Mixed Convection Boundary Layer Flow Research Articles

Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis

AbstractSteady incompressible magnetohydrodynamic mixed convection boundary layer flow of a Casson fluid on an exponentially vertical shrinking sheet using the non‐Newtonian heating equation is investigated in this paper. There are three main objectives of this study, namely, to develop a new mathematical model, to obtain multiple solutions, and to perform stability analysis. The governing partial differential equations have been changed into nonlinear ordinary differential equations. The resultant equations of boundary value problems are then converted into the equivalent initial value problems using the shooting method before they can be solved using Runge‐Kutta of order four. The numerical results are obtained and found to be in good agreement with the published literature. The results also indicate that the velocity boundary layer becomes thinner as the magnetic, slip, and Casson parameters increase. Dual solutions for temperature and velocity distributions are obtained. Furthermore, the results suggest that the presence of the force of buoyancy (opposing flow case) would cause the occurrence of dual solutions. However, based on the stability analysis, only the first solution is stable.

Soret- Dufour Effect on Mixed Convection Past a Vertical Plate in Non-Darcy Porous Medium Saturated With Buongiorno Nanofluid in the Presence of Thermal Dispersion

ABSTRACTNumerical analysis was investigated for steady two-dimensional double diffusive mixed convection boundary layer flow over a semi-infinite vertical plate embedded non-Darcy porous medium filled with nanofluid, in presence of thermal dispersion and under convective boundary conditions. The Buongiorno nanofluid model is used, while the porous medium is described by the Darcy-Forchheimer extension. The governing partial differential equations are transformed into four coupled nonlinear ordinary differential equations using an appropriate similarity transformations and the resulting system of equations is then solved numerically by the finite-difference method. Numerical results are presented to illustrate how the physical parameters affect the flow field, temperature, concentration and solid volume fraction profiles. In addition, the variation of heat, mass and nanoparticle transfer rates at the plate are exhibited graphically for different values of pertinent parameters.

Effect of Soret and Dufour numbers on double diffusive mixed convection boundary layer flow induced by a shrinking sheet

The numerical study of double diffusive mixed convection boundary layer flow over a shrinking sheet are presented in the presence of Soret and Dufour effects. Shrinking velocity, wall temperature and wall concentration are assumed to have exponential function forms. Non-similarity method is applied for the governing basic equations (flow, momentum, energy and concentration equations) before they are solved numerically using bvp4c program in Matlab software. The numerical results of velocity, temperature and concentration are reported graphically for various values of suction parameter, dimensionless coordinate along the plate parameter, shrinking parameter, mixed convection parameter, buoyancy ratio parameter, Soret parameter and Dufour parameter. Since dual solutions is obtained, stability analysis is performed to select the stable solution.

Mixed convection boundary layer flow and heat transfer over a vertical plate embedded in a porous medium filled with a suspension of nano-encapsulated phase change materials

The flow and thermal behavior of nano-encapsulated phase change materials (NEPCMs) dispersed in a liquid is investigated over a vertical flat plate. The NEPCM particles are consist of an encapsulation shell and a core made of phase change materials (PCMs). When the temperature of the liquid around the NEPCM particle is higher than the fusion temperature of the PCM core, the PCM core absorbs a notable amount of heat (the latent heat of the phase change) from the host fluid and melts. The vertical plate is embedded in a porous medium, and the porous medium is saturated with the suspension of NEPCM. There is a uniform flow over the plate, which can aid or oppose the natural convection flow over the plate. The partial differential governing equations for the flow and heat transfer of NEPCM suspension are introduced and transformed into a high order boundary value ordinary differential equation. The finite difference method with a colocation technique as the grid adaptation and automatic error control is utilized to integrate the governing equations. Validations are performed by comparing the results with the literature. It is found that there are two solution branches in the case of high opposing flows. The results indicate that the presence of NEPCM particles enhances the heat transfer over the plate. The decrease in the fusion temperature of NEPCM cores enhances the heat transfer.

MHD mixed convection boundary layer stagnation-point flow on a vertical surface with induced magnetic field

Purpose This study aims to perform a stability analysis on a steady magnetohydrodynamic (MHD) mixed convection boundary-layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a vertical flat plate. The effect of induced magnetic field is also considered. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB. Findings Dual solutions are found to exist for a certain range of the buoyancy parameter for both the assisting and opposing flows. The results from the stability analysis showed that the first solution (upper branch) is stable and valid physically, while the second solution (lower branch) is unstable. Practical implications This problem is important in many metallurgical processes, namely, drawing, annealing and tinning of copper wires. The results obtained are very useful for researchers to determine which solution is physically stable, whereby mathematically more than one solution exists for the skin friction coefficient and the heat transfer characteristics. Originality/value The present results of the stability analysis are original and new for the problem of MHD mixed convection stagnation-point flow of viscous conducting fluid over a vertical flat plate, with the effect of induced magnetic field.

Effect of viscous dissipation on finding dual solutions for mixed convection boundary layer flow for nanofluid

AbstractThe effect of viscous dissipation on mixed convection boundary layer flow for Ag‐water nanofluid under steady‐state condition has been studied numerically for both the buoyancy assisting and opposing flows over a vertical semi‐infinite flat plate. A new co‐ordinate system has been introduced to transform the governing partial differential equations (PDEs) to facilitate the numerical calculations. Then, the local similarity method has been used for approximating the transformed PDEs to ordinary differential equations. Further, the quasi‐linearization method has been introduced to linearize the nonlinear equations and then numerical integration has been carried out using implicit trapezoidal rule along with the principle of superposition. For higher Pr, the coupled differential equations behave like stiff differential equations. To overcome the situation, orthonormalization process has been introduced. The effects of solid volume fraction of nanoparticles , the mixed convection parameter , Prandtl number , and Eckart number have been analyzed on the heat transfer and flow characteristics. It has been observed that the dual solutions are obtained for buoyancy opposing flow only and the range of dual solutions have become wider with the increases in . Further, nanofluids enhance the heat transfer process as compared to conventional heat transfer fluids . Moreover, the addition of viscous dissipation causes less heat transfer in the boundary.

Navier’s Slip Effect on Mixed Convection Flow of Non-Newtonian Nanofluid: Buongiorno’s Model with Passive Control Approach

This article is devoted to the study of Navier’s slip effect on MHD mixed convection boundary layer flow of non-Newtonian nanofluid over a stretching surface. The flow is induced due to the continuously stretching surface. The mathematical modeling of the flow situation, is governed by Buongiorno’s nanofluid model with passively controlled nanoparticle boundary condition. To analyze the flow field behavior, the similarity transformation approach is adopted. The approximate similar solution of the problem is obtained using finite element method. Effects of active flow parameters on the quantities of engineering interests viz. skin friction coefficient, Nusselt number and flow variables viz velocity, temperature and nanoparticle concentration, are presented graphically. The Numerical results of the present investigation are validated with earlier published results. The findings suggest that the velocity slip plays a vital role in skin friction coefficient and Nusselt number of non-Newtonian nanofluid. It has been observed that the Brownian diffusion does not have very promising impact on Nusselt number as compared to results obtained in previous studies with active control of wall nanoparticles. The potential application of present investigation are in various industrial manufacturing processes such as cooling and/or drying of textile and paper, rolling sheet drawn from a die, manufacturing of crystalline materials, polymeric sheets, glass sheets, etc.

Bioconvection in Casson nanofluid flow with Gyrotactic microorganisms and variable surface heat flux

This paper presents a two-dimensional unsteady laminar boundary layer mixed convection flow heat and mass transfer along a vertical plate filled with Casson nanofluid located in a porous quiescent medium that contains both nanoparticles and gyrotactic microorganisms. This permeable vertical plate is assumed to be moving in the same direction as the free stream velocity. The flow is subject to a variable heat flux, a zero nanoparticle flux and a constant density of motile microorganisms on the surface. The free stream velocity is time-dependent resulting in a non-similar solution. The transport equations are solved using the bivariate spectral quasilinearization method. A grid independence test for the validity of the result is given. The significance of the inclusion of motile microorganisms to heat transfer processes is discussed. We show, inter alia, that introducing motile microorganisms into the flow reduces the skin friction coefficient and that the random motion of the nanoparticles improves the rate of transfer of the motile microorganisms.

Mixed Convection Boundary Layer Flow on a Vertical Surface in a Saturated Porous Medium: New Perturbation Solutions

Mixed Convection Boundary Layer Flow on a Vertical Surface in a Saturated Porous Medium: New Perturbation Solutions

Effects MHD and Heat Generation on Mixed Convection Flow of Jeffrey Fluid in Microgravity Environment over an Inclined Stretching Sheet

In this paper, Jeffrey fluid is studied in a microgravity environment. Unsteady two-dimensional incompressible and laminar g-Jitter mixed convective boundary layer flow over an inclined stretching sheet is examined. Heat generation and Magnetohydrodynamic MHD effects are also considered. The governing boundary layer equations together with boundary conditions are converted into a non-similar arrangement using appropriate similarity conversions. The transformed system of equations is resolved mathematically by employing an implicit finite difference pattern through quasi-linearization method. Numerical results of temperature, velocity, local heat transfer, and local skin friction coefficient are computed and plotted graphically. It is found that local skin friction and local heat transfer coefficients increased for increasing Deborah number when the magnitude of the gravity modulation is unity. Assessment with previously published results showed an excellent agreement.

Effects of surface roughness on mixed convection nanoliquid flow over slender cylinder with liquid hydrogen diffusion

The influence of surface roughness on boundary layer flow characteristics over moving surfaces is of considerable research interest in recent times. In the present study, the effects of surface roughness on flow over moving slender cylinder are analyzed in presence of mixed convection nanoliquid boundary layer flow. The problem is modelled in terms of highly nonlinear dimensional partial differential equations, which are written in non-dimensional form with the help of non-similar transformations. The resulting equations are reduced to linear partial differential equations by utilizing Quasilinearization technique, which are discretized using implicit finite difference scheme. The results obtained during the numerical simulation are then depicted through graphs in terms of various profiles and gradients and are analyzed with proper physical explanations. The roughness of slender cylinder surface is represented in a deterministic model as a sine wave form and yields sinusoidal variations in the values of skin-friction coefficient, wall heat and mass transfer rates. It is observed that the surface roughness effects are more prominent away from the orifice. The local frequency of gradients increases (i.e. wavelength decreases) with the increase in the frequency of surface roughness (n). The addition of nanoparticles into the ordinary fluid enhances the skin-friction coefficient and wall mass transfer rate. However, due to its effects, significant reduction is observed in the wall heat transfer rate. The phase difference of gradient oscillations arising in presence of nanoparticles is suppressed further away from the origin due to surface roughness. Interestingly, the amplitude of gradient oscillations remain higher in case of nanoliquid in comparison with that in case of ordinary fluid. Furthermore, the magnitude of wall mass transfer rate of liquid hydrogen is higher than that of nanoparticle wall mass transfer rate, which signifies the higher diffusivity of nanoparticles. The results of present study are of practical relevance to industrial applications such as polymer fibre coating and coating of wires.

The Onset of Instabilities in Mixed Convection Boundary Layer Flow Over a Heated Horizontal Circular Cylinder

AbstractThe purpose of this study is to examine the instabilities of a two-dimensional mixed convection boundary layer flow induced by an impinging ascending flow on a heated horizontal cylinder. A significant amount of works is done in recent years on this problem because of its wide range of applications. However, they did not check the stability of the flow in the face of small disturbances that occur in reality. For this, we adopt the linear stability theory by first solving the steady basic flow and then solving the linear perturbed problem. Thus, the governing equations of the basic flow are reduced to two coupled partial differential equations and solved numerically with the Keller-Box method. The corresponding steady solution is obtained, by varying the position along the cylinder’s surface, for different values of Richardson number (λ) and Prandtl number (Pr), up to, respectively, 3000 and 20. To examine the onset of thermal instabilities, the linear stability analysis is done using the normal mode decomposition with small harmonic disturbances. The Richardson number λ is chosen as the control parameter of these instabilities. The resulting eigenvalue problem is solved numerically by the use of the pseudospectral method based on the Laguerre polynomials. The computed results for neutral and temporal growth curves are depicted and discussed in detail through graphs for various parametric conditions. The critical conditions are illustrated graphically to show from which thermodynamic state, the flow begins to become unstable. As a main result, from ξ = 0 to ξ ≈ π/3, we found that forced and mixed convection flow cases are linearly stable in this region. However, in free convection case (λ > 100), it appears that the stagnation zone is the most unstable one and then the instability decreases along the cylinder’s surface up to the limit of its first third, thus giving the most stable zone of the cylinder. Beyond ξ ≈ 1.2, strong instabilities are noted also for low values of Richardson number, and the flow tends to an unstable state even in the absence of thermal effect, i.e., hydrodynamically unstable Ri = 0, probably due to the occurring of the boundary layer separation.

Mixed convection heat transfer of water about a vertical surface of variable heat flux with density inversion

Laminar mixed convection boundary layer flow of water about a vertical plate is studied including density inversion effects. The plate surface is subjected to an arbitrary heat flux that is a function of vertical distance from the leading edge. Both aiding and opposing mixed convection situations are considered in the study. The dimensionless forms of stream function and temperature are expanded in terms of perturbation elements and universal functions. The differentials of the heat flux, which are functions of vertical distance, are used as perturbation elements to obtain universal functions. The results for universal functions required to find temperature and velocity profiles are obtained. The obtained universal functions are valid for any arbitrary wall heat flux variation. The universal applicability of results is demonstrated for power-law variation of wall heat flux. The velocity and temperature variation, boundary layer thickness, Nusselt numbers and skin friction coefficient are presented for various values of mixed convection parameter, wall flux power index, for both aiding and opposing mixed convection. For a given combination of Grashof and Reynolds numbers, the heat transfer rates and skin friction coefficient are found to increase almost linearly with wall flux power index, in the parameter range of the study, for both the cases of aiding and opposing mixed convection. The present results of special cases are found to match well with the results available in the literature.

Analysis of mixed convection in water boundary layer flows over a moving vertical plate with variable viscosity and Prandtl number

PurposeThe purpose of the present study is to analyze the mixed convection water boundary layer flows over moving vertical plate with variable viscosity and Prandtl number. The non-linear partial differential equation governing the flow and thermal fields are presented in non-dimensional form by using appropriate transformation. The quasi-linearization technique in combination with implicit finite difference scheme has been adopted to solve the nonlinear-coupled partial differential equation. The numerical results are displayed graphically to illustrate the influence of various non-dimensional physical parameters on velocity and temperature. Further, the numerical results for local skin-friction coefficient and local Nusselt number are also reported. The present findings are compared with previously reported results, and these comparisons are found to be in excellent agreement.Design/methodology/approachThe nonlinear partial differential equations governing the flow and thermal fields have been solved numerically using the implicit finite difference scheme in combination with the quasi-linearization technique. The numerical results are presented in terms of skin friction and heat transfer rate which are useful in determining the surface heat requirements for stabilizing the laminar boundary layer flow over a moving plate in water.FindingsThe effect of the ratio of free-stream velocity to the composite reference velocity is significant on the velocity profile. Near the wall region, as ratio of free stream velocity to composite reference velocity increases form 0.1 to 0.5, the velocity overshoot gets enhanced from 3 per cent to 41 per cent. The influence of buoyancy parameter and ration of free stream velocity to composite reference velocity on temperature profile is comparatively less than on velocity profiles. The increase in the skin friction coefficient is dependent on the increase in the value of ratio of free stream velocity to composite reference velocity if the buoyancy parameter λ is fixed and vice versa and increases in ΔT results in a decrease in N and Pr.Originality/valueThe present investigation is to deal with the solution of steady laminar water boundary layer flows over a moving plate with temperature-dependent viscosity and Prandtl number applicable for water using practical data. The fluid considered here is water, as it is one of the most common working fluids found in engineering applications.

Transient Mixed Convection Boundary Layer Flow of an Incompressible Fluid Past a Wedge in Presence of Magnetic Field

In this paper, an analysis is performed to explorethe transient, laminar two-dimensional, mixed convection boundary layer flow of a viscous and incompressible fluid past a vertical wedge taking into account the effect of magnetic field. With appropriate transformations the boundary layer equations are reduced to a local nonsimilarity equations and the solutions are obtained employing three distinct methods, namely, (i) perturbation method for small time; (ii) asymptotic solution method for large time; (iii) straight forward finite difference method for any time. The agreement between the solutions obtained from prescribed methods is found to be excellent. In this study the evaluation of skin-friction coefficient and the local Nusselt number with the effects of different governing parameters such as different time, τ, the exponent, m (= 0.4, 0.5, 1.0), mixed convection parameter, λ (= 0.0, 0.2, 0.4) and magnetic field parameter, M (=0.0, 1.0) for fluids having Prandtl number, Pr= 0.72, 1.0 and 7.0have been discussed. It is observed that both the local skin friction and local Nusseltnumber decreases due to an increase in the value of M. It is also found that an increase in the value of Prandtl number, Pr, leads to a decrease in the value of local skin friction coefficient and the value of local Nusselt number coefficient increases with the increasing values of Prandtl number.

Unsteady transport of MHD mixed convection inspired by thermal radiation and partial slip performance: Finite difference approach

Background: In this article mixed convection boundary layer flow of MHD fluid on permeable stretching surface is investigated under the effects of velocity and thermal slip. The physical unsteady problem is examined by considering thermal radiation effects on momentum and thermal boundary-layer flow. Different from available literature, in the present study we consider mix convective flow, thermal radiation, transverse applied magnetic field, velocity, and thermal slip. Methodology: The transform non-linear system of differential equation is tackled numerically by the aid of finite difference scheme named as Keller-Box. Stable solution is correct up to six decimal places and special cases overlaps with the existing results in literature validating the present analysis. Conclusion: It is concluded that mixed convection leads to accelerate fluid-flow and reduce temperature profile. Injection contributes in rising magnitude of velocity and temperature when compared with suction effects. Velocity and thermal slip parameter influence in lowering fluid-flow while temperature profile decrease for velocity slip parameter and opposite trend is witness corresponding to thermal slip parameter. Both velocity and temperature are increasing function of thermal radiation. In addition, the skin friction coefficient and the local Nusselt number are tabulated and analyzed. Novelty: Present study is concerned with fluid-flow applications in plastic films, polymer extrusion, glass fiber, metallurgical processes, and metal spinning.

On dissipative MHD mixed convection boundary-layer flow of Jeffrey fluid over an inclined stretching sheet with nanoparticles: Buongiorno model

Present paper utilizes a combination of non-Newtonian fluid model (Jeffrey fluid) with Buongiorno model (nanofluid). The Jeffery fluid, which is regarded as a base fluid, together with suspended nanoparticles are examined over an inclined stretching sheet with the amalgamated impacts of mixed convection and viscous dissipation. The mathematical formulation of this model is done by choosing the appropriate similarity variables for the aim to reduce the complexity of governing partial differential equations. The Runge-Kutta-Fehlberg (RKF45) method is then applied to the resulting of non-linear ODE to generate numerical results for highlighting the impact of emerging parameters towards specified distributions. Both the graphical and tabular representations of vital engineering physical quantities are also shown and deliberated. For the increase of Eckert number, thermophoresis diffusion, and Brownian motion parameters, the elevation of temperature profiles is observed. Besides, the thermophoresis diffusion parameter tends to accelerate the nanoparticle concentration profile while Brownian motion parameter displays the opposite behavior.

On the Convex and Convex-Concave Solutions of Opposing Mixed Convection Boundary Layer Flow in a Porous Medium

In this paper, we are concerned with the solution of the third-order nonlinear differential equation f″′+ff″+βf′(f′-1)=0, satisfying the boundary conditions f(0)=a∈R, f′(0)=b<0, and f′(t)→λ, as t→+∞, where λ∈{0,1} and 0<β<1. The problem arises in the study of the opposing mixed convection approximation in a porous medium. We prove the existence, nonexistence, and the sign of convex and convex-concave solutions of the problem above according to the mixed convection parameter b<0 and the temperature parameter 0<β<1.

Computational Modelling and Solutions for Mixed Convection Boundary Layer Flows of Nanofluid from a Non-Isothermal Wedge

Buoyancy-driven (“Falkner-Skan”) mixed convection flow of a nanofluid from a nonisothermal wedge has been investigated numerically using an implicit finite difference scheme. The model used for nanofluid includes the effects of Brownian motion, buoyancy ratio and thermophoresis. A non-similarity solution is developed which depends on the Prandtl number (Pr), Schmidt number (Sc), Brownian motion number (Nb), buoyancy ratio parameter (Nr), thermophoresis number (Nt), mixed convection parameter (λ) and pressure gradient parameter (m). The variation of the skin friction, the reduced heat transfer rate and reduced mass transfer rate with Nb, Nr and Nt for various values of Pr, m and Sc are also tabulated.

Exploration of Non-Linear Thermal Radiation and Suspended Nanoparticles Effects on Mixed Convection Boundary Layer Flow of Nanoliquids on a Melting Vertical Surface

Exploration of Non-Linear Thermal Radiation and Suspended Nanoparticles Effects on Mixed Convection Boundary Layer Flow of Nanoliquids on a Melting Vertical Surface