Marangoni Boundary Layer Research Articles

Significance of heat generation and thermophoretic particle deposition in Marangoni convective driven boundary layer flow of cross nanofluid with activation energy

The thermo-solutal Marangoni boundary layer flow has been studied because it has a number of real-world uses, such as drying silicon wafers, applying thin coats of paint or glue, employing adhesive in heat exchangers, and growing crystals in space. The physical phenomenon of Cross (FeSO4−(CMC−H2O(<0.4%)) nanofluid flow in a porous medium with thermophoretic particle deposition and Marangoni convective flow is explored. Non-Newtonian Cross nanofluid flow is explored in relation to the effect of activation energy. The process of thermophoretic particle deposition, which is important in both electrical engineering and aero-solution, is one of the most fundamental methods for transferring small particles across a heat gradient. Cross nanofluid containing FeSO4 as nanoparticle, and based fluid is (CMC- water). Using the appropriate similarity variables, the set of governing PDEs is transmuted into a set of ODEs. The RKF-45th method is used to numerically solve these simplified equations. The graphic examination of the concentration, velocity and thermal fields is developed for the embedded non-dimensional characteristics. By raising the Marangoni ratio parameter, the surface tension gradient gets stronger, causing the induced flows to get stronger through the liquid more effectively. The concentration and thermal profiles fall with an enhancement in Marangoni ratio parameter.

Heat transfer transmission in a Marangoni boundary layer flow along an inclined disk in a porous medium

Effects of thermal radiation and pressure work on Marangoni boundary layer flow and heat transfer over an inclined disk through a porous medium are numerically discussed. The partial differential equations dominant flow phenomenon are switched into ordinary differential equations with the aid of appropriate similarity transformations. The switched ordinary differential equations are solved numerically by Rung-Kutta. The influence of the different parameters on the velocity and temperature of the fluid are discussed and analysed. Nusselt number is computed and investigated for different embedded parameters in the problem statements.

The Effect of MHD on Marangoni Boundary Layer of Hybrid Nanofluid Flow Past a Permeable Stretching Surface

Numerous researchers studied on the properties of hybrid copper-alumina/water nanofluid in order to have better thermal efficiency that could be used in industrial applications. Therefore, the present study accentuates the effect of MHD on Marangoni boundary layer of hybrid copper-alumina/water nanofluid flow over a stretching surface. Furthermore, the governing boundary layer equations which is partial differential equations (PDEs) are transformed into a set of ordinary differential equations (ODEs) using similarity transformations. Then, these problems are solved numerically using shooting method through Maple software. It is shows that the rate of heat transfer decreases with the increase in magnetic parameter. The velocity and temperature profiles, as well as local Nusselt number are observed with the specific parameter namely, magnetic parameter, nanoparticles volume fraction and suction. By increasing the volume fraction for copper and magnetic parameter, the velocity profiles decrease while the temperature profiles increase.

Magnetohydrodynamic Marangoni boundary layer flow of nanoparticles with thermal radiation and heat transfer in a porous sheet

This study is based on heat transfer and a two-dimensional MHD Walters’ liquid B flow containing copper nanoparticles driven by a stretching sheet in a porous medium. Mass transpiration and thermal radiation effects are considered. The set of partial differential equations affected by the Marangoni boundary condition is used. A nonlinear system of equations is solved to obtain the coupled ordinary differential equations using the similarity transformations and Laplace transform technique. An exact solution is obtained for the transformed system. In the analysis, it is noted that the inclusion of smaller copper nanoparticles provides superior thermal conductivity with temperature. The velocity and temperature distributions are analysed for radiation number, Prandtl number, magnetic parameter, viscoelastic parameter and permeability parameter. Results revealed that heat transfer rate was improved by the coupled effect of enhanced conductivity and thermal radiation. Thermal performance judgements by radiation provide design guidance in thermal engineering applications.

Optimized heat transport in Marangoni boundary layer flow of a magneto nanomaterial driven by an exponential interfacial temperature distribution

AbstractIn a small boundary layer of the fluid interface, the temperature distribution deviates from being linear with the spatial coordinate and exhibits an exponential form. Hence, the Marangoni convective flow of a nanoliquid driven by an exponential interfacial temperature distribution is modeled in this study. Due to practical applicability, the working fluid is chosen to be ethylene glycol‐based magnesium oxide nanoliquid, which is modeled using experimentally estimated properties. In the system, the external effects of an inclined magnetism, thermal radiation, and an internal heat source are considered. Heat transport is rigorously analyzed using an empirical model, which is estimated using the robust response surface methodology (RSM) to find the optimal working conditions and to estimate the sensitivity. The modeled problem is simulated numerically using the finite difference‐based scheme and a parametric analysis is conducted to study the effect of magnetic field, inclination of magnetic field, radiation, and internal heat source parameters. The internal heat generation (increase of 0.94%) factor dominates the augmentation in the thermal field but at some distance, the thermal radiation factor has a predominant impact (58.99%). The inclination angle of the magnetic field has a prominent decremental impact on the velocity profile. Also, the radiative heat flux enhances the temperature profile. Optimal working conditions are estimated to be with a magnetic inclination of 10° and using a liquid with 0.25% volume fraction of 100 nm. This study finds applicability in crystal growth, drying silicon wafers, and heat exchangers.

An MHD Marangoni Boundary Layer Flow and Heat Transfer with Mass Transpiration and Radiation: An Analytical Study

This examination is carried out on the two-dimensional magnetohydrodynamic problem for a steady incompressible flow over a porous medium. The Cu−Al2O3 nanoparticles are added to the water base fluid in order to improve thermal efficiency. The transverse magnetic field with strength B0 is applied. The governing equations formed for the defined flow form a system of partial differential equations that are then converted to a system of ordinary differential equations upon applying the suitable similarity transformations. On analytically solving the obtained system, the solutions for velocity profile and temperature distribution are obtained in terms of exponential and Gamma functions, respectively. In addition, the physical parameter of interest, the local Nusselt number, is obtained. The results are analyzed through plotting graphs, and the effect of different parameters is analyzed. Furthermore, we observe that the suction/injection parameter enhances the axial velocity. The porous and radiation parameters enhance the temperature distribution, and the suction/injection parameter suppresses the temperature distribution.

Analysis of Marangoni boundary layer flow and heat transfer with novel constitution relationships

Based on traditional constitutive relationships of Maxwell fluid flow and Cattaneo heat transfer, a modified model of unsteady Marangoni convective boundary layer flow and heat transfer behavior is constructed, which introduces the distributed fractional-order derivative. The governing equations and the corresponding initial and boundary conditions are derived, in which the finite difference method with L1 scheme is used to solve the obtained equations and the solvability is analysed. Afterwards, a pair of source terms are added into the momentum equation and energy equation respectively to facilitate obtaining the exact solution, and the validity of the numerical scheme is verified by comparing with the exact solution. The influences of the physical parameters on the thickness of the velocity and temperature boundary layer and rheological characteristics with the flow and heat transfer mechanism are discussed and analysed in detail.

Heat transfer optimization and sensitivity analysis of Marangoni convection in nanoliquid with nanoparticle interfacial layer and cross-diffusion effects

Heat and mass transfer induced by Marangoni forces occur frequently in crystal growth and heat pipes, especially in microgravity situations. Therefore, the heat and mass transfer optimization in the thermosolutal Marangoni boundary layer flow of a nanomaterial with cross-diffusion effects is carried out in this study. Thermal radiation, magnetic field, and cross-diffusion are also incorporated in the thermal phenomena. The flow fields with nanolayer and without it are compared. The nanoparticle interfacial layer aspect accounted for in the nanofluid model makes the modeling more realistic. The optimization procedure is based on the Response Surface Methodology (RSM) model that utilizes the face-centered Central Composite Design (fc-CCD). The external constraining factors of the system like thermal radiation, magnetic field, and nanoparticle loading are explored for interactive impacts. The sensitivity of the heat and mass transfer is scrutinized. The interfacial layer aspect leads to an enhanced magnitude of the temperature field whereas the effect on the concentration profile is negligible. The inclination of the magnetic field augments the flow profiles significantly. The highest sensitivity of the heat and mass transfer is towards the thermal radiation aspect. The optimized output of heat and transfer rate is estimated to be when R = 1.6639, M = 1, and ϕ = 1 % .

System of Equations for the Marangoni Boundary Layer in Media with Ladyzhenskaya Rheological Law

System of Equations for the Marangoni Boundary Layer in Media with Ladyzhenskaya Rheological Law

Effect of radiation on thermosolutal Marangoni convection in a porous medium with chemical reaction and heat source/sink

Thermosolutal Marangoni boundary layer flows are of great interest due to their applications in industrial applications such as drying of silicon wafers, thin layers of paint, glues, in heat exchangers, and crystal growth in space. The present analysis deals with the effect of chemical radiation and heat absorption/generation of the viscous fluid flow on a thermosolutal Marangoni porous boundary with mass transpiration and heat source/sink. The physical flow problem is mathematically modeled into Navier–Stokes equations. These nonlinear partial differential equations are then mapped into a set of nonlinear ordinary differential equations using similarity transformation. The analytical solutions for velocity, temperature, and concentration profiles are rigorously derived. The solutions so obtained are analyzed through various plots to demonstrate the effect of various physical parameters such as mass transpiration parameter Vc, inverse Darcy number Da−1, Marangoni number Ma, Schmidt number Sc, chemical reaction coefficient (K), Prandtl number (Pr), thermal radiation parameter (NR), and the heat source/sink parameter (I) on the momentum/thermal boundary, and their physical insights are also reported.

Influence of Magnetic Field on Thermal Radiation and Particle Shapes of Copper-Water Nanofluid Considering Marangoni Boundary Layer

This problem aims to address hydrodynamic Marangoni boundary layer flow of incompressible nanofluid along different shapes of particle like sphere, tetrahedron, column and lamina with exponential temperature. Choosing appropriate transformations, the governing equations are reduced to non-linear ordinary differential equations and then solved by using a perturbation technique. Impacts in velocity and temperature profiles for the relevant considering parameters namely nanoparticle volume fraction, magnetic parameter, empirical shape factor and radiation parameter are evaluated and shown through graphs. Moreover, computational values for influences of physical parameters on local surface heat flux are presented in table.

Marangoni Boundary Layer Flow and Heat Transfer of Graphene–Water Nanofluid with Particle Shape Effects

Graphene nanofluids have attracted the attention of many researchers because of a variety of remarkable properties such as extraordinary electronic transport properties, high thermal conductivity, and large specific surface areas. This paper investigates the shape effects of nanoparticles on the Marangoni boundary layer of graphene–water nanofluid flow and heat transfer over a porous medium under the influences of the suction parameter. The graphene–water nanofluid flow was contained with various shapes of nanoparticles, namely sphere, column, platelet, and lamina. The problem is modeled in form of partial differential equations (PDES) with boundary conditions. The governing transport equations are converted into dimensionless form with the help of some suitable nondimensional variables. The solution of the problem was found numerically using the NDSolve technique of Mathematica 10.3 software. In addition, the numerical solutions were also compared with analytical results. The homotopy analysis method (HAM) is used to calculate the analytical results. The results show that lamina-shaped nanoparticles have better performance on temperature distribution while sphere-shaped nanoparticles are more efficient for heat transfer than other shapes of nanoparticles.

Simulation and modeling of entropy optimized MHD flow of second grade fluid with dissipation effect

Here entropy optimized magnetohydrodynamic flow of second-grade fluid is addressed. The energy equation is developed through Joule heating and dissipation effects. Mass transportation along with an interface between two liquids due to surface tension gradient is called Gibbs–Marangoni effect (Marangoni effect). On the other hand, if there is thermal dependence case, then the phenomenon is called Bénard–Marangoni convection (thermo-capillary convection). Marangoni convection depends upon the difference of surface pressure computed by the gradient of temperature, magnetic effect, and concentration gradients. The basic concept of mass and heat transportation phenomenon in Marangoni boundary layer flow are comprehensively discussed. The physical feature of irreversibility exploration is developed with the help of thermodynamics second law. Here we discussed both first and second laws of thermodynamics. Nonlinear ODE's are obtained through adequate variables. Optimal homotopy analysis method (OHAM) is employed to construct the convergent solutions. Entropy optimization, temperature, Bejan number, concentration, and velocity variations for various secondary parameters are deliberated. Velocity enhances via the Marangoni ratio parameter. For larger Hartmann number the temperature and velocity have a reverse effect. The velocity field is amplifying against second grade fluid variable. A similar effect is noticed versus a larger fluid parameter and Eckert number. For a higher approximation of the Marangoni ratio variable, the concentration reduces. Larger fluid parameter rises the entropy generation rate.

Marangoni flow and mass transfer of power-law non-Newtonian fluids over a disk with suction and injection

We scrutinize the approximate analytical solutions by the optimal homotopy analysis method (OHAM) for the flow and mass transfer within the Marangoni boundary layer of power-law fluids over a disk with suction and injection in the present paper. Concentration distribution on the surface of a disk varies in a power-law form. The non-Newtonian fluid flow is due to the surface concentration gradient without considering gravity and buoyancy. According to the conservation of mass, momentum and concentration, the governing partial differential equations are established, and the appropriate generalized Kármán transformation is found to reduce them to the nonlinear ordinary differential equations. OHAM is used to access the approximate analytical solution. The influences of Marangoni the number, suction/injection parameters and power-law exponent on the flow and mass transfer are examined.

MHD Marangoni boundary layer problem for hybrid nanofluids with thermal radiation

PurposeThe purpose of this paper is to study flow of the Marangoni boundary layer pasta surface embedded in a porous medium saturated by a hybrid nanofluid in the presence of a magnetic field and thermal radiation.Design/methodology/approachThe governing model was converted into ordinary differential equations applying proper similarity transformations. Therefore, Laplace transform was used to exactly solve the resulted equations. Hence, the influence of the velocity profile and temperature distribution was investigated under impacts of the involved parameters.FindingsIn the case of regular fluid, i.e. the solid volume fractions are zeros, the current results are in a very good agreement with those in the literature. It was found that the velocity decreases (increases) on increasing the parameters of copper-nanoparticles volume fraction, magnetic field and suction (permeability and injection). Further, the temperature increases (decreases) with an increase of the copper-nanoparticles volume fraction, magnetic field, injection and radiation (permeability and suction).Originality/valueThe current results of the Marangoni boundary layer problem for hybrid nanofluids are new, original and extend the previous problems investigated by many authors for the case of regular/nano fluids.

Marangoni Driven Boundary Layer Flow of Carbon Nanotubes Toward a Riga Plate

The objective of this article is to explore the radiative marangoni boundary layer flow on the existence of carbon nanotubes through a surface embedded is an electromagnetic actuator defined as a riga plate. To judge the performance of Lorentz forces on the bases of nanoparticles temperature fluxes, two different types of carbon nanotubes, namely single wall carbon nanotube and multi wall carbon nanotubes saturated into water used as base fluid. With the introduction of some viable dimensionless variables into the system of nonlinear partial differential equations, the resulting nonlinear designed flow of marangoni boundary layer flow over riga plate is developed. The proposed schemes of governing equations are then converted into ordinary differential equations by similarity transformation. To sort out characteristics of thermal radiation and effect of Hartmann number through marangoni boundary layer flow of nanofluid, some suitable boundary conditions are utilized. The solution of indicated governing equations and for the convergence of control parameters, one of best analytical method is utilized. The velocity and temperature profiles of various parameters are deliberated in detail for numerical significance. Numerical survey of embedded parameters is then depicted on graphs and tables. Finally, some accomplished comments are also our part of consultation.

The effects of radiation on heat and mass transfer of magnetohydrodynamic Marangoni flow in the boundary layer over a disk

This study investigated the problem of radiation effects on the flow heat and mass transfer of magnetohydrodynamic steady laminar Marangoni convection in the boundary layer over a disk in the presence of a linear heat source and first-order chemical reactions. The governing partial differential equations of the disk model were established and transformed to a series of ordinary differential equations via suitable self-similar transformations, which were solved numerically by the shooting technique coupled with Runge-Kutta scheme and Newton’s method. The Marangoni number related to temperature and concentration was derived, the effects of the magnetic Hartmann number, Marangoni number, radiation number, heat source number and chemical reaction number related to velocity, temperature, and concentration profiles were analyzed. The results demonstrate that the Hartmann number and Marangoni number have significant impacts on the heat and mass transfer of the Marangoni boundary layer flow. The temperature tends to increase with heat generation and decrease with heat absorption, and it exhibits a delay phenomenon for significant heat generation cases. Negative/positive chemical reactions tended to increase/decrease the concentration, similar to the effect of heat generation/absorption on the temperature.

Radiation Effects on Marangoni Boundary Layer Flow in Micropolar Fluid with Suction/Injection

The influence of radiation on the Marangoni boundary layer flow in micropolar fluid with suction/injection is studied in this study. It is the extension of the previous study by Saleh et al. where the interface temperature is assumed to be a quadratic function of the distance x along the interface. A set of nonlinear ordinary differential equations are obtained by using the technique of similarity transformations, transformed from the general governing partial differential equations and solved numerically by using the shooting method. The solutions of each profiles is presented in the form of tables and figures along with the results of the velocity, microrotation gradient and heat transfer at the surface. The problem is considered for two different values of n which is n = 0 and n = 0.5 where it is represented the strong and the weak concentration, respectively with different values of radiation parameter along with the suction/injection parameter.

Emergence of Fluid Rotation in the Marangoni Boundary Layer in the Region of Local Cooling of the Free Boundary

Rotation bifurcation in a steady axisymmetric thermocapillary flow of an incompressible fluid filling a semi-infinite space bounded by the free surface with a nonuniform distribution of temperature is studied. The fluid flow is calculated on the basis of Navier–Stokes equations under the assumption of small diffusion coefficients. It is shown that the bifurcation triggers rotational motion in a thin Marangoni boundary layer in the case of local cooling of the free boundary near the axis of symmetry and in the presence of an external flow; there is no rotation outside this layer. In the case of local heating of the free boundary, rotation is not observed.

Magneto-Marangoni nano-boundary layer flow of water and ethylene glycol based γ Al2O3 nanofluids with non-linear thermal radiation effects

For the first time, a numerical investigation is performed to study the influences of magnetic field on Marangoni boundary layer flow of water and ethylene glycol based γ Al2O3 nanofluids over a flat surface in the presence of non-linear thermal radiation. Experimental based thermo-physical properties and an effective Prandtl number model for γ Al2O3 nanofluids are considered to analyse the Marangoni convection. To study the magnetic field effects, the electric conductivities of both nanoparticles and base fluids are taking into account. Numerical solutions of resulted equations are obtained using fourth order Runge-Kutta method with shooting technique. The combined effect of magnetic parameter with other involved parameters is discussed on velocity and temperature distributions and the local Nusselt number via graphical illustrations.