channel. The governing partial differential equations have been transformed through appropriate similarity functions into nonlinear ordinary differential equations. The emerging equations were solved numerically using both a sixth-order Runge-Kutta-Fehlberg and the shooting technique. The influences of pertinent parameters such as plate inclination angle, magnetic field, buoyancy ratio, and the convective heating term on the temperature, velocity, and concentration profiles were investigated graphically. Key findings indicate that an increase in magnetic field and permeability leads to a decline in the fluid’s velocity while the temperature and nanoparticle concentration are significantly enhanced. The results obtained are in close correlation with existing body of knowledge discussed in the literature.

The effects of thermal radiation, internal heat generation (absorption) on unsteady MHD free convection flow about a truncated cone in presence of pressure work

The aim of present paper is to analyse the effect of radiation, internal heat generation (absorption) on unsteady laminar natural convective boundary layer flow over a truncated cone considering pressure work and magnetic field due to the variation in fluid flow behavior in various physical conditions. Suitable transformation is used to form system of coupled non linear partial differential equations is to governing the flow and heat transfer. These equations have been solved numerically by using an implicit finite difference scheme along with quasilinearization technique. According to numerical findings, the pressure work, internal heat generation (absorption), radiation, and magnetic field have a significant impact on both skin friction and heat transfer. Further, skin friction is found to decrease 12.13%, 30.3% and 41.67% for various values (from 0.0 to 0.5) of pressure work, magnetic field and heat generation (absorption) alongside the cone surface whereas heat transfer rate rises 17.19%, 17.65% and 73.51% respectively due to unsteadiness in the flow. It is observed that the thickness of boundary layer enhances for various values (from 0.0 to 0.5) of heat generation and radiation parameter but diminishes for pressure work and Prandtl number.

Numerical solutions of free convective flow from a moving cone in the presence of non-uniform surface temperature

This computational study intends to determine the impact of non-isothermal surface temperature on the natural convective boundary layerflow of fluid along a moving vertical cone. The governing equation deals with continuity, momentum, and energy along with thermal fluctuations are reduced into dimensionless unsteady non-linear coupled PDE. The non-dimensional governing equations of the boundary layer are then illuminated by a systematic and unconditionally stable method of implicit finite difference Crank-Nicolson scheme. Analyzing the stability and convergence of the system has helped in the optimization of parameters and accuracy of the system. Using a tabular approach, we validate the present numerical methodology by comparing it to the previously discussed results. Through a table of values, the physical impacts of parameters are analyzed and graphical representations are provided. From the graphs, it is evident that an increment in Pr and n results in lower temperature and velocity profiles.

Unified scale laws for transient convective boundary layers: From flat to curved boundary layers

Transient natural convection boundary layer flow is studied at Pr>1 and the curvature effect is specifically and fundamentally explored. Important scale laws, i.e. boundary layer thickness \ensuremath{\delta}t and characteristic velocity ${u}_{z}$ of the transient and steady states and the cut-off time ${t}_{s}$ of the initial growth, are proposed and validated. We find that for cylinder radius much larger than the boundary layer thickness, the present scaling relations reduce to those of the classic flat boundary layer. The most curved boundary layer we examine is 26 times thicker than the cylinder radius. We show that the present scaling set is accurate for all flow conditions bounded by the two limiting scenarios.

Transpiration effect on unsteady natural convection boundary layer flow around a vertical slender body

In this paper, the transpiration effect on unsteady natural convection boundary layer flow around a vertical slender body has been studied numerically. Applying the similarity transformation together with Boussinesq's approximation, the governing PDEs have been modified into ODEs. These equations have been solved by applying the shooting technique with the help of “ODE45 MATLAB” software. The influences of the pertinent parameters/numbers namely transpiration parameter (FW), the radius of slender body (R0), Prandtl number (Pr) and the driving parameter (β) on the velocity and temperature of the fluid within the boundary layer has been analyzed. The velocity and temperature decrease with increasing the values of the suction parameter but a reverse trend is found for increasing values of blowing parameter from the wall to the free stream. Rising values of the suction parameter (0.5–1.0) increase the local skin friction and the heat transfer rate by approximately about 35% and 31%. The velocity of the fluid decreases for uplifting values of the kinematic viscosity. When the thermal conductivity decreases then the temperature of the fluid decreases. Rising values of the body radius parameter the skin-friction and the rate of heat transfer increase.

Effects of temperature dependent viscosity and thermal conductivity on natural convection flow along a curved surface in the presence of exothermic catalytic chemical reaction.

The natural convection boundary layer flow of a viscous incompressible fluid with temperature dependent viscosity and thermal conductivity in the presence of exothermic catalytic chemical reaction along a curved surface has been investigated. The governing non dimensional form of equations is solved numerically by using finite difference scheme. The numerical results of velocity profile, temperature distribution and mass concentration as well as for skin friction, heat transfer rate and mass transfer rate are presented graphically and in tabular form for various values of dimensionless parameters those are generated in flow model during dimensionalization. From the obtained results, it is concluded that the exothermic catalytic chemical reactions is associated with temperature dependent viscosity and thermal conductivity. Further, it is concluded that the body shape parameter also plays an important quantitative role for change in velocity profile, temperature field and mass concentration behavior in the presence of exothermic catalytic chemical reaction.

Numerical solution for MHD natural convective boundary layer flow of a nanofluid over a convectively heated inclined plate in the presence of heat generation and chemical reaction

Numerical solution for MHD natural convective boundary layer flow of a nanofluid over a convectively heated inclined plate in the presence of heat generation and chemical reaction

Nonlinear Approximation for Natural Convection Flow Near a Vertical Plate With Thermal Radiation Effect

Abstract A nonlinear approximation for natural convection boundary layer flow near a vertical wall under the influence of thermal radiation is analyzed. The governing nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The final dimensionless equations are solved numerically using the Runge Kutta Ferlberg fourth-fifth order (RKF45) method. The effects of the embedded parameters affecting the flow formation, temperature distribution, Nusselt number, and skin friction are thoroughly examined. It is found out that the temperature gradient is directly proportional to the thermal radiation parameter near the vertical plate whereas it is inversely proportional to the temperature gradient far away from the vertical plate. It is also found that the flow formation near the vertical wall could be enhanced with the increase in thermal radiation parameter. However, this increase remains unaffected in the freestream region. Furthermore, results also show that the rate of heat transfer could be enhanced with the increase in thermal radiation whereas decreases with the increase in other embedded flow parameters.

Unsteady natural convection boundary layer flow and heat transfer past a vertical flat plate with novel constitution models

Seeking proper and reasonable constitutive relations to study the characteristics of flow and heat transfer of viscoelastic fluid is a hot topic in recent years. In this work, a new distributed order time fractional constitution model is put forward to analyse the unsteady natural convection boundary layer flow and heat transfer, in which the magnetic field effect is considered. The mid-point quadrature method is applied to approach the distributed order integrals and the L1-formula is employed to discrete the time fractional derivatives. The influences of different involved parameters on the velocity and temperature distributions and the comparisons of the distributions with different constitution models are presented by graphical illustrations and discussed in detail.

Comparative Heat Transfer Analysis of MoS2/C2H6O2 and SiO2-MoS2/C2H6O2 Nanofluids with Natural Convection and Inclined Magnetic Field

This article explores the comparative analysis of MoS2/C2H6O2 nanofluid and SiO2-MoS2/C2H6O2 hybrid nanofluid natural convective boundary layer flow through a stretching area. Uniform inclined magnetic field is applied together with viscous dissipation. The governing model of the flow is solved by Runga-Kutta fourth orde method using appropriate similarity transformations. Temperature and velocity field are presented for various flow pertinent parameters. It is conclude that if we give an increment in the convection parameter the velocity profile increases and opposite effect is noticed for the temperature profile for both fluids. Also with increased volume fraction parameter Φ2, we get increased velocity and temperature profiles for both nanofluids.

Influence of undulating wall heat and mass flux on MHD natural convection boundary layer flow from a vertical wall

AbstractCurrent study expounds an unsteady magnetohydrodynamic natural convective flow along a vertical wall in presence of variable transverse magnetic field. Small amplitude undulation in wall heat flux and wall mass flux are imposed at the vertical wall to generate the boundary layer flow. The flow governing equations are divided into sets of steady and unsteady equations and then transformed into the similarity and nonsimilarity equations, respectively, by introducing stream function formulations. The sets of nonsimilarity equations are solved numerically by using three different techniques, namely, perturbation solution technique, asymptotic solution technique and implicit finite difference technique applied, respectively, for lower, higher, and all frequencies (ξ). Results are illustrated in connection with the amplitude and phase angles of shear stress, wall temperature, and concentration against the frequency (ξ) for wide ranges of physically significant parameters. Likening of the results obtained by above mentioned numerical methods are presented in every figure and table. Results reveal that the amplitude of undulating shear stress and wall temperature dwindle and the amplitude of wall concentration increases due to increment in Prandtl number (Pr). Besides, on incrementing Schmidt number (Sc) the amplitude of undulating shear stress and wall concentration dwindle and the amplitude of wall temperature increases. Results also reveal that on incrementing magnetic parameter (M) the amplitude of transient shear stress dwindles while the amplitude of transient wall temperature and concentration increase.

Unsteady MHD natural convective boundary layer flow and heat transfer over a truncated cone in the presence of pressure work

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Prandtl number scalings for unsteady natural convection boundary-layer flow on an evenly heated vertical plate in a homogeneous Pr > 1 fluid

Scalings for the thicknesses of the thermal and velocity boundary layers, the plate temperature, and the maximum vertical velocity in a homogeneous Pr > 1 fluid are validated against numerical results for unsteady natural convection boundary-layer flow on an evenly heated vertical plate. Results have been obtained for Rayleigh number and Prandtl number and the scaling relations are shown to provide a good description of the flow for both the initial conduction dominated, one-dimensional, unsteady phase and the fully developed convection dominated, two-dimensional, steady phase of the flow. Scaling constants have been obtained for all relations.

A Spectral Simulation of Magnetohydrodynamic Convective Nanofluid Slip Flow with Newtonian Heating and Radiative Heat Transfer

In this paper, we present a numerical analysis of natural convection boundary layer flow of a nanofluid over a stretching sheet under the influence of a variable magnetic field in the presence of nonlinear radiative heat transfer, hydrodynamic slip and Newtonian heating effects. The Brownian diffusion and thermophoresis effects are employed to describe the nanofluid flow model consisting of non-linear partial differential equations, which is transformed into a similarity form and then treated with the spectral local-linearization method (SLLM) to present an in-depth analysis of the flow and heat transfer characteristics of the fluid flow. The fluid flow problem finds applications in many engineering devices including geothermal heat source pump and in cooling of electronic devices and stretched wires.

Application of numerical transition control method to enhance turbulence in a natural convection boundary layer over a vertical heated plate

The present paper describes the application of local perturbations in Large Eddy Simulation to enhance transition to turbulence applied on the heated wall of a natural convection boundary layer. Simulations are carried out with a Prandtl number Pr=0.71 and a maximum Grashof number of Gr=4.1×1011. The purpose of this work is to accelerate the transition process in the numerical domain, reducing the needed simulation effort to reach the turbulent regime in a natural convection boundary layer flow. A parametric study has been performed to identify the fastest transition to turbulence in the proposed technique. The obtained results are compared with experimental, empirical and other numerical reference data to assess the method’s performance. The analysis of the transition method contemplates its effect in the mean flow field, as well as in the resolved Reynolds stresses and turbulent heat fluxes.

On an equation arising in natural convection boundary layer flow in a porous medium

A generalization of a boundary value problem treated previously by Magyari et al. (ZAMP 53:782–793, 2002a; Transp Porous Medium 46:91–102, 2002b), Zhang (Math Anal Appl 417:361–375, 2014) and Paullet (Appl Math E Notes 14:123–126, 2014) for a prescribed wall temperature and by Zhang (Appl Math Comput 339:367–373, 2018) for a prescribed wall heat flux is considered. The problem involves a parameter lambda and an exponent p. Numerical solutions are obtained for representative values of lambda and p, a feature of which is the existence of critical values lambda _c of lambda with two solution branches in lambda >lambda _c, with lambda _c dependent on p. Asymptotic solutions for large lambda and large p are derived for both types of boundary condition. For large lambda , the nature of the solution is essentially different on upper and on the lower branches with similar feature being seen in the behaviour for p large.

Natural convection boundary-layer flow on an evenly heated vertical plate with time-varying heating flux in a stratified Pr < 1 fluid

The transient natural convection boundary-layer flow adjacent to a vertical plate heated with a time-dependent heat flux in an initially linearly stratified ambient fluid with Prandtl number (Pr) smaller than one was studied. Scaling analysis was used to obtain the scaling relations for the main parameters characterizing the flow behavior in terms of Pr, s, and fn at the four development stages, i.e., the startup, transitional, steady, and the decay stage, where s is the dimensionless temperature stratification parameter which represents the relative extent of the background stratification with respect to the temperature gradient across the plate and fn is the dimensionless natural frequency of the time-dependent heat flux applied to the plate. These parameters include the plate temperature, maximum vertical velocity, thermal and viscous boundary-layer thicknesses, and the corresponding time scales. The direct numerical simulation results over and show that these scaling relations provide a good representation of the flow behavior.

Natural Convection Flow of Power-Law Fluids over a Heated Horizontal Plate Surface

Abstract The current work attempts to investigate the existence of similarity solution for the natural convection boundary layer flow of a power-law fluid over a heated horizontal semi-infinite plate surface. Three types of surface temperature variation are considered, namely (i) constant surface temperature (CST), (ii) power-law variation of surface temperature (PST) and (iii) power-law variation of surface heat flux (PHF). A reduction of the governing partial differential equations is achieved by using a suitable similarity transformation. But, a careful mathematical verification confirms that the similarity solution does not exist in the CST case and for the PST case it exists only under a particular value of the wall temperature parameter r = 1/3. It also ensured the existence of similarity solution for the PHF case and this will happen only when the plate surface is held at a constant heat flux situation. A new fundamental parameter S arises from the dimensionless analysis which is reduced to the reciprocal of the usual Prandtl number Pr for Newtonian fluids. A novel result of this analysis is that the salient features of the Grashof number Gr which differentiates the thermal responses of the shear-thinning fluid (0 &lt; n &lt; 1) flows from the shear-thickening fluid (n &gt; 1) flows while the Newtonian fluid (n = 1) flows remain unaffected by this parameter no matter what be the value of S.