Mixed Convection Boundary Layer Flow Research Articles

MHD Mixed Convection Boundary Layer Casson Nanofluid Flow over an Exponential Stretching Sheet

This paper investigates the effects of radiation, internal heat source and magnetohydrodynamics (MHD) on the mixed convective boundary layer flow of a Casson nanofluid within a porous medium that is saturated and subject to an exponentially stretching sheet. The nanofluid model incorporates Brownian motion and thermophoresis, and the Darcy model is employed for the porous medium. By applying an appropriate similarity transformation, the nonlinear governing boundary layer equations are converted into a set of nonlinear coupled ordinary differential equations. These equations are then solved numerically using the Hermite wavelet method, with simulations conducted through the MATHEMATICA programming language. The analysis covers various aspects including temperature distribution, velocity, solute concentration and several engineering parameters such as skin friction coefficients, the Nusselt number (rate of heat transfer) and the Sherwood number (rate of mass transfer), all evaluated based on dimensionless physical parameters. The results indicate that elevated radiation intensifies temperatures and leads to thicker thermal boundary layers. As the Casson parameter increases, both the velocity and the momentum boundary layer become narrower. Additionally, a more pronounced chemical reaction rate reduces the thickness of the solutal boundary layer. The accuracy and reliability of the numerical Hermite wavelet method are validated through a comparative analysis with previous studies, demonstrating excellent concordance and confirming the robustness of the computational approach.

Dual characteristics of mixed convection flow of three-particle aqueous nanofluid upon a shrinking porous plate

Purpose This study aims to analyze the thermo-hydrodynamic characteristics for the mixed convection boundary layer flow of three-particle aqueous nanofluid on a shrinking porous plate with the influences of thermal radiation and magnetic field. Design/methodology/approach The basic equations have been normalized with the help of similarity transformations. The obtained equations have been solved numerically using the shooting method in conjunction with the sixth-order Runge–Kutta technique. Numerical results for the velocity and temperature are illustrated with varying relevant parameters. Findings The results reveal that the local drag coefficient increases with higher values of the magnetic field parameter, nanoparticle volume fraction and suction parameter. On the other hand, boosting the radiation parameter and nanoparticle concentration notably enhances heat transfer. Furthermore, it is noted that the suction parameter and magnetic field parameter both lead to an increase in velocity and promote the occurrence of dual solutions within the problem conditions. Research limitations/implications The limitations are that the model is appropriate for thermal equilibrium of base fluid and nanoparticles, and constant thermo-physical properties. Originality/value To the best of the authors' knowledge, no study has taken an attempt to predict the flow and heat transfer characteristics of unsteady mixed convection ternary hybrid nanofluid flow over a shrinking sheet, particularly under the influence of magnetic field and radiation. The findings obtained here may hold particular significance for those interested in the underlying theoretical and practical implications.

Mixed Convection Boundary Layer Flow on A Vertical Flat Plate in Al203-Ag/Water Hybrid Nanofluid with Viscous Dissipation Effects

Mixed Convection Boundary Layer Flow on A Vertical Flat Plate in Al203-Ag/Water Hybrid Nanofluid with Viscous Dissipation Effects

The variational approach to study the mixed convection boundary layer flow over a permeable Riga plate

AbstractThe physical problem of steady state, laminar, mixed convection (Ri) with double‐diffusive (N) in an electrically low conducting fluid past a semi‐infinite electromagnetic () influenced flat plate with internal uniform heat generation (Q) in the presence of suction/injection (H) by considering viscous dissipation (Ec), thermophoresis (Nt) and thermal diffusion effects (Sr) is mathematically modeled as a simultaneous system of nonlinear partial differential equations. To achieve the solution of the problem numerically, Gyarmati's variational principle known as the “Governing Principle of Dissipative Processes” on the basis of nonequilibrium thermodynamic processes in the theory of continua, is adopted. This research work correlates the phenomenon of fluid around submersibles/space vehicles and provides related insights. To estimate the transportation fluid fields within the boundary layer, the appropriate trial polynomials have been employed, and functionals for the integral variational principle are determined. Next, the Euler–Lagrange equations of the functionals are obtained as a system of polynomial equations involving boundary layer thicknesses of momentum, temperature, and concentration. The expressions of local shear stress, local Nusselt, and local Sherwood numbers have been derived and the effects of various physical factors involved in the problem are explored. A comparison with the previously published results in the literature is provided to confirm the validity of the solution procedure. The results depict that injection () and opposing buoyancy () decrease the skin friction about 38% in sea water and 11% in ionized air when compared to impermeable plate for . The aiding buoyancy () plays a dominant role in heat and mass transfers, respectively, with the massive gradients of 340% and 763% in magnitude for the heavier fluid sea water flow while 47% and 3% for the lighter fluid ionized air flow when . The buoyancy parameters (Ri, N) decrease the heat transfer, but increase the mass transfer.

Mixed Convection Boundary Layer Flow over a Solid Sphere in AL203-Ag/Water Hybrid Nanofluid with Viscous Dissipation Effects

The current study aims to investigate how heat transfer and skin friction develop by modifications in the fundamental advantages of fluids in the presence of mixed convection boundary layer flow over on a sphere in hybrid nanofluids. The numerical solutions for the reduced Nusselt number, local skin friction coefficient temperature profile, and velocity profiles are discovered and clearly presented. The Eckert number, the mixed convection parameter λ, and the nanoparticle volume fraction are all investigated and described. It is found that increasing the volume percentage of nanomaterial in nanofluid enhanced the value of the skin friction coefficient. The low density of nano oxides in hybrid nanofluids, such as alumina, also contributes to reduced friction between fluid and body surface. The findings of a computational investigation demonstrate that the use of a hybrid nanofluid, composed of nanometal and nano-oxide in the form of , has the potential to decrease skin friction while maintaining heat transfer characteristics comparable to that of Ag/water nanofluid. The findings in this publication are new and will be useful to boundary layer flow researchers. It can also be applied as a guideline for experimental investigations with the goal of reducing the cost of operation

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.

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.

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.

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.

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<0 and〖 f〗^'→λ as t→+∞ where λ∈{0,1} and β<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<0, the permeable parameter a∈R and the temperature parameter β<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.

Mixed convection flow of Cu-water nanofluid having differently shaped nanoparticles past a moving wedge

Steady boundary layer mixed convection flow over a wedge moving parallel to a free stream in nanofluid having differently shaped nanoparticles is numerically investigated. The aspire of this article is to examine the combined influences of mixed convection, suction/blowing and variable shape of nanoparticles on motion of nanoliquid past a moving wedge moving faster/slower than the free stream. Nanofluid flow past a moving wedge is commendable of extraordinary concentration owing to its escalating applications in industrialized processes and technologies and so, the significance of this study is that the model is pertinent to a variety of manufacturing sectors for submissive control of nanoelements. The overriding equations under boundary layer approximations along with the matching conditions at the boundary are transformed to ordinary differential equations with the help of similarity alterations. Shooting technique is adapted to solve these equations numerically via Runge Kutta method using MATHEMATICA. Outcomes of the present study for a number of meticulous cases are assessed with the existing outcomes in open text and found a very well conventionality. The effects of various crucial parameters on velocity and temperature profiles of the fluid are accessible and analyzed graphically. The velocity of Cu-water nanofluid increases with the enhanced strengths of suction parameter, wedge angle parameter and also with the enhanced values of nanoparticle volume fraction. In comparison to spherical shaped nanoparticles, elevated temperature is experienced for nanoparticles of non-spherical shape. Also, the skin friction coefficient and surface heat transfer rates for some of the parameters are explored numerically. The outcomes of this learning depict numerous inspiring features that merit supplementary learning of the problem.

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.

Thermal and solutal energy transport analysis in entropy generation of hybrid nanofluid flow over a vertically rotating cylinder

An investigation of an axisymmetric mixed convective boundary layer flow of silver-titanium dioxide/water (Ag−TiO2/H2O) hybrid nanofluid towards vertically and rotating stretching cylinder with entropy generation is conducted. The Cattaneo-Christov theory and joule heating effect are used to analyze the features of thermal energy. Moreover, the magnetic impact and convective boundary conditions on the vertical surface also considered in the current investigation. The developing equations for momentum, energy and entropy generation are modelled and by the usage of similarity variables to transform into the system of nonlinear ordinary differential equations (ODEs). The solutions of nonlinear ODEs are obtained numerically with the assistance of BVP4C MATLAB built-in scheme. The graphical consequences and relevant physical reasoning regarding the velocity, temperature, and concentration profiles are discussed. It is noteworthy that strong estimation of buoyancy ratio and mixed convection parameter enhances axial velocity, but the swirl velocity is diminished. The fluid temperature and concentration both are diminished due to thermal and solutal stratification effects. It is also seen that thermal Biot and Eckert numbers enhance the temperature distribution. Further, the Reynold number improves entropy generation.