Convection Boundary Layer Flow Research Articles

Scale law investigation of the curved boundary layer flow around a horizontal cylinder – for Pr

In this paper, the convective boundary layer flow that evolves on the external surface of a heated horizontal cylinder is investigated with the scaling analysis. Two thermal boundary conditions at the heated surface are considered: an isothermal and an iso-flux heating condition. The calculated data demonstrate that, similar to the extensively studied flat-plate boundary layer flows, development of the present curved boundary layer also consists of three states, i.e., an initial growth, a transitional state and a steady state. Scale laws of the characteristic velocity and thickness describing the initial and steady states are determined based on the calculated cases. The results show that unlike flat-plate boundary layers, the present characteristic velocity depends on both time and streamwise location and therefore the curved boundary layer flow follows a two-dimensional startup. The obtained scale law also indicates that the maximum characteristic velocity in the initial state is symmetrical about θ = π/2 as it is caused by the tangential component of the buoyancy force. In the steady state, the characteristic velocity occurs at approximately θ = 7π/9 and we show that this value is independent of the governing parameters. Comparison between the proposed scale laws and the calculated cases suggests that the regression constants R2 are above 0.995. Hence, the obtained scale laws could appropriately quantify the present curved boundary layer flow.

Numerical simulation of MHD two‐dimensional flow incorporated with joule heating and nonlinear thermal radiation

AbstractThe current investigation presents a numerical simulation of boundary layer flow with heat transfer. The study primarily emphasizes heat generation due to the influence of nonlinear thermal radiation. Moreover, the simultaneous effects of Joule heating and viscous dissipation have been incorporated for the thermal enhancement of the magnetohydrodynamics (MHD) on the convective boundary layer flow over a flat plate. Dimensional analysis is brought into use to determine the hydro and thermal boundary layer thickness for the two‐dimensional flow. Subsequently, the application of the suitable similarity transformation yields a nonlinear coupled flow problem with is solved numerically with the help of the Runge–Kutta Fehlberg (RKF) method incorporated with the Shooting technique. Moreover, this theoretical study highlights the immense mechanical and aeronautical applications of thermal radiation. In view of computational findings and simulating results, linear and nonlinear thermal radiation effects can also be investigated on fluids passing through a cylinder and channels. Finally, computational data tabulated against some pertinent parameters and parametric study reveal that non‐linear thermal radiation is more effective for highly viscous fluids.

A Study of Magnetic/Nonmagnetic Nanoparticles Fluid Flow under the Influence of Nonlinear Thermal Radiation

The present research work scrutinizes numerical heat transfer in convective boundary layer flow having characteristics of magnetic ( Fe 3 O 4 ) and nonmagnetic ( Al 2 O 3 ) nanoparticles synthesized into two different kinds of Newtonian (water) and non-Newtonian (sodium alginate) convectional base fluids of casson nanofluid which integrates the captivating effects of nonlinear thermal radiation and magnetic field embedded in a porous medium. The characterization of electrically transmitted viscous incompressible fluid is taken into account within the Casson fluid model. The mathematical formulation of governing partial differential equations (PDEs) with highly nonlinearity is renovated into ordinary differential equations (ODEs) by utilizing the suitable similarity transform that constitutes nondimensional pertinent parameters. The transformed ODEs are tackled numerically by implementing b v p 4 c in MATLAB. A graphical illustration for the purpose of better numerical computations of flow regime is deliberated for the specified parameters corresponding to different profiles (velocity and temperature). To elaborate the behavior of Nusselt and skin friction factor, a tabular demonstration against the distinct specific parameters is analyzed. It is perceived that the velocity gradient of Newtonian fluids is much higher comparatively to non-newtonian fluids. On the contrary, the thermal gradient of non-Newtonian fluid becomes more condensed than that of Newtonian fluids. Graphical demonstration disclosed that the heat transfer analysis in non-Newtonian (sodium alginate)-based fluid is tremendously influenced comparatively to Newtonian (water)-based fluid, and radiation interacts with the highly denser temperature profile of non-Newtonian fluid in contrast to that of Newtonian fluid. Through such comparative analysis of magnetic or nonmagnetic nanoparticles synthesized into distinct base fluids, a considerable enhancement in thermal and heat transfer analysis is quite significant in many expanding engineering and industrial phenomenons.

Scale law analysis of the curved boundary layer evolving around a horizontal cylinder at Pr > 1

The convective boundary layer flow on the external surface of an isothermally heated horizontal cylinder is investigated in this study. Numerical simulations are first carried out for a wide range of flow parameters, i.e., Rayleigh and Prandtl numbers, and scale relations quantifying the boundary layer flow are then determined from the simulation data. The numerical results suggest that the curved boundary layer experiences an initial growth state, a transitional state, and a developed state, which are essentially identical to the extensively studied flat boundary layers. Scale relations quantifying the local flow variables are obtained, and the proposed scale laws indicate that during the initial growth, the present curved boundary layer flow follows a two-dimensional growth rather than the well-known one-dimensional startup of flat boundary layers. It is further demonstrated that the characteristic velocity of the boundary layer flow maximizes at π/2, but its thickness is circumferential location independent. In the steady state, however, the maximum streamwise velocity of the boundary layer shifts to approximately 7π/9 and the thickness consistently increases with the circumferential location. It is also shown that the thickness of the inner viscous boundary layer could be obtained by properly considering the Prandtl number effect, i.e., by the term (1 + Pr−1/2)−1. The proposed scale relations could reasonably describe the curved boundary layer flow, and all regression constants are above 0.99.

Convective boundary layer flow and heat transfer of polar fluid in vertical concentric annuli with thermal slip

This study deals with natural convective flow of a polar fluid between two concentric open-ended cylinders when the inner surface temperature is higher than the outer or at a constant heat flux. Due to rotation of inner cylinder with angular velocity proportional to gradient of radial/linear velocity with thermal slip at the inner cylinder, a sheared flow is generated. The flow sets in due to momentum as well as thermal energy transport within the annular region. The equations for the velocity, microrotation and temperature fields are solved analytically. There exists a limit to the gap between the cylinders to augment linear velocity as well as microrotation and also a limit to the ratio of vortex viscosity to the dynamic viscosity to override the effects of surface thermal conditions. The thermal slip has an adverse effect on destabilising properties of polar fluid flow.

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.

Stable and convective boundary-layer flows in an urban array

In this paper non-neutral approaching flows were employed in a meteorological wind tunnel on a regular urban-like array of rectangular buildings. As far as stable stratification is concerned, results on the flow above and inside the canopy show a clear reduction of the Reynolds stresses and an increment of the Monin-Obukhov length up to 80%. The roughness length and displacement height were also affected, with a reduction up to 27% for the former and an increment up to 5% for the latter. A clear reduction of the turbulence within the canopy was observed. In the convective stratification cases, the friction velocity appears increased by both the effect of roughness and unstable stratification. The increased roughness causes a reduction in the surface stratification, reflected in an increase of the Monin-Obukhov length, which is double over the array compared to the approaching flow. The effect on the aerodynamic roughness length and displacement height are specular to the SBL case, an increase up to 55% of the former and a reduction of the same amount for the latter.

MHD FREE CONVECTION BOUNDARY LAYER FLOW OF A NANO FLUID OVER A PERMEABLE SHRINKING SHEET WITH NTH ORDER CHEMICAL REACTION

An analysis is presented to study the free convective unsteady magnatohydrodynamic boundary layer flow of a Nano fluid over a permeable shrinking sheet in the presence of nth order chemical reaction. Magnetic field of varying strength is applied normal to the sheet. The Nano fluid model under consideration includes Brownian motion, thermophoresis effects and nth order chemical reaction. The governing partial differential equations are transformed into a set of ordinary differential equations by applying the local similarity transformations and then the highly coupled nonlinear differential equations are solved by the method of lines. The effect of various controlling flow parameters on the dimensionless velocity, temperature and nanoparticle volume fraction profiles are analyzed.

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.

Effect of Mesoscale Land Use Change on Characteristics of Convective Boundary Layer: Semi-Idealized Large Eddy Simulations over Northwest China

Although large-scale topography and land use have been properly considered in weather and climate models, the effect of mesoscale and microscale heterogeneous land use on convective boundary layer (CBL) has not been fully understood yet. In this study, the influence of semi-idealized strip-like patches of oases and deserts, which resemble irrigated land use in Northwest China, on the CBL characteristics, is investigated based on the Weather Research and Forecasting (WRF)-large eddy simulation (LES) driven by observed land surface data. The influences of soil water content in oases on aloft CBL flow structure, stability, turbulent kinetic energy (TKE), and vertical fluxes are carefully examined through a group of sensitivity experiments. The results show that secondary circulation (SC)/turbulent organized structures (TOS) is the strongest/weakest when soil water content in oases is close to saturation (e.g., when the oases are irrigated). With the decrease of soil water content in oases (i.e., after irrigation), SC (TOS) becomes weak (strong) in the lower and middle CBL, the flux induced by SC and TOS becomes small (large), which has a dramatic impact on point measurement of eddy covariance (EC) fluxes. The flux induced by SC and TOS has little influence on EC sensible heat flux, but great influence on EC latent heat flux. Under this circumstance, the area averaged heat flux cannot be represented by point measurement of flux by the EC method, especially just after irrigation in oases. Comparison of imbalance ratio (i.e., contribution of SC and TOS to the total flux) reveals that increased soil moisture in oases leads to a larger imbalance ratio as well as enhanced surface heterogeneity. Moreover, we found that the soil layer configuration at different depths has a negligible impact on the CBL flux properties.

Aligned magnetic field flow of Williamson fluid over a stretching sheet with convective boundary condition

The analysis on mathematical model of Williamson fluid on the convective boundary layer flow and heat transfer over a horizontal stretching sheet has been carried out. The model is constructed by introducing the aligned magnetic field on the flow region under the case of convective boundary conditions which is implies the fluid heated from the stretching surface. The numerical method of Runge-Kutta Fehlberg (RKF45) is employed to the ordinary differential equations after being transformed from the governing equations by using suitable similarity transformation. The solutions of several influencing parameters on the velocity and temperature profiles are discussed and displayed in graphical form. The results of this study indicate that the increasing magnetic field parameter decreases the fluid velocity which suppressed the fluid motion.

Magnetohydrodynamics effect on convective boundary layer flow and heat transfer of viscoelastic micropolar fluid past a sphere

The main interest of this study is to investigate the effect of MHD on the boundary layer flow and heat transfer of viscoelastic micropolar fluid. Governing equations are transformed into dimensionless form in order to reduce their complexity. Then, the stream function is applied to the dimensionless equations to produce partial differential equations which are then solved numerically using the Keller-box method in Fortran programming. The numerical results are compared to published study to ensure the reliability of present results. The effects of selected physical parameters such as the viscoelastic parameter, K, micropolar parameter, K1 and magnetic parameter, M on the flow and heat transfer are discussed and presented in tabular and graphical form. The findings from this study will be of critical importance in the fields of medicine, chemical as well as industrial processes where magnetic field is involved.

Convection Boundary Layer Flow and Heat Transfer in an Eyring - Powell Fluid Past a Horizontal Circular Cylinder in Porous Medium

Convection Boundary Layer Flow and Heat Transfer in an Eyring - Powell Fluid Past a Horizontal Circular Cylinder in Porous Medium

Influence of Thermal Radiation on Convective Boundary Layer Flow and Heat Transfer of Nanofluids Over a Moving Wedge

Influence of Thermal Radiation on Convective Boundary Layer Flow and Heat Transfer of Nanofluids Over a Moving Wedge

Temperature Dependent Variable Properties on Mixed Convective Unsteady MHD laminar Incompressible fluid Flow with Heat Transfer and Viscous Dissipation

In the present paper we investigated that the numerical solution of mixed convective laminar boundary layer flow with uniform transverse magnetic field for a vertical porous plate. The fluid properties are considered the nonlinear functions of temperature as μ = μ∞(T / T∞)A and κ = κ∞(T / T∞)C For flue gases the values of the exponents A and C are taken as A=0.7, and C=0.83. Also time dependent suction velocity is considered. The governing equations are reduced into ordinary differential equations by introducing the suitable similarity variables and then solved numerically by using sixth ordered Runge-Kutta method and Nachtsheim Swigert iteration technique. The numerical results of our physical interest are shown graphically and tabular form.

Convective boundary layer flow and heat transfer in a nanofluid in the presence of second order slip, constant heat flux and zero nanoparticles flux

In this work, the effects of the second order slip, constant heat flux, and zero normal flux of the nanoparticles due to thermophoresis on the convective boundary layer flow and heat transfer characteristics in a nanofluid using Buongiorno's model over a permeable shrinking sheet is studied theoretically. The nonlinear coupled similarity equations are solved using the function bvp4c using Matlab. Similarity solutions of the flow, heat transfer and nanoparticles volume fraction are presented graphically for several values of the model parameters. The results show that the application of second order slip at the interface is found to be increased the rate of shear stress and decreased the rate of heat transfer in a nanofluid, so need to be taken into account in nanofluid modeling. The results further indicate that multiple solutions exist for certain values of the parameter space. The stability analysis provides guarantee that the lower branch solution is unstable, while the upper branch solution is stable and physically realizable.

Investigation of the effects of different models of nanofluids on their flow and heat transfer characteristics

This paper is devoted to an investigation of the influences of thermal radiation on an unsteady, mixed, convection boundary layer flow and the heat transfer over a vertical heated permeable stretching sheet embedded in a porous medium. Different models of the nanofluid based on different formulae for the thermal conductivity and the dynamic viscosity and their effects on the fluid flow and the heat transfer characteristics are discussed. Using the similarity transformation, we transform the governing equations into similarity, non-linear, ordinary differential equations which are solved by employing a numerical shooting technique with a fourth-order Runge-Kutta integration scheme. The obtained results are presented graphically, and the physical aspects of the problem are discussed.

The Numerical Analysis of the Capping Inversion Effect in a Convective Boundary Layer Flow on the Contaminant Gas Dispersion

Contaminant gas dispersion is of great concern to public health and social security. In the atmosphere, heating and cooling within a boundary layer due to the daily solar cycle result in a temperature differences, which introduces buoyancy forcing. Especially, a convective boundary layer (CBL) capped by a temperature inversion is one of the common cases in the atmospheric boundary layers during daytime conditions. Wind tunnel experimental studies have focused on the characteristics of plume dispersion under a certain thermal condition in a CBL flow. However, CBL flows have shear- and/or buoyancy-driven flows depending on atmospheric stability conditions and the influence of CBLs on plume dispersion behaviours has not been fully discussed. In this study, we performed numerical simulations of CBL flows capped by a temperature inversion with a wide range of atmospheric stability conditions and categorized distribution patterns of plume concentrations. It is found that the critical value of u*/w* in which the patterns of plume dispersion are different is around 0.4.

Non-Newtonian Mixed Convection Flow along an Isothermal Horizontal Circular Cylinder

The mixed convective laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is studied along an isothermal horizontal circular cylinder using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively. Here, it is found that heating the cylinder delays separation and if the cylinder is warm enough, suppress it completely. Cooling the cylinder brings the separation point nearer to the lower stagnation point and for a very cold cylinder there will not be boundary-layer on the cylinder.

NATURAL CONVECTION BOUNDARY LAYER FLOW ALONG A SPHERE EMBEDDED IN A POROUS MEDIUM FILLED WITH A NANOFLUID

A boundary-layer analysis is presented for the natural convec tion boundary layer flow about a sphere embedded in a porous medium filled with a nanofluid using Brinkman-ForchheimerDarcy extended model. The model used for the nanofluid incorporates the ef fects of Brownian motion and thermophoresis. The governing partial differential equa tions are transformed into a set of nonsimilar equations and solved numerically by an efficient implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity, temperature, and nanoparticles volume fraction profiles as well as the local skin-friction coefficient, local Nusselt and Sherwood numbers is illustrated graphically to show interesting features of the solutions.