Mixed Convection Boundary Layer Research Articles

Theoretical investigation of the convective heat transfer mechanism along a cantilever shape

The present study aims to investigate the steady state mixed convection flow for a viscous incompressible fluid along a cantilever shape. The study has analyzed the impact of mixed convection boundary layer flow behavior and heat transfer characteristic of the cantilever shape. The leading equations for the said problem are the Navier-Stokes and energy equations. These leading equations are converted into ordinary differential equations using the stream function formulation, and the numerical solution is obtained using the shooting technique with BVP4C and built in MATLAB program. The impact of dimensionless parameters such as n, Pr, and λ on the velocity and temperature profile within the boundary layer of the cantilever cylinder is presented graphically. The results for velocity slope and temperature gradient under the effects of various emerging parameters are presented in tables. The study has concluded that mixed convection parameter has a significant impact on the velocity and temperature distribution, as well as on the velocity slope and temperature gradient rates along a cantilever shape geometry. The outcomes of the current study can be utilized for the design and optimization of various engineering devices involving cantilever shapes. Further, research regarding the impact of other parameters on the cantilever shape including heat transfer characteristics can be conducted using the approach presented in this study. The novelty of the current work can be claimed by saying that for reduced gravity, other forces involved in the flow model induced the fluid motion and temperature gradient.

Radiative Mixed Convection Flow of Casson Nanofluid through Exponentially Permeable Stretching Sheet with Internal Heat Generation

This paper investigates the mixed convection boundary-layer flow of Casson nanofluid with an internal heat source on an exponentially stretched sheet. The Buongiorno model, incorporating thermophoresis and Brownian motion, describes fluid temperature. The modeled system is solved numerically using bvp4c routine to analyze the impact of different fluid parameters on velocity, temperature, and concentration profiles. The analysis reveals that the suction effect, magnetic field, and Casson parameter reduce momentum boundary layer thickness and hence slow fluid motion. Conversely, buoyancy forces increase mass boundary layer thickness which results in accelerating fluid motion. Temperature and concentration profiles show similar trends for Brownian motion, radiation, and thermophoresis.

Further insights into mixed convective boundary layer flows of internally heated Jeffery nanofluids: Stefan's blowing case study with convective heating and thermal radiation impressions

Motivating by the importance of viscoelastic nanofluids in the nanotechnological and biomedical fields, the current analysis intends mainly to examine the aspects of 2D steady Jeffery nanofluid flows near a vertically elongating surface, in the case where the thermal radiation affects linearly on the driven viscoelastic nanofluid flows with the effective thermal contribution of a non-uniform internal heat source. By invoking Buongiorno's model together with the convective heating and Stefan blowing conditions, the leading boundary layer differential formulation is achieved successfully based on reasonable hypotheses. Moreover, the corresponding solutions are computed numerically using BVP4C's method. In this respect, BVP4C's outcomes reveal that the convective heating and Stefan blowing mechanisms exhibit both an upsurging tendency towards the thermal and mass profiles. On the other hand, a declining impression is witnessed for Sherwood's number when strengthening these processes, whilst a dissimilar impression is seen for Nusselt's number. Furthermore, the involved rheological parameters exhibit reverse dynamical and frictional sways on the viscoelastic nanofluid motion.

Influences of blowing and internal heating processes on steady MHD mixed convective boundary layer flows of radiating titanium dioxide‐ethylene glycol nanofluids

AbstractThe present analysis intends predominantly to explore the multiple behaviors of radiating ethylene glycol‐based titanium dioxide nanofluids during their steady boundary layer flows near a vertical permeable surface under the prominent impacts of uniform blowing and nonuniform internal heating processes. By incorporating the dynamical contribution of Lorentz and buoyancy forces in the momentum equation and adopting the single‐phase nanofluid approach along with the constitutive equations of the second‐grade rheological model and Corcione's correlations, the governing partial differential equations and their appropriate boundary conditions are derived mathematically based on the boundary layer theory and other admissible physical approximations. After several simplifications, the aforesaid differential formulation is converted into a set of ordinary differential equations and realistic boundary conditions, which are solved thereafter numerically using GDQ's‐NT method. Moreover, it is demonstrated that the strengthening in the blowing and internal heating processes has a boosting effect on the velocity and temperature profiles. However, the other influencing parameters show dissimilar dynamical and thermal trends. Furthermore, it is witnessed that the mixed convective heat transfer, the viscoelasticity trend of the nanofluidic medium, and the nanoparticles’ loading exhibit an enhancing impression on the surface heat transfer rate.

Mixed Convection Boundary Layer Flow over a Horizontal Circular Cylinder in AL2O3-Ag/Water Hybrid Nanofluid with Viscous Dissipation

This paper investigated the mathematical modelling for mixed convection boundary layer flow over a horizontal circular cylinder in hybrid nanofluid with viscous dissipation. The transformed partial differential equations (PDEs) are numerically solved using an implicit finite-difference approach known as the Keller-box method. The numerical solutions for the reduced Nusselt number, , local skin friction coefficient, , temperature profile, and velocity profiles are found and graphically presented in detail. Effects of the Eckert number, Richardson number and nanoparticle volume fraction are all examined and explained. It is found that the increase of volume fraction of nano material in nanofluid has increased the value of skin friction coefficient. The low density of nano oxides such as alumina in hybrid nanofluids also contribute to reduce friction between fluid and body surface. Based on numerical analysis, the combination of nanoparticles in the form of hybrid nanofluid may reduce skin friction phenomena while sustaining heat transfer characteristics comparable to nanofluid. The results in this paper are original and will assist researchers working in the field of boundary layer flow. It can also be utilised as a reference in experimental studies to reduce operating costs.

Entropy optimization in mixed convective boundary layer flow of CNTs Casson nanoliquid through a vertical cylinder moving with nonlinear velocity

This article inspects entropy generation and mixed convection boundary layer flow of carbon nanotubes (CNTs) Casson nanoliquid via semi-infinite vertical cylinder which moves with nonlinear velocity in Darcy-Forchheimer porous medium. Appropriate similarity variables have been employed to convert the original partial differential equations into ordinary differential equations that have been solved using overlapping grid spectral quasilinearisation method (SQLM). Comparison of accuracy, convergence and stability between the two methods is made. Rate of entropy generated, flow fields and engineering quantities are discussed for different embedding parameters. It is revealed that single-wall CNTs are more efficacious to improve heat transport features than multi-wall CNTs. The fluid flow and thermal dispersion processes improve with consideration of curved surface, CNTs, non-Newtonian fluid and injection of the fluid. The curvature surface and suction of the fluid contribute towards growth of skin friction factor and rate of thermal transference. Entropy generated expands by accounting for viscous nature of the fluid, strong nonlinearity, suction, non-Newtonian fluid, convective boundary condition and CNTs. The study finds applications in various processes, which are massively impacted by heat transport enhancement and high porosity. Boundary layer flow and heat transfer analysis through cylinders are relevant to various metallurgical and engineering solicitations.

Radiative magneto-cross Eyring-Powell flow with activation energy past porous stretching wedge considering suction/injection and ohmic heating effect

A semi-numeric study is presented to explore the nonlinear, radiative, mixed convective boundary layer flow of non-Newtonian Eyring-Powell fluid (EPF) over a porous stretching wedge in the existence of suction/injection, viscous dissipation, activated energy, and ohmic heating. The governing coupled partial differential equations (PDEs) in the flow regime are transformed into coupled ordinary differential equations (ODEs) under suitable boundary conditions (BCs). Computations are performed for variations of various pertinent parameters on velocity, temperature distribution, surface drag force, and heat transfer rate number. It is noted that with increasing Eyring Powell parameter velocity increases for stretching parameter greater than free stream velocity, but decreases when wedge stretches slowly than free stream velocity. An increase in the local non-Newtonian fluid parameter decreases velocity when the wedge stretches faster as compared to free stream velocity. However, velocity increases when the wedge stretches faster. Temperature velocity decreases for both cases of wedge stretches faster or slower as the local non-Newtonian fluid parameter increases. Similar behavior is seen in the case of Eyring Powell parameter. Increasing heat generation or absorption decreases the momentum as well as thermal boundary layer thickness. When the suction/injection parameter is enhanced the velocity shows a declines behavior for both the cases of stretching parameter as it increases. Temperature profiles decline as the mass transfer parameter is enhanced for both the case's velocity ratio parameters, respectively. Excellent agreement is achieved with the differential transform method and numerical result.

Stability Analysis on Mixed Convection Nanofluid Flow in a Permeable Porous Medium with Radiation and Internal Heat Generation

We investigated the mixed convection boundary layer flow over a permeable surface embedded in a porous medium, filled with a nanofluid and subjected to thermal radiation, magnetohydrodynamics (MHD) and internal heat generation. The nanofluid consists of water (H2O) as the base fluid and nanoparticles such as copper (Cu), aluminium oxide (Al2O3) and titanium dioxide (TiO2). The governing system nonlinear partial differential equations is transformed into a set of ordinary differential equations using a similarity transformation, which are then solved numerically for various parameter values. The numerical solutions are obtained using the shooting technique method and bvp4c method, via MAPLE and MATLAB, respectively. Our findings revealed that the velocity distribution decreases with the shrinking parameter, while the presence of nanoparticles enhances the respective profiles. The velocity profiles were also observed to exhibit mixed patterns influenced by magnetic, radiation, and suction parameters. Further, the solutions bifurcated into two branches prior to the shrinking parameter. A stability analysis is performed to determine the stability of the solutions between two branches. We thoroughly discussed the characteristics of the respective solutions and their stability in detail.

Analysis of entropy generation in the flow of MHD water–ethylene glycol nanofluid over a spinning down pointing vertical cone

ObjectivesEntropy generation is investigated by considering the consequence of Magnetic field in H2O − C2H6O2 (50:50) mixture based Al2O3 and Fe3O4 nanoparticles. The 2D magnetohydrodynamic mixed convective boundary layer fluid flow characteristics are assumed to be independent of time at every point. The boundary conditions are mathematically formulated with the slip conditions (velocity and thermal). Significant outcomesThe investigation discloses that the F′(η) (tangential and swirl) drops for the increasing effects of the M. Fe3O4 shows a rise in velocity compared to Al2O3. In case of Magnetic parameter Fe3O4 shows 0.71% and 0.89% of Cf and Nu respectively compared to Al2O3. For changed estimation of the Brinkman number, both the Entropy generation and Bejan number shows opposite behavior. To verify the exactness of the numerical method, a comparison is made between the obtained outcomes and previously published results, corresponding to the skin friction and Nusselt number and the results are reliable. Practical implicationsThis work is developed to multiply the rate of energy transference and increasing the execution as well as effectiveness of energy delivering in industrial field. This model considers the effect of magnetic field, since it helps in achieving energy circulation in numerous devices like refrigerators and in other heating applications. Especially using the magnetized nanofluid helps in improved energy transmission in biomedical imaging. Additionally, the entropy generation model is verified using the thermodynamics second law.

Impact of Exponentially Decaying Internal Heat Generation on Mixed Convection Boundary Layer Slip Flow from a Thermally Radiated Vertical Plate

Impact of Exponentially Decaying Internal Heat Generation on Mixed Convection Boundary Layer Slip Flow from a Thermally Radiated Vertical Plate

MHD mixed convection flow for Maxwell Hybrid nanofluid with Soret, Dufour and Morphology effects

We have investigated the two-dimensional mixed convective Maxwell hybrid nanofluid boundary layer mass and heat flows over a linearly stretching porous surface with the applied external magnetic flux. Thermal radiations along with the Dufour and Soret effects are also incorporated. The governing model of partial differential equations (PDE) is altered into ordinary differential equations (ODE) with an appropriate similarity transformation. The finite difference-based numerical method BVP4c is applied to solve the system of nonlinear ODEs. The flow features and the heat transfer characteristics have been illustrated with graphical representations and a numerical table. For varied values of the flow-related variables, organized and graphical data for the Nusselt number and skin friction coefficient are indicated. In most cases, spherical-shaped nanoparticles have a better influence on stream function, velocity and temperature distributions. This behavior is the opposite of the mass concentration profile. It has been observed that stream function decreases as increase the value of the magnetic field but opposite for mass concentration distribution and temperature profile. The temperature gradient is enhanced as a result of stronger convective flow when Soret number Sr values increase, which causes the boundary layer thickness to grow. A comparative study of hybrid nanofluid and nanofluid showed that the hybrid nanofluid has superior shear stress/skin friction and Sherwood number/surface mass flux than nanofluid flow.

Impact of Non-Similar Modeling for Thermal Transport Analysis of Mixed Convective Flows of Nanofluids Over Vertically Permeable Surface

In the current article, non-similar model is developed for mixed convective boundary layer flow over a permeable vertical surface immersed in nanofluid. The flow is initiated due to the plate stretching in vertical direction and by natural means such as buoyancy. The governing dimensional equations are converted to non-dimensional equations through characteristic dimensions. Furthermore the non-similar modeling is done by choosing ξ (X) as non-similarity variable and η(X, Y) as pseudo-similarity variable. The non-similar partial differential system (PDS) is then solved by using local non-similarity method via bvp4c. The heat and mass transfer analysis are carried out by studying local Nusselt and Sherwood numbers in tabular form for some important parameters involved in the non-similar flow. The concentration, velocity and temperature profiles are graphically represented for various dimensionless number such as Prandtl number (Pr), Brownian motion (Nb), Lewis number Le and thermophoresis (Nt). Reversed flow is observed for the velocity profile as non-similar variable is varied. Enhancement in thermal profile is witnessed for Nb, Nt and reduction in temperature is observed for Pr. Concentration is reduced for different values of Pr, Le, Nb. Finally this article intends to develop an intuitive understanding of non-similar models by emphasizing the physical arguments. The authors developed the nonsimilar transformations and tackled the dimensionless non-similar structure by employing the local non-similarity technique. To the best of authors’ observations, no such study is yet published in literature. This study may be valuable for the researchers investigating towards industrial nanofluid applications, notably in geophysical and geothermal systems, heat exchangers, solar water heaters, biomedicine, and many other fields.

Stability and receptivity analyses of mixed convection in unstably stratified horizontal boundary layers

A linear stability analysis is employed to investigate thermal effects in shear flows. The cases analysed consist of unstably stratified horizontal boundary layers under a mixed convection regime, where forced and free convection mechanisms compete. Governing equations are given by the incompressible Navier–Stokes equations with the Oberbeck–Boussinesq approximation, where the base flow comes from their boundary layer approximation. Modal and non-modal analyses are used to investigate the behaviour of small-amplitude disturbances superposed to this base flow. An evaluation of the inertial, shearing and buoyancy mechanisms in the mixed convection boundary layer stability is performed through variations in the Reynolds, Prandtl and Richardson numbers. On the one hand, the spectra lead to the parametric conditions for the time-asymptotic onset of instability, which is still caused by Tollmien–Schlichting (TS) waves as in the traditional Blasius case. However, thermal effects have a destabilizing effect on them, more so for liquids than gases. On the other hand, the pseudospectra obtained from a resolvent analysis indicate the existence of transient growth at this same onset. However, contrary to the traditional Blasius case, thermal effects cause it to be dominated by the continuous frequency spectrum instead of the discrete TS modes. In order to elucidate this qualitative change, a componentwise input–output analysis is employed to quantify the receptivity to specific external disturbances. It shows that thermal effects directly impact the conversion of thermal to kinetic linear disturbance energy, causing a strong amplification of the flow response due to the non-normality of the linear operator. Results reveal that heating from below causes the forcing and response modes of the input–output analysis to have a free-stream spatial support due to non-modal excitation of the continuous spectrum. Such a behaviour suggests that the unstably stratified boundary layer is susceptible to free-stream thermal disturbances, which can potentially impact bypass transition.

Application of Successive Linearisation Method on Mixed Convection Boundary Layer Flow of Nanofluid from an Exponentially Stretching Surface with Magnetic Field Effect

The this paper, we investigate the heat and mass transfer in MHD nanofluid flow from an exponentially stretching surface numerically. The partial governing equations are transformed into a system of ordinary differential equations and then solved using a Successive Linearisation Method (SLM). The velocity, temperature and concentration profiles are shown graphically for various flow parameters and the physical quantities such as Skin-friction, Nusselt and Sherwood numbers are computed for different values of governing parameters. It is was observed from results that the SLM provides highly numerical solution and converges rapidly for nonlinear differential equations. It is concluded that an increase in the value of magnetic field parameter reduces the velocity field while the opposite trend is observed for temperature and concentration distributions. An increase in the value of nanoparticle volume fractions enhances the velocity field and the temperature distributions while the concentration distribution reduces.

Computational modeling of hybrid micropolar nanofluid flow over a solid sphere

The current study discusses the mixed convection boundary layer around an isothermal solid sphere utilizing numerical simulation; two fluid types of hybrid and mono micropolar nanofluids with constant wall temperature in an MHD field are examined. To improve a base fluid's thermophysical, optical, rheological, and morphological qualities, two different types of nanoparticles Copper oxide CuO and Graphite oxide (GO) are combined to create hybrid nanofluids. The sensitivity analysis was made to unveil the impacts of the mixed convection factor, the field strength and the micro-rotation factor. The results reveal that the improving effect of using NF by the induced micro-rotational effect is more prominent at lower angles and diminished at higher angles. Another point that could be obtained is that the thermal boundary layer thickness is directly proportional to the magnetic parameter; by increasing the M value from 0.5 to 2, the thermal boundary layer thickness increases from 1.4 to 1.8. Also, using hybrid instead of mono NF has nearly no effect on altering the angular velocity at y > 4; for other ones (y < 4), the difference is<15 %.

NEW RESULTS ON A MIXED CONVECTION BOUNDARY LAYER FLOW OVER A PERMEABLE VERTICAL SURFACE EMBEDDED IN A POROUS MEDIUM

The objective of this paper is to prove the existence, non-existence and the sign of convex and convex-concave solutions of the third-order non-linear differential equation f^'''+ff^''+βf^' (f^'-1)=0, satisfying the boundary conditions f(0)=a∈R, f^' (0)=b&lt;0 and〖 f〗^'→λ as t→+∞ where λ∈{0,1} and β&lt;0. The problematic arises in the study of the Mixed Convection Boundary Layer flow over a permeable vertical surface embedded in a Porous Medium according to the mixed convection parameter b&lt;0, the permeable parameter a∈R and the temperature parameter β&lt;0.

Radiation Effects on Inclined Magnetohydrodynamics Mixed Convection Boundary Layer Flow of Hybrid Nanofluids over a Moving and Static Wedge

Nowadays, hybrid nanofluids play an important role in heat transfer systems. They are a good alternative to increase the efficiency of heat transfer and save the energy. Thermal radiation and mixed convection flow of hybrid nanofluids past a permeable moving and stationary wedge were studied in this research. This research uses water as a base fluid to investigate the effects of silver (Ag) and magnesium oxide (MgO) nanoparticles. Similarity transformation techniques are used to convert the partial differential equations of hybrid nanofluids to ordinary differential equations, which is then solved numerically by applying the implicit finite difference Keller box method. The results of the research are illustrated graphically to show the behavior of velocity and temperature profiles, as well as skin friction and Nusselt number. Increasing the parameters of the aligned magnetic field, magnetic field interaction, mixed convection, and wedge angle parameter results in higher velocity profiles but lower temperature profiles. As the radiation parameter and the nanoparticle volume fraction increase, the temperature rises and the velocity decreases. With the exception of the radiation parameter, the skin friction and Nusselt number increase as the alignment angle of the magnetic field, the interaction of the magnetic field, the mixed convection, the wedge angle parameter, and the volume fraction of nanoparticle Ag and MgO rise. As a result of these findings, the velocity profiles and Nusselt numbers of moving wedges are higher, but the temperature profiles and skin friction are lower than those of stationary and moving against flow wedges. In addition, a comparison with previously published research is presented, with excellent agreement discovered. The results of this research will contribute to the field of knowledge in mathematics by bringing additional information for mathematician interested in future research on hybrid nanofluids.

Magnetite water based ferrofluid flow and convection heat transfer on a vertical flat plate: Mathematical and statistical modelling

The unique magnetic properties of ferrofluid when exposed to the magnetic field led to the ferrofluid formulation in wide applications, especially as a thermal transfer. To picture the effective ferrofluid flow configurations and heat transfer mechanism at a surface, it is crucial to figure out the phenomenology of boundary layer and convective heat transfer. This study investigates a numerical solution of the mixed convection boundary layer flow of ferrofluid at the stagnation point on a vertical flat plate. Ferrofluid composed of magnetite (Fe3O4) water based exposure to the magnetic field and thermal radiation is considered. The complicated governing differential equations of fluid flow and heat transfer are simplified into simple equations using boundary layer approximation, Boussinesq approximation and similarity transformations. Then, the equations are solved numerically by employing the Keller-box method. Numerical results discovered that the ferroparticles volume fraction is the predominant factor in contributing to the trend of ferrofluid velocity, reduced skin friction and reduced Nusselt number. Further, the influence of the ferroparticles volume fraction on reduced skin friction and reduced Nusselt number are analyzed using regression analysis.

Numerical and asymptotic solutions of the unsteady mixed convection boundary-layer flow over an expanding/contracting vertical cylinder

PurposeThe purpose of this study is to obtain both the numerical and asymptotic solutions of the unsteady mixed convection flow and heat transfer over an expanding or contracting cylinder which is placed vertically.Design/methodology/approachSolutions of the governing ordinary (similarity) differential equations for the fluid flow and temperature field are obtained using the function bvp4c from MATLAB. The problem involves the Prandtl number σ, the mixed convection parameter λ and unsteadiness parameter S that characterize an expanding or contracting cylinder. This solution approach is capable of producing multiple solutions once the necessary assumptions are provided.FindingsIt is found that solutions exist for all negative values of S, expanding cylinder, and only for small positive values of S, contracting cylinder. Further, more than one solution is observed; numerical computation shows that the critical point of S becomes singular as λ approaching zero. For the case of expanding cylinder, the mixed convection parameter has a significant effect on both the flow and heat transfer characteristics. Asymptotic analysis also shows that when σ is large, dual solutions exist for some values of S and λ.Originality/valueThe present results are new and original for the study of the unsteady mixed convection flow and heat transfer over an expanding/contracting cylinder where numerical solutions are obtained for representative values of the involved parameters. Asymptotic solutions for large λ and large σ are derived.

Thermal stable properties of solid hybrid nanoparticles for mixed convection flow with slip features

Following to improved thermal impact of hybrid nanomaterials, wide range applications of such materials is observed in the thermal engineering, extrusion systems, solar energy, power generation, heat transfer devices etc. The hybrid nanofluid is a modified form of nanofluid which is beneficial for improving energy transfer efficiency. In current analysis, the solid nanoparticles aluminium (phi_{{{text{Al}}_{2} {text{O}}_{3} }}) and copper (phi_{{{text{Cu}}}}) have been mixed with water to produce a new hybrid nanofluid. The investigation of a steady two-dimensional mixed convection boundary layer flow of the resultant hybrid nanofluid on a vertical exponential shrunk surface in the existence of porous, magnetic, thermal radiation, velocity, and thermal slip conditions is carried out. Exponential similarity variables are adopted to transform the nonlinear partial differential equation into a system of ordinary differential equations which has been then solved by employing the shooting method in Maple software. The obtained numerical results such as coefficient of skin friction f^{prime prime } left( 0 right), heat transfer rate - theta^{prime } left( 0 right), velocity f^{prime } left( eta right) and temperature left( {theta left( eta right)} right) distributions are presented in the form of different graphs. The results revealed that duality exists in solution when the suction parameter S ge S_{ci} in assisting flow case. Due to non-uniqueness of solutions, a temporal stability analysis needs to be performed and the result indicates that the upper branch is stable and realizable compared to the lower branch.