Natural Convection Boundary Layer Flow Research Articles

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

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

MHD natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination

The aim of this article is to study the natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination. Existing solutions of similar models can be recovered as the limiting cases of horizontal and vertical plates from our generalized problem. Moreover, porous effects and the influence of transverse magnetic field; fixed to the fluid or the plate are accounted. The dimensionless velocity, in conjunction with the corresponding skin friction, have been presented as the sum of mechanical, thermal and concentration components. Furthermore, the contribution of the system parameters to the fluid motion in question has been depicted graphically. The novelty of the present study is to analyze the effect of angle of inclination of the plate and the case when the magnetic field is fixed relative to the fluid or to the plate on the fluid motion.

Natural convection boundary layer flow of nanofluids around different stations of the sphere and into the plume above the sphere

AbstractThe main intent of the present study is to investigate the natural convection boundary layer flow of nanofluids around different stations of the sphere and eruption of the fluid from the boundary layer in to the plume above the sphere. It is pertinent to point out that in this study heated sphere is treated as point source. The system of transport boundary layer equations is based on the effects of Brownian motion and thermophoresis. The system of dimensioned boundary layer equations is transformed into nondimensional form. Later, the nondimensional form of the mathematical model is solved numerically by using implicit finite difference method. The solution of the problem depends on a controlling parameters Prandtl number Pr, Lewis number , thermophoresis parameter , and Brownian motion parameter . Particularly, it is observed that for Lewis number , Prandtl number Pr, Brownian motion parameter , and thermophoresis parameter the velocity profile is maximum at station and minimum at station . On the other hand temperature distribution is uniform at each station around the sphere and slightly reduced for . It is also observed that nanoparticles concentration is maximum at station and minimum at station We also established the result that with the increase of skin friction is reduced while the heat and mass flux are increased in the plume region‐III.

Natural bioconvection flow of a nanofluid containing gyrotactic microorganisms about a truncated cone

Abstract A mathematical model is presented to investigate the natural convection boundary-layer flow of a water-based nanofluid containing gyrotactic microorganisms over a truncated cone with convective boundary condition at the surface. The governing partial differential equations are converted into ordinary differential equations by using suitable transformations. These equations are solved numerically using RKF7 with shooting method. Several comparisons with previously published works are reported and the results are found to be in excellent agreement. The numerical results are obtained and discussed for nanoparticle concentration, density of motile microorganisms profiles as well as the local skin-friction coefficient local Nusselt number, the local Sherwood number, the local density number of the motile microorganisms. It is found that density number of motile microorganisms, Sherwood number, Nusselt number and skin friction increase along the surface.

Heat transfer flow of Cu-water and Al2O3-water micropolar nanofluids about a solid sphere in the presence of natural convection using Keller-box method

Natural convection boundary layer flow over a solid sphere in micropolar nanofluid with prescribed wall temperature is studied. Copper (Cu) and alumina (Al2O3) in water-based micropolar nanofluid has been considered. Tiwari and Das’s nanofluid model with realistic empirical correlations are considered to analyze the nanoparticles effects on natural convective flow. The nonlinear partial differential equations of the boundary layer are first transformed into a non-dimensional form and then solved numerically using an implicit finite difference scheme known as Keller-box method. The effects of nanoparticles volume fraction, Prandtl number, micro-rotation parameter on temperature, velocity and angular velocity are plotted and discussed. Further, numerical results for the local Nusselt number and the local skin friction coefficient are obtained. It is found that Cu has a low heat transfer rate as compare to Al2O3 water-based micropolar nanofluid with increasing micro-rotation parameter. The present results of local Nusselt number and the local skin friction for viscous fluid are found to be in good agreement with the literature.

Simulation of Natural Convective Boundary Layer Flow of a Nanofluid Past a Convectively Heated Inclined Plate in the Presence of Magnetic Field

This paper deals with the numerical simulation of transient magnetohydrodynamics natural convective boundary layer flow of a nanofluid over an inclined plate. In the modeling of nanofluids, dynamic effects including the Brownian motion and thermophoresis are taken into account. Numerical solutions have been computed via the Galerkin-finite element method. The effects of angle of inclination, buoyancy-ratio parameter, Brownian motion, thermophoresis and magnetic field are taken into account and controlled by non-dimensional parameters. To compute the rate of convergence and error of the computed numerical solution, the double mesh principle is used. Similarity solutions are calculated and presented graphically for non-dimensional velocity, temperature, local rate of heat and mass transfer with pertinent parameters. The modified Nusselt number decreases with increasing inclination angle, buoyancy-ratio parameter, Brownian motion and thermophoresis parameter, whereas it increases with increasing Prandtl number. Validation of the results is achieved with earlier results for forced convective flow and non-magnetic studies. Such problems have several applications in engineering and petroleum industries such as electroplating, chemical processing of heavy metals and solar water heaters. External magnetic fields play an important role in electrical power generation, inclination/acceleration sensors, fine-tuning of the final materials to industrial specification because of their controlling behaviour on the flow characteristics of nanofluids.

MHD natural convection of ferrofluid from a fixed vertical plate with aligned, transverse magnetic field and convective boundary condition

The present study analyzed the influence of aligned and transverse magnetic field on two dimensional natural convection boundary layer flow of a ferrofluid over a semi-infinte fixed vertical plate in the presence of convective boundary condition. It is assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid on the right surface. Two different base fluids (water and kerosene) containing magnetite (Fe3O4) as ferroparticle are considered. The governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations using similarity variables. The resultant system of equations is then solved numerically by using Keller-Box method. Numerical results for the skin friction coefficient and local Nusselt number were presented whilst the velocity and temperature profiles illustrated graphically and analyzed. The effect of the inclined angle, magnetic field parameter, volume fraction, Grashof number and Biot number on the flow field were discussed. It is found that the heat transfer rate at the plate surface with Fe3O4- kerosene ferrofluid is higher than Fe3O4- water.

The effects of wall transpiration on the unsteady free convection boundary-layer flow near a stagnation point in a heat generating porous medium

The natural convection boundary-layer flow near a stagnation point on a permeable surface embedded in a porous medium is considered when there is local heat generation within the boundary layer at a rate proportional to (T-T_infty )^p, p ge 1, where T is the fluid temperature and T_infty the ambient temperature. There is mass transfer through the surface characterized by the dimensionless parameter gamma, with gamma >0 for fluid injection and gamma <0 for fluid withdrawal. The steady states are considered where it is found that, for p >1, there is a critical value gamma _c of gamma with solutions existing for gamma ge gamma _c if 1<p<2 and for gamma le gamma _c if p>2. The initial-value problem reveals that, for 1 le p<2, the nontrivial steady states are stable and the solution evolves to this state at large times. However, for p>2 these steady states are unstable and the solution either approaches the trivial state with the local heating dying out or a finite-time singularity develops for sufficiently large initial inputs.

MHD natural convective flow of nanofluids past stationary and moving inclined porous plate considering temperature and concentration gradients with suction

PurposeThis paper aims to focus on the mathematical modeling of magnetohydrodynamic natural convective boundary layer flow of nanofluids past a stationary and moving inclined porous plate considering temperature and concentration gradients with suction effects.Design/methodology/approachThe transformed non-dimensional and coupled governing partial differential equations are solved numerically using the finite element method.FindingsThe obtained numerical results for physical governing parameters on the velocity, temperature and concentration distributions are exemplified graphically and presented quantitatively. The boundary layer thickness increased with the increasing values of Soret, Dufour and Grashof numbers, while the thickness of boundary layer decreased with increasing values of suction for both stationary and moving plate cases. The primary and secondary velocity profiles are decreasing with an angle of inclination for moving plate and inclination has no significant effect for the stationary plate. An increase of the Soret number and Dufour number tend to increase the heat and mass transfer, while an increase of suction reduces the heat and mass transfer.Originality/valueThe problem is an important contribution to the field of nanofluid science and technology and is relevant to high temperature rotating chemical engineering systems exploiting magnetized nanofluids. This study is relatively original in nanofluids.

Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature

This paper discusses the natural convection boundary layer flow of a micropolar nanofluid over a vertical permeable cone with variable wall temperatures. Non-similar solutions are obtained. The nonlinearly coupled differential equations under the boundary layer approximations governing the flow are solved numerically using an efficient, iterative, tri-diagonal, implicit finite difference method. Different experimental correlations for both nanofluid effective viscosity and nanofluid thermal conductivity are considered. It is found that as the vortex-viscosity parameter increases, both the velocity profiles and the local Nusselt number decrease. Also, among all the nanoparticles considered in this investigation, Cu gives a good convection.

THERMAL RADIATION EFFECT ON MHD NATURAL CONVECTION BOUNDARY LAYER FLOW OVER A PLATE WITH SUCTION (INJECTION) AND VARIABLE VISCOSITY

The effect of thermal radiation on steady natural convection boundary layer flow over a plate with variable viscosity and magnetic field has been studied in this paper. The effect of suction and injection is also considered in the investigation. The system of partial differential equations governing the nonsimilar flow has been solved numerically using implicit finite difference scheme along with a quasilinearization technique. The thermal radiation has significant effect on heat transfer coefficient and thermal transport in presence of viscosity variation parameter and magnetic field in case of suction and injection.

Unsteady natural convection flow of multi-phase nanofluid past a vertical plate with constant heat flux

The objective of the present study is to investigate the two-dimensional transient natural convective boundary-layer flow of multi-phase nanofluid past a vertical plate with constant heat flux. The effects of Brownian motion and thermophoresis are incorporated in this nanofluid model. It is further considered that the nanoparticle volume fraction on the boundary is passively rather than actively controlled. An effective implicit finite difference technique of Crank-Nicolson method has been used to solve the governing non-linear coupled partial differential equations. The effects of time, Brownian motion parameter, thermophoresis parameter, buoyancy ratio parameter, Prandtl number and Lewis number on the dimensionless velocity, temperature and nanoparticle volume fraction have been illustrated graphically and analyzed in detail. The results for local as well as average skin-friction and Nusselt number are also presented graphically and discussed thoroughly. It is found that the velocity, temperature and nanoparticle volume fraction evolves with time and reached steady state as time progressed. The local Nusselt number is found to be slightly increased with increasing Brownian motion parameter and it decreased with increasing thermophoresis parameter, but the influence of buoyancy ratio parameter does not show any impact on the local Nusselt number. To validate the present numerical results, a comparison study has been carried out between the present steady state local Nusselt number results for a limiting case of regular fluid with the well-established experimental correlation results and an excellent agreement is found between the results.

CFD solutions for magnetohydrodynamic natural convection over horizontal and vertical surfaces

This paper investigates the effects of a magnetic field on the natural convective boundary layer flow of an electrically conducting fluid adjacent to horizontal as well as vertical surfaces. This has allowed us to establish overall similarities and several subtle differences between the two cases. Previously published studies concentrated on obtaining self-similar solutions at the cost of assuming very restrictive variation of the magnetic field along the surface. In the present work, a numerical model and an in-house computer program have been developed to solve directly the non-linear boundary layer equations which can accommodate any arbitrary variation of the magnetic field. Special emphasis is given to the case of uniform magnetic field which perhaps represents the most practical case and which cannot be solved by the similarity theory. Computations show that the Nusselt number and the skin-friction coefficient decrease as the magnetic field increases. It is shown that the detailed characteristics of the velocity profiles and the values of Nusselt number and skin-friction coefficient for the case of a magnetic field which admits similarity are significantly different from those when a uniform magnetic field is applied, thus showing the importance of the present model.

Double Diffusive Natural Convection Flow Over a Wavy Surface Situated in a Non-absorbing Medium

This analysis discuss the influence of heat and mass transfer on natural convection boundary layer flow of thermally radiating wavy surface. To make the surface radiating; Stephan-Boltzmann law is used in the boundary conditions. Therefore, convection and thermal radiation interact simultaneously with the aid of Stephan-Boltzmann law and ultimately producing highly nonlinear boundary conditions. The governing coupled boundary layer equations are switched into suitable form by using primitive variable formulations over which two-point iterative finite difference scheme is applied to obtain the unknown quantities. Physical quantities like wall shear stress, rate of heat transfer and rate of mass transfer are expressed graphically by varying significant emerging parameters: surface radiation (R), radiative length parameter (ξ), buoyancy ratio parameter (N) and amplitude of the wavy surface (α). Comparison of numerical results is also done in tabular form with the earlier study of Siddiqa et al. (2013) in order to validate the results.

Numerical Study of Nonlinear Heat Transfer from a Wavy Surface to a High Permeability Medium with Pseudo-Spectral and Smoothed Particle Methods

Motivated by petro-chemical geological systems, we consider the natural convection boundary layer flow from a vertical isothermal wavy surface adjacent to a saturated non-Darcian high permeability porous medium. High permeability is considered to represent geologically sparsely packed porous media. Both Darcian drag and Forchheimer inertial drag terms are included in the velocity boundary layer equation. A high permeability medium is considered. We employ a sinusoidal relation for the wavy surface. Using a set of transformations, the momentum and heat conservation equations are converted from an (x, y) coordinate system to an ( $$x, \eta )$$ dimensionless system. The two-point boundary value problem is then solved numerically with a pseudo-spectral method based on combining the Bellman–Kalaba quasi linearization method with the Chebyschev spectral collocation technique (SQLM). The SQLM computations are demonstrated to achieve excellent correlation with smoothed particle hydrodynamic (SPH) Lagrangian solutions. We study the effect of Darcy number (Da), Forchheimer number (Fs), amplitude wavelength (A) and Prandtl number (Pr) on the velocity and temperature distributions in the regime. Local Nusselt number is also computed for selected cases. The study finds important applications in petroleum engineering and also energy systems exploiting porous media and undulating (wavy) surface geometry. The SQLM algorithm is shown to be exceptionally robust and achieves fast convergence and excellent accuracy in nonlinear heat transfer simulations.

Transient two-dimensional natural convection flow of a nanofluid past an isothermal vertical plate using Buongiorno’s model

PurposeThe purpose of this paper is to present a numerical investigation of the transient two-dimensional natural convective boundary-layer flow of a nanofluid past an isothermal vertical plate by incorporating the effects of Brownian motion and thermophoresis in the mathematical model.Design/methodology/approachThe problem is formulated using the Oberbeck–Boussinesq and the standard boundary-layer approximations. The governing coupled non-linear partial differential equations for conservation of mass, momentum, thermal energy and nanoparticle volume fraction have been solved by using an efficient implicit finite-difference scheme of the Crank–Nicolson type, which is stable and convergent. Numerical computations are performed and the results for velocity, temperature and nanoparticle volume fraction are presented in graphs at different values of system parameters such as Brownian motion parameter, thermophoresis parameter, buoyancy ratio parameter, Prandtl number, Lewis number and dimensionless time. The results for local and average skin-friction and Nusselt number are also presented graphically and discussed thoroughly.FindingsIt is found that the velocity, temperature and nanoparticle volume fraction profiles enhance with respect to time and attain steady-state values as time progresses. The local Nusselt number is found to decrease with increasing thermophoresis parameter, while it increases slightly with increasing Brownian motion parameter. To validate the present numerical results, the steady-state local Nusselt number results for the limiting case of a regular fluid have been compared with the existing well-known results at different Prandtl numbers, and the results are found to be in an excellent agreement.Research limitations/implicationsThe present analysis is limited to the transient laminar natural convection flow of a nanofluid past an isothermal semi-infinite vertical plate in the absence of viscous dissipation and thermal radiation. The unsteady natural convection flow of a nanofluid will be investigated for various physical conditions in a future work.Practical implicationsUnsteady flow devices offer potential performance improvements as compared with their steady-state counterparts, and the flow fields in the unsteady flow devices are typically transient in nature. The present study provides very useful information for heat transfer engineers to understand the heat transfer enhancement with the nanofluid flows. The present results have immediate relevance in cooling technologies.Originality/valueThe present research work is relatively original and illustrates the transient nature of the natural convective nanofluid boundary-layer flow in the presence of Brownian motion and thermophoresis.

Heat and mass transfer effects on natural convection flow along a horizontal triangular wavy surface

An analysis is carried out to thoroughly understand the characteristics of heat and mass transfer for the natural convection boundary layer flow along a triangular horizontal wavy surface. Combine buoyancy driven boundary layer equations for the flow are switched into convenient form via co-ordinate transformations. Full non-linear equations are integrated numerically for Pr = 0.051. Interesting results for the uneven surface are found which are expressed in the form of wall shear stress, rate of heat transfer and rate of mass transfer. Solutions are also visualized via streamlines, isotherms, and isolines for concentration. Computational results certify that, shear stress, temperature gradient and concentration gradient enhances as soon as the amplitude of the wavy surface, a, increases, but complex geometry do not allow to carry simulations for a &gt; 1.5. This factor probably ensures that sinusoidal waveform is better than triangular waveform. &lt;br&gt;&lt;br&gt;&lt;font color="red"&gt;&lt;b&gt; This article has been corrected. Link to the correction &lt;u&gt;&lt;a href="http://dx.doi.org/10.2298/TSCI170525126E"&gt;10.2298/TSCI170525126E&lt;/a&gt;&lt;u&gt;&lt;/b&gt;&lt;/font&gt;

Magnetohydrodynamics Flow of Non-Newtonian Fluid from a Vertical Permeable Cone in the Presence of Thermal Radiation and Heat Generation/Absorption

The nonlinear, steady state magnetohydrodynamics natural convection boundary layer flow, heat and mass transfer of an viscoelastic incompressible Jeffrey’s fluid from a vertical permeable cone with thermal radiation and heat generation/absorption effects is investigated in this article. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite-difference Keller box technique. The Rosseland diffusion algebraic approximation is utilized to simulate thermal radiation effects. The surface of the cones is maintained at a constant temperature and concentration with mass flux present. Excellent correlation of the present results with previous studies is obtained to validate the numerical code. The influence of Deborah number (De), ratio of relaxation to retardation times ( $$\lambda $$ ), radiation parameter (F), heat generation/absorption parameter ( $$\Delta $$ ), suction/injection parameter ( $$f_{w}$$ ), magnetic parameter (M) and dimensionless tangential coordinate ( $$\xi $$ ) on velocity, temperature and concentration evolution in the boundary layer regime are examined in detail. Also, the effects of these parameters on local skin friction, heat transfer rate and mass transfer rate are investigated.

Periodic magnetohydrodynamic natural convection flow of a micropolar fluid with radiation

This article is concerned with the problem of periodic magnetohydrodynamic (MHD) natural convection boundary-layer flow of a radiating micropolar fluid near a vertical surface. Such type of problems are posed by induction electromagnetic pumps and generators. The governing equations are reduced to a convenient form by the introduction of stream function formulations and are simulated by the implicit finite difference method along with the Keller-box scheme. The results of the surface shear stress, rate of heat transfer, distribution of couple stress, velocity profile, temperature profile and angular velocity profile are shown graphically for a range of parameters. Excellent agreement is found when present solutions are compared with the previous studies. It is shown that the heat transfer rate remains insensitive when magnetic field parameter, micropolar parameter and micro-inertia density parameter increases. Further, the micropolar parameter, K, has dominant effect on skin friction coefficient and couple stress coefficient.

Non-Darcy Natural Convection Boundary Layer Flow Over a Vertical Cone in Porous Media Saturated with a Nanofluid Containing Gyrotactic Microorganisms with a Convective Boundary Condition

Non-Darcy Natural Convection Boundary Layer Flow Over a Vertical Cone in Porous Media Saturated with a Nanofluid Containing Gyrotactic Microorganisms with a Convective Boundary Condition