Problem Of Boundary Layer Flow Research Articles

Incompressible boundary layer flow past a hump with temperature-dependent viscosity

The problem of boundary layer flow past a hump placed on a flat surface, where viscosity is coupled with temperature, is investigated using triple-deck theory. The incompressible Navier–Stokes equations supplemented by the heat and viscosity equations are considered in the limit that the Reynolds number is large. The triple-deck scalings are adopted, and asymptotic expansions are used to obtain some novel triple-deck equations coupled with the thermal boundary layer. We have used the same viscosity–temperature dependence as in Jasmine and Gajjar [Int. J. Heat Mass Transfer 48, 1022–1037 (2005)], in which viscosity varies inversely proportional to the temperature. The linear analysis is performed, and the nonlinear equations are solved numerically. Our results show that increasing the characteristic constant of the viscosity leads to enhanced peaks and troughs in the pressure and in the skin friction over the hump, as compared to the constant viscosity case. This suggests that temperature-dependent viscosity is more likely to provoke separation.

Influence of activation energy and variable thermal conductivity on magneto-convective nonlinear thermo-radiative Casson nanofluid containing motile microorganisms over a sinusoidal surface

The activation energy of convective-radiative nanoliquids with sinusoidal walls has garnered significant academic interest in recent years. This focus arises due to the pivotal applications of nanoparticles in thermal engineering, industrial processes, and medical sciences. This article investigates the magnetohydrodynamic heat transfer characteristics of Casson nanofluids containing microorganisms influenced by an oscillatory surface. The study incorporates temperature-dependent viscosity and utilizes Buongiorno’s mathematical model to account for nonlinear thermal radiation, Brownian motion, and thermophoretic effects from using nanomaterials in Casson fluids. These effects enhance thermal conductivity, improving the heat transportation phenomenon while considering gyrotactic microorganism density distributions. The boundary layer flow problem is formulated using partial differential equations and associated boundary conditions, subsequently numerically simulated using the bvp4c function. The investigation explores the thermal behavior of nanoparticles in the presence of bioconvection phenomena, Lorentz force, chemical reactions, and activation energy. As a result, this model addresses variable thermal conductivity and bioconvection aspects in Casson nanofluids over a sinusoidal surface. Numerically computed results for the Nusselt number, motile density, and Sherwood number provide insights into several essential features. The findings reveal that an increase in the Casson fluid parameter correlates with a decreased velocity profile. The assumptions of variable thermal conductivity and temperature-dependent viscosity prove more effective in raising the temperature of nanoparticles. The nanoparticle concentration profile rises noticeably for smaller Schmidt number Sc values when the activation energy parameter is higher than larger Sc values. Additionally, the presence of microorganisms in Casson nanofluids leads to increased temperatures due to an elevation in the bioconvection Rayleigh number. Moreover, heightened oscillating frequency parameters decrease nanoparticle concentration and microorganism density. Including activation energy and oscillating frequency parameters further enhances the understanding of nanoparticle concentration and microorganism density dynamics, offering valuable contributions to theoretical research and practical applications across multiple interdisciplinary fields.

Numerical Study of the Boundary Layer Flow Problem over a Flat Plate by Finite Difference Method

Numerical Study of the Boundary Layer Flow Problem over a Flat Plate by Finite Difference Method

Magnetohydrodynamic Effects on the Flow of Nanofluids Across a Convectively Heated Inclined Plate Through a Porous Medium with a Convective Boundary Layer

The study explores the problem of Magnetohydrodynamic natural convection boundary layer flow of a nanofluid past a convectively heated inclined porous channel. The governing partial differential equations have been transformed through appropriate similarity functions into nonlinear ordinary differential equations. The emerging equations were solved numerically using both a sixth-order Runge-Kutta-Fehlberg and the shooting technique. The influences of pertinent parameters such as plate inclination angle, magnetic field, buoyancy ratio, and the convective heating term on the temperature, velocity, and concentration profiles were investigated graphically. Key findings indicate that an increase in magnetic field and permeability leads to a decline in the fluid’s velocity while the temperature and nanoparticle concentration are significantly enhanced. The results obtained are in close correlation with existing body of knowledge discussed in the literature.

Numerical simulation of the laminar boundary layer flow over a flat plate

Understanding the dynamic and thermal characteristics of the boundary layer (BL) flows is an essential step toward the best design and operational conditions for many engineering devices. Flow characteristics within the boundary layer are governed by two forces that are in a mutual race to dominate the flow, the viscous and inertial forces. The state of the flow is determined by the relative domination of these two forces inside the boundary layer zone. Theoretical solutions for many BL flow types existed since the beginning of the 20th century. Theoretical solutions are strictly possible for simple boundary layer flow configurations within the laminar range and before flow separation occurs. For practical situations where boundary layer flow problems are prescribed with complex flow configurations, CFD techniques represent the most suitable approach to tackle such types of flows. In this study, the laminar boundary layer flow over a flat plate has been solved numerically leading to a detailed analysis of the boundary layer flow with accuracy comparable to that of the theoretical solution

MHD Boundary Layer Flow due to an Exponentially Stretching Surface Through Porous Medium with Radiation Effect and Chemical Reaction

In this study, the numerical solutions for an exponentially stretching sheet with radiation effects, chemical reaction and a heat sink is obtained for the problem of MHD boundary layer flow. By using similarity transformation, the PDEs ruling system is converted into an ODEs system. The resulting nonlinear equations governing the flow problem are numerically solved by a successive linearization method (SLM) using MATLAB software. The significance of this paper is to show and compare the results of solving velocity, temperature, and concentration equations in the existence of changes through SLM for presenting it as appropriate and accurate method for solving nonlinear differential equations. Tables with the numerical data are created for comparison and displayed graphically. Analysis and studies of the effects of different parameters are conducted. The numerical values for the local skin friction coefficient, local Sherwood number, and local Nusselt number are tabulated and explained. The study demonstrates that different parameters have a substantial impact on the fluid flow profiles. It was noted that the concentration patterns were impacted by the reaction rate parameter. In addition, it was found that as the magnetic and radiation parameters increase in value, the local heat transfer rate at the surface decreases.

Physics-informed deep learning for melting heat transfer analysis with model-based transfer learning

We present an adaptive deep collocation method (DCM) based on physics-informed deep learning for the melting heat transfer analysis of a non-Newtonian (Sisko) fluid over a moving surface with nonlinear thermal radiation. Fitted neural network search (NAS) and model based transfer learning (TL) are developed to improve model computational efficiency and accuracy. The governing equations for this boundary-layer flow problem are derived using Buongiorno's and a nonlinear thermal radiation model. Next, similarity transformations are introduced to reduce the governing equations into coupled nonlinear ordinary differential equations (ODEs) subjected to asymptotic infinity boundary conditions. By incorporating physics constraints into the neural networks, we employ the proposed deep learning model to solve the coupled ODEs. The imposition of infinity boundary conditions is carried out by adding an inequality constraint to the loss function, with infinity added to the hyper-parameters of the neural network, which is updated dynamically in the optimization process. The effects of various dimensionless parameters on three profiles (velocity, temperature, concentration) are investigated. Finally, we demonstrate the performance and accuracy of the adaptive DCM with transfer learning through several numerical examples, which can be the promising surrogate model to solve boundary layer problems.

Theoretical and numerical study of a fluid flow of a slightly rarefied gas-free stream past a moving wall inside a porous medium

This study investigates the boundary layer flow problem arising in the viscous fluid flow of a slightly rarefied gas-free stream over a moving plate embedded in a porous medium. Previous works were mainly focused on numerically, and some properties of the solutions were discussed from numerical results. But, numerical solutions are only sometimes guaranteed the solution’s existence. In this work, we have adopted the famous topological shooting argument to prove the existence result of the solution. We have shown that the solution may be convex or concave depending on the parameter values. Also, for these reasons, there arise some difficulties. However, we have rectified all the challenges and proved that unique solutions exist for all the particular governing parameter values. Nevertheless, we found an exact solution for some specific parameter values. Furthermore, the Haar wavelet collocation method is used to address the numerical results of the nonlinear boundary value problem. We first validate the obtained results with the existing numerical outcomes. The impacts of permeability and slip parameters on the velocity profiles and shear stress are elucidated through tables and figures, and probable arguments are explained in detail.

Falkner-Skan Boundary Layer Flow Over a Static Wedge

The objective of the present study is to analyse the problem of Falkner-Skan boundary layer flow past a wedge considering velocity slip condition. The governing partial differential equations for physical system are converted into an ordinary differential equation using similarity transformations. The resulting equation is then solved by differential transform method(DTM) empowered by Pade approximations. The velocity profiles are shown and the influence of slip parameter on the flow is discussed. The validity of our solutions is verified by published results.

Nonsimilar analysis of magnetized Sisko nanofluid flow subjected to heat generation/absorption and viscous dissipation

This research explores the nonsimilar magnetohydrodynamic (MHD) boundary-layer (BL) Sisko nanofluid flow over a vertically placed sheet under the impacts of heat generation/absorption and viscous dissipation. The flow is propagated under vertical stretching of the sheet and utilizing natural forces. Flow problem is formulated by employing governing relations and equations are transformed into dimensionless form through the nonsimilar methodology. This dimensionless partial differential system is simulated computationally by using the analytical local nonsimilarity method (LNM) via numerical finite difference based built-in Matlab algorithm bvp4c. Impacts of the effective dimensionless emerging parameters on convective transport analysis are examined. Furthermore, the correlations of drag coefficient, local Nusselt, and Sherwood numbers for significant parameters have been developed. It is noted that the material parameter augments the nanofluid velocity, temperature, and concentration field. The higher the magnetic field drops the fluid velocity however the thermal and concentration profiles increase. The greater estimations of the thermophoresis parameter have a rising impact on the concentration profile, while the higher Lewis number and Prandtl number have an inverse response against the concentration profile. Most of the real-world boundary layer flow problems are nonsimilar, which is an innovative point of this article. So, here we discussed the nonsimilar analysis for the considered problem. According to the author's observations, the declaration of non-similar analysis for the problem under consideration hasn't yet been analyzed in published literature.

Mathematical modelling of boundary layer flow over a permeable and time-dependent shrinking sheet – A stability analysis

Micropolar fluid is one type of non-Newtonian fluid which consists of non-deformable spherical particles that suspended in viscous medium. In this paper, the problem of two-dimensional boundary layer flow over a permeable shrinking sheet with time dependent velocity in strong concentration micropolar fluid is studied theoretically. The mathematical model is governed by continuity, momentum and microrotation equations. Similarity variables are introduced so that, after performing the similarity transformation on the governing equations, the resulting system of nonlinear ordinary differential equations is then numerically solved using the program bvp4c in Matlab software. The effects of the micropolar material parameter, the unsteadiness parameter, the shrinking parameter and the mass suction parameter to the skin friction coefficient, velocity profiles and microrotation profiles are investigated. It is found that triple solutions exist for some values of the parameters that were considered. Based on the stability analysis that was performed, it showed that only two branches of solutions are categorized as stable, whereas one solution branch is unstable.

A Chebyshev Spectral Collocation Method-Based Series Approach for Boundary Layer Flow and Heat Transfer in a Micropolar Fluid past a Permeable Flat Plate

This paper demonstrates the applicability of the large parameter spectral perturbation method (LSPM) to a coupled system of partial differential equations that cannot be solved exactly. The LSPM is a numerical method that employs the Chebyshev spectral collocation method in the solution of a sequence of ordinary differential equations (ODEs) that are derived from decomposing coupled systems of nonlinear partial differential equations (PDEs) using series expansion about a large parameter. The validity of the LSPM is applied to the problem of boundary layer flow and heat transfer in a micropolar fluid past a permeable flat plate in the presence of heat generation and thermal radiation. The coupled nature of the PDEs that define the problem under investigation precludes the option of using series-based methods that seek to generate analytical solutions even in the presence of small or large parameters. The present study demonstrates that the LSPM can easily overcome this limitation while giving very accurate results in a computationally efficient manner. For qualitative validation of the results and the numerical method used, calculations were carried out to graphically obtain the velocity, microrotation, and temperature profiles for selected physical parameter values. The results obtained were found to correlate with the results from a published literature. For quantitative confirmation of our findings, the LSPM numerical solutions were again validated against known results from the literature and against results obtained using the multidomain bivariate spectral quasilinearisation method (MD-BSQLM), and the results were observed to be in perfect agreement. Further accuracy validation is displayed by using residual error and solution error analysis on the governing PDEs and their underlying solutions. This study’s findings indicate that the heat generation and thermal radiation parameters have related effects on the temperature profile, enhancing both the fluid temperature and the thermal boundary layer thickness.

Mutual Interdependence of the Physical Parameters Governing the Boundary-Layer Flow of Non-Newtonian Fluids

We consider non-Newtonian boundary-layer fluid flow, governed by a power-law Ostwald-de Waele rheology. Boundary-layer flows of non-Newtonian fluids have far-reaching applications, and are very frequently encountered in physical, as well as, engineering and industrial processes. A similarity transformation results in a BVP consisting of an ODE and some boundary conditions. Our aim is to derive highly accurate analytical relationships between the physical and mathematical parameters associated with the BVP and boundary-layer flow problem. Mathematical analyses are employed, where the results are verified at the numerical computational level, illustrating the accuracy of the derived relations. A set of “Crocco variables” is used to transform the problem, and, where appropriate, techniques are used to deal with the resulting singularities in order to establish an efficient computational setting. The resulting computational setting provides an alternative, which is different from those previously used in the literature. We employ it to carry out our numerical computations.

Effect of viscous dissipation and thermal radiation on MHD flow and heat transfer for a power-law fluid with variable fluid properties over a permeable stretching sheet

This manuscript considers the problem of MHD boundary layer flow and heat transfer of power – law fluid with variable fluid properties over a nonlinear stretching sheet in the presence of viscous dissipation and thermal radiation subject to a non-uniform transverse magnetic field and non-uniform heat generation. The governing boundary layer equations are transformed into a system of non-linear ordinary differential equations using suitable transformation which are solved numerically using fourth order Rung-Kutta integration scheme coupled with the shooting method. The effects of various parameters on the velocity, temperature, local skin-friction and the local Nusselt number are presented and discussed. We found that is as the radiation parameter R increases the temperature of a power-law fluid and the Nusselt number increase, while the viscosity parameter increasing leads to decreasing on the velocity of the fluid and local skin-friction.

Bödewadt Flow and Heat Transfer in Nanofluid over a Permeable and Radially Stretching Disk

A Bödewadt boundary layer flow and heat transfer problem in nanofluid was investigated in this study for suction/injection as well as combined effects of suction/injection and radial stretching disk. Similarity variables were introduced to transform the three-dimensional flow into a system of ordinary differential equations. Moreover, similar to the Bödewadt heat transfer problem in a viscous fluid, adequate suction is also required so that similarity solutions exist for nanofluid problems with no other boundary effects such as a partial slip or stretching disk. Both the suction and stretching disk effects can suppress the natural oscillatory behavior of flow apart from reducing the momentum and thermal boundary layer thicknesses. As expected, injection acts oppositely. However, the skin friction coefficient and heat transfer rate for Bödewadt flow increase with the increasing suction and stretching parameters. As for stagnant disk, increasing the nanoparticle volume fraction can enhance the wall shear stress, whereas nanofluid can only enhance the heat transfer when both the suction and nanoparticle volume fraction are sufficiently small. For radially stretching disk, both the local skin friction coefficient and local Nusselt number increase as the nanoparticle volume fraction increases. However, for larger suction, a smaller volume fraction of nanoparticles yielded enhanced heat transfer than the larger volume fraction of nanoparticles.

Unsteady Three-Dimensional Flow in a Rotating Hybrid Nanofluid over a Stretching Sheet

The problem of an unsteady 3D boundary layer flow induced by a stretching sheet in a rotating hybrid nanofluid is studied. A dimensionless set of variables is employed to transform the system of partial differential equations (PDEs) to a set of nonlinear ordinary differential equations (ODEs). Then, the system of ODEs is solved numerically using the MATLAB software. The impacts of different parameters, such as copper nanoparticles volume fraction, radiation, rotation, unsteadiness, and stretching parameters are graphically displayed. It is found that two solutions exist for the flow induced by the stretching sheet. Furthermore, the increasing nanoparticle volume fraction enhances the skin friction coefficient. It is noticed that the skin friction coefficient, as well as the heat transfer rate at the surface, decrease as the rotating parameter increases. Additionally, the thermal radiation as well as the unsteadiness parameter stimulate the temperature.

Heat Transfer Analysis over the Boundary Layer Stagnation-Point Flow of Couple Stress Fluid over an Exponentially Stretching Sheet

The present study provides a comprehensive discussion for the problem of boundary layer flow and heat transfer analysis of stagnation point flow of couple stress fluid over an exponentially stretching surface. The governing equations of couple stress fluid model are assumed under boundary layer approach. The nonlinear partial differential equations are simplified by using similar similarity transformations. The analytical solutions of abridged equations are computed with the help of homotopy analysis method (HAM). The convergence of the HAM solutions have been deliberated by plotting <i>ћ </i>- curves and also through homotopy pade approximation. The physical features of pertinent parameters have been discussed through graphs.

Duality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle

Recently, the topic of convection of heat transfer has created an interest among researchers because of its numerous applications in the daily life. The objective of this paper was to study theoretically the problem of mixed convection boundary layer flow and heat transfer of single-wall carbon nanotube (SWCNT) and multi-wall carbon nanotube (MWCNT) in presence of hydromagnetic effects. The problem was initiated by formulating a mathematical model in partial differential equation (PDE) for the hybrid nanofluid flow with appropriate boundary conditions. The similarity equation was used to transform the PDE into an ordinary differential equation (ODE) and solved using bvp4c in MATLAB. The graphical results on variation of skin friction coefficient, Cf, local Nusselt number, Nux, shear stress, f″c and local heat flux, −θ′c with the effects of magnetic, M, size of needle, c, mixed convection parameter, λ and volume fraction of nanoparticles, φ were presented and discussed in detail. The study revealed that duality of solutions appears when the buoyance force is in opposing flow of the fluid motion, λ&lt;0. The presence of M in hybrid nanofluid reduced the skin friction coefficient and heat transfer. On the other hand, the Cf and Nux increased as different concentrations of φ1 and c were added. It gives an insight into the medical field, especially in treating cancer cells. By means, it reveals that CNTs hybrid nanofluid shows high potential in reaching the site of tumors faster compared with nanofluid. A stability analysis has to be carried out. It is noticed that the first solution was stable and physically realizable.

THIRD-ORDER GENERALIZED DISCONTINUOUS IMPULSIVE PROBLEMS ON THE HALF-LINE

In this paper, we improve the existing results in the literature by presenting weaker sufficient conditions for the solvability of a third-order impulsive problem on the half-line, having generalized impulse effects. More precisely, our nonlinearities do not need to be positive nor sublinear and the monotone assumptions are local ones. Our method makes use of some truncation and perturbed techniques and on the equiconvergence at infinity and the impulsive points. The last section contains an application to a boundary layer flow problem over a stretching sheet with and without heat transfer.

RETRACTED: Aqueous aluminium–copper hybrid nanofluid flow past a sinusoidal cylinder considering three-dimensional magnetic field and slip boundary condition

We analyzed the problem of the steady general three-dimensional magnetohydrodynamics stagnation-point boundary layer flow past an impermeable wavy circular cylinder considering aluminium–copper/water hybrid nanofluid as the working fluid and velocity slip as well as temperature jump boundary conditions. The induced magnetic field effect was also taken into account. The analytical procedure is based on the model that implements the nanoparticles and base fluid masses to formulate the equivalent volume fraction, equivalent density, and equivalent specific heat at constant pressure which is then substituted in the chosen single-phase thermophysical properties. Then, the foregoing relations were used in basic governing PDEs (partial differential equations), according to Tiwari–Das nanofluid scheme. It is worth mentioning that the bvp4c code from MATLAB software that is a famous finite-difference method has been exploited for solving the final similarity ODEs (ordinary differential equations). Results demonstrate that the developed mass-based model can be successfully employed with great confidence to study the flow and heat transfer of hybrid nanofluid in other similar problems. Moreover, it is proved that the nodal stagnation points possess higher values of skin friction coefficients and local Nusselt numbers relative to those for the saddle stagnation points. Besides, enhancing the second nanoparticle's mass leads to increase in all parameters of engineering interest including skin friction coefficients along x and y directions as well as local Nusselt number.