Mixed Convection Boundary Layer Flow Research Articles

Mixed convective boundary layer flow over a vertical cylinder embedded in a porous medium saturated with a nanofluid

Purpose – The purpose of this work is to study the mixed convection boundary layer flow past a vertical cylinder in a porous medium saturated with a nanofluid. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le. The dependency of the surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed. Design/methodology/approach – Solutions of the set of non-similarity equations are obtained by employing the implicit finite difference method together with Keller box elimination method. Findings – It was found that the heat transfer rate decreases and mass transfer rates increase as Lewis number increases. The heat and mass transfer rates increase as the buoyancy ration parameter increases. As the thermophoresis parameter Nt increases, the heat transfer rate decreases where as the mass transfer rate increases. As the Brownian parameter Nb increases, the heat transfer rate decreases. Brownian motion decelerates the flow in the nanofluid boundary layer. Brownian diffusion promotes heat conduction. The heat and mass transfer rates increase as the buoyancy ratio number Nr increases. The Brownian motion and thermophoresis of nanoparticles increases the effective thermal conductivity of the nanofluid. Both Brownian diffusion and thermophoresis give rise to cross diffusion terms that are similar to the familiar Soret and Dufour cross-diffusion terms that arise with a binary fluid. Research limitations/implications – The analysis is valid for steady, mixed convection two-dimensional boundary layer flow in a nanofluid-saturated Darcy porous medium. An extension to non-Darcy porous medium is left as a part of future study. Practical implications – The research is applicable for enhancing heat exchanger effectiveness by employing nanofluids. Originality/value – The study is useful to engineers interested in designing heat exchangers, water and atmospheric pollution.

Unsteady mixed convection boundary layer flow over a vertical cone with non-uniform slot suction (injection)

The non-similar solution of an unsteady mixed convection laminar boundary layer flow over a vertical cone in the presence of non-uniform surface mass transfer through slot has been obtained while the axis of cone is inline with the flow. The unsteadiness is caused by the time dependent free stream velocity. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting coupled non-linear partial differential equations have been solved numerically by the combination of quasi-linearization technique and an implicit finite difference scheme. Numerical computations are performed for different values of the parameters to display the velocity and temperature profiles graphically. Both accelerating and decelerating free stream velocities are considered. Numerical results are reported to display the effects of non-uniform single and double slot suction (injection) on skin friction and heat transfer coefficients at the wall. Further, the effects of Prandtl number, buoyancy and mass transfer (suction or injection) parameters at different stream-wise locations for various times on velocity and temperature profiles, and on skin friction and heat transfer coefficients are also presented in this paper.

Explicit numerical study of unsteady hydromagnetic mixed convective nanofluid flow from an exponentially stretching sheet in porous media

A numerical investigation of unsteady magnetohydrodynamic mixed convective boundary layer flow of a nanofluid over an exponentially stretching sheet in porous media, is presented. The transformed, non-similar conservations equations are solved using a robust, explicit, finite difference method (EFDM). A detailed stability and convergence analysis is also conducted. The regime is shown to be controlled by a number of emerging thermophysical parameters i.e. combined porous and hydromagnetic parameter (R), thermal Grashof number (G r ), species Grashof number (G m ), viscosity ratio parameter (Λ), dimensionless porous media inertial parameter (∇), Eckert number (E c ), Lewis number (L e ), Brownian motion parameter (Nb) and thermophoresis parameter (Nt). The flow is found to be accelerated with increasing thermal and species Grashof numbers and also increasing Brownian motion and thermophoresis effects. However, flow is decelerated with increasing viscosity ratio and combined porous and hydromagnetic parameters. Temperatures are enhanced with increasing Brownian motion and thermophoresis as are concentration values. With progression in time the flow is accelerated and temperatures and concentrations are increased. EFDM solutions are validated with an optimized variational iteration method. The present study finds applications in magnetic nanomaterials processing.

Non-uniform slot suction/injection into mixed convection boundary layer flow over vertical cone

The aim of this work is to study the effect of non-uniform single and double slot suction/injection into a steady mixed convection boundary layer flow over a vertical cone, while the axis of the cone is inline with the flow. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting coupled non-linear partial differential equations are solved numerically by employing the quasi-linearization technique and an implicit finite-difference scheme. Numerical computations are performed for different values of the dimensionless parameters to display the velocity and temperature profiles graphically. Also, numerical results are presented for the skin friction and heat transfer coefficients. Results indicate that the skin friction and heat transfer coefficients increase with non-uniform slot suction, but the effect of non-uniform slot injection is just opposite.

EXISTENCE AND NON-UNIQUENESS OF SOLUTION FOR A MIXED CONVECTION FLOW THROUGH A POROUS MEDIUM

In this paper we reconsider the problem of steady mixed convection boundary-layer flow over a vertical flat plate studied in [6],[7] and [13]. Under favorable assumptions, we prove existence of multiple similarity solutions, we study also their asymptotic behavior. Numerical solutions are carried out using a shooting integration scheme.

Non-uniform slot suction (injection) on an unsteady mixed convection flow over a wedge with chemical reaction and heat generation or absorption

The aim of this work is to study the effect non-uniform single and double slot suction (injection) on an unsteady mixed convection boundary layer flow over a vertical wedge with chemical reaction and heat generation or absorption. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. Non-similar solutions are obtained by solving the coupled non-linear partial differential equations using the quasi-linearization technique in combination with an implicit finite-difference scheme and numerical computations are carried out for different values of dimensionless parameters to display the effects of non-uniform single and double slot suction (injection) along with chemical reaction and heat generation or absorption. Results indicate that the skin friction, heat and mass transfer coefficients increase with non-uniform slot suction but the effect of non-uniform slot injection is just the opposite. As the slot moves in downstream direction, the skin friction, heat and mass transfer coefficients decrease by non-uniform slot suction whereas non-uniform slot injection has the reverse effect.

Numerical study of transient magnetohydrodynamic radiative free convection nanofluid flow from a stretching permeable surface

Transient mixed convective laminar boundary layer flow of an incompressible, viscous, dissipative, electrically conducting nanofluid from a continuously stretching permeable surface in the presence of magnetic field and thermal radiation flux is studied. The model used for the unsteadiness in the momentum, temperature, and concentration fields is based on the time-dependent stretching velocity and surface temperature and concentration. Similarity transformations are used to convert the governing time-dependent nonlinear boundary layer equations for momentum, thermal energy, and concentration to a system of nonlinear ordinary coupled differential equations with appropriate boundary conditions. The transformed model is shown to be controlled by a number of thermophysical parameters, namely the magnetic parameter, thermal convective parameter, mass convective parameter, suction parameter, radiation-conduction parameter, Eckert number, Prandtl number, Lewis number, Brownian motion parameter, thermophoresis parameter, and the unsteadiness parameter. Numerical solutions are obtained with the robust Nactsheim–Swigert shooting technique together with Runge–Kutta sixth-order iteration schemes. Comparisons with previously published work are performed and are found to be in excellent agreement. The effects of selected parameters on velocity, temperature, and concentration distributions and furthermore on skin friction coefficients, heat transfer rate (Nusselt number), and mass transfer rate (Sherwood number) are presented graphically. The current study has applications in high-temperature nano-technological materials processing.

UNSTEADY HEAT AND MASS TRANSFER BY MHD MIXED CONVECTION FLOW OVER AN IMPULSIVELY STRETCHED VERTICAL SURFACE WITH CHEMICAL REACTION AND SORET AND DUFOUR EFFECTS

This work considers unsteady, laminar, and coupled heat and mass transfer by MHD mixed convective boundary-layer flow of an electrically conducting fluid over an impulsively stretched vertical surface in an unbounded quiescent fluid with aiding external flow in the presence of a transverse magnetic field, homogeneous chemical reaction, and Soret and Dufour effects. The stretching velocity and surface temperature and concentration are assumed to vary linearly with the distance along the surface. The flow is impulsively set into motion and both the temperature and concentration at the surface are also suddenly changed from those of the ambient fluid. The governing partial differential equations are transformed into a set of nonsimilar equations and solved numerically by an efficient implicit, iterative, finite-difference method. A parametric study illustrating the influence of various physical parameters is performed. Numerical results for the steady-state velocity, temperature, and concentration profiles as well as the time histories of the skin-friction coefficient, local Nusselt number, and local Sherwood number are presented graphically and discussed.

Steady Mixed Convection Flow on a Horizontal Circular Cylinder Embedded in a Porous Medium Filled by a Nanofluid Containing Gyrotactic Micro-Organisms

In this paper, the steady mixed convection boundary layer flow past a horizontal circular cylinder with a constant surface temperature embedded in a porous medium saturated by a nanofluid containing both nanoparticles and gyrotactic micro-organisms in a stream flowing vertically upwards for both cases of a heated and cooled cylinder is numerically studied. The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite-difference scheme. By considering the governing parameters, namely, the mixed convection parameter λ, the bioconvection Lewis number Lb, the traditional Lewis number Le, the bioconvection Péclet number Pb, the buoyancy ratio Nr, the bioconvection Rayleigh number Rb, the Brownian motion Nb, and the thermophoresis Nt, the numerical results are obtained and discussed for the skin friction coefficient, the local Nusselt number, the local Sherwood number, the local density number of the motile micro-organisms as well as the velocity, temperature, nanoparticle volume fraction, and density motile micro-organisms profiles.

Mixed convection boundary-layer flow past a horizontal circular cylinder embedded in a porous medium filled with a nanofluid under convective boundary condition

The steady mixed convection boundary-layer flow past a horizontal circular cylinder in a stream flowing vertically upwards embedded in porous medium filled with a nanofluid is studied, taking into account the thermal convective boundary condition is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing partial differential equations are transformed into a set of non-similar 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 nanoparticle 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.

VIM Solution for Mixed Convection over Horizontal Moving Porous Flat Plate

The non-viscous, laminar mixed convection boundary-layer flow over a horizontal moving porous flat plate, with chemical reaction, is considered. The governing equations are expressed in non-dimensional form and the series solutions of coupled system of equations are constructed for velocity, temperature and concentration functions using variational iteration method. The investigated parameters are: buoyancy parameter, chemical reaction parameter, order of chemical reaction, Prandtl number and Schmidt number.

Mixed Convection Boundary-layer Flow of a Nanofluid Near Stagnation-point on a Vertical Plate with Effects of Buoyancy Assisting and Opposing Flows

In this study, the steady laminar mixed convection boundary layer flow of a nanofluid near the stagnation-point on a vertical plate with prescribed surface temperature is investigated. Here, both assisting and opposing flows are considered and studied. Using appropriate transformations, the system of partial differential equations is transformed into an ordinary differential system of two equations, which is solved numerically by shooting method, coupled with Runge-Kutta scheme. Three different types of nanoparticles, namely copper Cu, alumina Al R 2 R O R 3 R and titania TiO R 2 R with water as the base fluid are considered. Numerical results are obtained for the skin-friction coefficient and Nusselt number as well as for the velocity and temperature profiles for some values of the governing parameters, namely, the nanoparticle volume fraction parameter ���� and mixed convection parameter λ It is found that the highest rate of heat transfer occurs in the mixed convection with assisting flow while the lowest one occurs in the mixed convection with opposing flow. Moreover, the skin friction coefficient and the heat transfer rate at the surface are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids.

Mixed Convection Boundary-Layer Flow on a Vertical Surface in a Porous Medium with a Constant Convective Boundary Condition

The mixed convection boundary-layer flow on a vertical surface heated convectively is considered when a constant surface heat transfer parameter is assumed. The problem is seen to be chararterized by a mixed convection parameter \(\gamma \). The flow and heat transfer near the leading edge correspond to forced convection solution and numerical solutions are obtained to determine how the solution then develops. The solution at large distances is obtained and this identifies a critical value \(\gamma _c\) of the parameter \(\gamma \). For \(\gamma > \gamma _c\) a solution at large distances is possible and this is approached in the numerical integrations. For \(\gamma <\gamma _c\) the numerical solution breaks down at a finite distance along the surface with a singularity, the nature of which is discussed.

Influence of thermal stratification on the radiative flow of Maxwell fluid

We carried out analysis of the effects of thermal stratification in the boundary layer mixed convection flow of Maxwell fluid. The thermal radiation effect is considered. The derived equations with appropriate boundary conditions are solved for series solutions of velocity and temperature. Graphical results lead to the interesting observations. Local Nusselt number is tabulated and discussed. It is found that there is an opposite effect of fluid characteristics on the velocity and temperature. However, the velocity and temperature have similar effects for thermal stratification and radiation.

A New Insight into the Convective Boundary Condition

The steady mixed convection boundary layer flows over a vertical surface adjacent to a Darcy porous medium and subject respectively to (i) a prescribed constant wall temperature, (ii) a prescribed variable heat flux, $$q_\mathrm{w} =q_0 x^{-1/2}$$ , and (iii) a convective boundary condition are compared to each other in this article. It is shown that, in the characteristic plane spanned by the dimensionless flow velocity at the wall $${f}^{\prime }(0)\equiv \lambda $$ and the dimensionless wall shear stress $$f^{\prime \prime }(0)\equiv S$$ , every solution $$(\lambda , S)$$ of one of these three flow problems at the same time is also a solution of the other two ones. There also turns out that with respect to the governing mixed convection and surface heat transfer parameters $$\varepsilon $$ and $$\gamma $$ , every solution $$(\lambda , S)$$ of the flow problem (iii) is infinitely degenerate. Specifically, to the very same flow solution $$(\lambda , S)$$ there corresponds a whole continuous set of values of $$\varepsilon $$ and $$\gamma $$ which satisfy the equation $$S=-\gamma (1+\varepsilon -\lambda )$$ . For the temperature solutions, however, the infinite degeneracy of the velocity solutions becomes lifted. These and further outstanding features of the convective problem (iii) are discussed in the article in some detail.

Mixed convection flow over a solid sphere embedded in a porous medium filled by a nanofluid containing gyrotactic microorganisms

In this paper, the steady mixed convection boundary layer flow about a solid sphere with a constant surface temperature embedded in a porous medium saturated by a nanofluid containing gyrotactic microorganisms in a stream flowing vertically upwards for both cases of a heated and cooled sphere, is studied numerically. One such characteristic of nanofluid is the anomalous high thermal conductivity at very low concentration of nanoparticles and the considerable enhancement of convective heat transfer. However, without external factor introduced, instability occurs and causing the nanoparticles to aggregate and agglomerate. The microorganisms are imposed into the nanofluid to stabilize the nanoparticles to suspend due to a phenomenon called bioconvection. The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite-difference scheme known as the Keller box method. By considering the governing and bioconvection parameters, the numerical results are obtained and discussed for the skin friction coefficient, the local Nusselt number, the local Sherwood number, the local density number of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and density motile microorganisms profiles. It is found that the bioconvection parameters have strong influence towards the velocity and density of motile microorganisms transport rates.

Mixed Convection Boundary Layer Flow over a Moving Vertical Flat Plate in an External Fluid Flow with Viscous Dissipation Effect

The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.

Mixed convection boundary-layer flow on a horizontal flat surface with a convective boundary condition

The steady mixed convection boundary-layer flow on an upward facing horizontal surface heated convectively is considered. The problem is reduced to similarity form, a necessary requirement for which is that the outer flow and surface heat transfer coefficient are spatially dependent. The resulting similarity equations involve, apart from the Prandtl number, two dimensionless parameters, a measure of the relative strength of the outer flow M and a heat transfer coefficient γ. The free convection, M=0, case is considered with the asymptotic limits of large and small γ being derived. Results for the general, M>0, case are presented and the asymptotic limit of large M being treated.

Mixed Convection Boundary-Layer Flow Over a Vertical Surface Embedded in a Porous Material Subject to a Convective Boundary Condition

The mixed convection boundary-layer flow on one face of a semi-infinite vertical surface embedded in a fluid-saturated porous medium is considered when the other face is taken to be in contact with a hot or cooled fluid maintaining that surface at a constant temperature \(T_\mathrm{{f}}\). The governing system of partial differential equations is transformed into a system of ordinary differential equations through an appropriate similarity transformation. These equations are solved numerically in terms of a dimensionless mixed convection parameter \(\epsilon \) and a surface heat transfer parameter \(\gamma \). The results indicate that dual solutions exist for opposing flow, \(\epsilon 0\), the solution is unique. Limiting asymptotic forms for both \(\gamma \) small and large and \(\epsilon \) large are also discussed.

Joule heating effect on magnetohydrodynamic mixed convection boundary layer flow with variable electrical conductivity

PurposeThe paper's aim is to investigate the mixed convection flow of an electrically conducting and viscous incompressible fluid past an isothermal vertical surface with Joule heating in the presence of a uniform transverse magnetic field fixed relative to the surface. It was assumed that the electrical conductivity of the fluid varies linearly with the transverse velocity component.Design/methodology/approachThe governing boundary layer equations were solved numerically. The boundary layer equations were first reduced to a convenient form by using two different formulations, namely, (i) the stream function formulation (SFF) and (ii) primitive variable formulation (PVF).FindingsIt was observed that both the local shear‐stress and Nusselt number increase with increasing value of local magnetic parameter, ξ.Research limitations/implicationsIn the present investigation, we investigated the effects of Joule heating on MHD mixed convection boundary layer flow of an electrically conducting viscous incompressible fluid past an isothermal vertical flat plate in the presence of a transverse magnetic field fixed relative to the surface of the plate. The analysis was valid for a steady, two dimensional laminar flow. An extension to three dimensional flow case is left for future work.Practical implicationsHere we have analyzed the problem of mixed convection flow of electrically conducting and viscous incompressible fluid past an isothermal vertical surface with viscous and Joule heating in presence of a uniform transverse magnetic field fixed relative to the surface. The work would be useful in the thermal management of heat transfer devices.Originality/valueThe results of this study may be of interest to engineers interested in heat exchanger design.