Semi-infinite Flat Plate Research Articles

Significance of Viscous Dissipation on Hydromagnetic Oscillatory Flow Affected by Nanoparticles Through a Boundary Layer Regime

In this article, the implications of viscous dissipation on buoyancy-induced heat and mass transfer of a nanofluid flow along a semi-infinite flat plate in an oscillating system is performed, taking into account the impacts of magnetohydrodynamics (MHD), chemical reaction, porous medium and heat sink. The consequences of various flow parameters on the velocity, temperature, and concentration distribution of the nanofluid, as well as the skin friction coefficient, Nusselt number, and Sherwood number has been solved semi-analytically. The basic governing equations have been determined by employing appropriate transformations techniques which result in high nonlinear coupled differential equations with physical conditions. Different types of nanoparticles are considered, and the salient features of all the embedded parameters on velocities, temperature and concentration fields have been displayed graphically and illustrated. It is concluded from the computational analysis that application of viscous dissipative parameter improves the temperature distributions, which consequently speed up the fluid velocity. This model has practical applications in the fields of biomedicine and resonance imaging. In addition, graphical comparison between Narayana and Venkateswarlu (2016) with the present work demonstrate an excellent relationship, thereby authenticating the precision and accuracy of this present work.

Second-order water wave properties over Roseau’s three-parameter bottom topography

Summary In his book Asymptotic Wave Theory (North-Holland 1976), Roseau develops the only known exact solution for linear wave propagation over a shoal. Remarkably, almost half a century later, the only properties of that solution which appear to have been used to validate more wide-ranging models are the limiting values of wave height in the far field. The primary aim of this work is to remedy this situation by providing a robust computational setting where the solution may be fully evaluated randomly both on the surface and the interior, speedily and to a high degree of accuracy. Such ‘benchmark’ solutions will facilitate a much more rigorous approach to validation of more general alternative approximation models. One such has some of its numerical results here examined and subsequently largely vindicated by the present calculations. Computation of the absolutely convergent solution integrals is supported by cubic spline approximation of an integrand component which satisfies a certain difference equation and the work is extended to cover bottom profiles with overhang including the extreme case where the overhang degenerates to a semi-infinite flat plate. The further development of solutions at second-order reveals details of mean Eulerian current and the attendant Stokes drift enabling mass transport computations; all illustrated through the entire depth with a range of contouring and arrows plots. The force field that drives a second harmonic component is calculated and shows excellent agreement with its equivalent in the more general modal expansion model applied to a non-identical but somewhat similar profile. This further validates the modelling approach and application described in that work.

Heat and mass transfer analysis of Casson-based hybrid nanofluid flow in the presence of an aligned magnetic field: An application toward mechanical engineering

This examination explores the flow of a hybridized nanofluid (HyNf) containing silica and tin oxide nanoparticles mixed with engine oil (EO/SnO2-SiO2). The flowing occurs via a permeable material constrained by a semi-infinite flat plate. The study takes into account various factors such as convective heat and mass transference, chemical reactions, the Dufour effect, the Lorentz force, thermal radiative fluxing, and radiative absorbing. The research involves converting the managing formulas of the flowing model into a dimensionless form and applying the regular perturbation procedure to find solutions for the rate of fluid flow, temperature, and species diffusion. The surface frictional factor, Nusselt quantity, and Sherwood quantity reflect the shearing stress, rates of heat transference, and rates of mass transport at the plate, respectively. An analysis is conducted on the impact of several factors, including the suction variable, magnetic variable, radiation-absorbing factor, Casson parameter, and Dufour number, on the flow and related quantities. This analysis is based on an examination of graphs and tables. The findings suggest that the heat transference rate in the Casson hybridized nanofluid is better than that in the mono nanofluid. It is exposed that the temperature reduces at the plate having improved frequency of oscillation and also fluid velocity declines for improving values of aligned magnetized field [Formula: see text], but it shows the reverse phenomenon with Gr1 and Gc1.

Analytical solution of the steady magnetohydrodynamic (MHD) free convection flow over a semi-infinite flat vertical plate moving in a porous medium with viscous dissipation

Analytical solution of the steady magnetohydrodynamic (MHD) free convection flow over a semi-infinite flat vertical plate moving in a porous medium with viscous dissipation

Chemical Reaction and Dufour Effects on MHD Flow of Cu-TiO2 Nanofluids Past an Unbounded Vertical Porous Moving Plate

The effects of chemical reaction, radiation absorption, diffusion thermo on MHD free convective flow of a nanofluid bounded by porous medium past a semi-infinite flat plate are analyzed. The plate is moved with a constant velocity, temperature and the concentration are assumed to be fluctuating with time harmonically from a constant mean at the plate. The solutions of the governing equations are evaluated by using the perturbation technique. We have considered the nano-fluids namely Cu-water and TiO2-water nanofluids. The effects of governing flow parameters on velocity, temperature and concentration are discussed through graphs. For engineering interest, we evaluated the skin friction, Nusselt number and Sherwood number and computationally discussed.

Finite element simulation of Soret-Dufour and conjugate heating effects on mixed convective heat absorbing hydromagnetic Casson fluid flow with suction/blowing from flat semi-infinite vertical porous plate

The finite element simulations of the Soret-Dufour and angled magnetic field effects on conjugate heat and mass transportation of unsteady heat absorbing hydromagnetic Casson flow across a semi-infinite flat oscillatory plate engrafted in a porous medium with suction/blowing, radiation and chemical reaction is performed. The dimensionless coupled flow guiding nonlinear PDEs of the physical structure is handled numerically by the dynamic Galerkin finite element scheme. The demeanor of the velocity, concentration and the temperature profiles due to the alterations in the regulating flow parameters are examined graphically whereas the wall-friction, mass and heat transfer rates explicated by utilizing the tabular data. The research discovered that radiation; conjugate heat transfer and diffusion thermo effects heighten the temperature and velocity distributions whereas heat absorption has a reverse effect. Likewise, conjugate mass transfer and thermo-diffusion effects intensify the concentration and velocity distributions whereas the chemical reaction display overturns aspect. Increased radiation absorption, inclined magnetic field and porosity parameter stimulate fluid velocity whereas the Casson and magnetic parameters exhibit the converse impact. In the instance of suction, the profiles of concentration, velocity and temperature displayed a downturn nature but for the case of blowing, it was noticed a reversal trend. Further, a comparative analysis between the current findings and existing research works in the literature demonstrates our results are exact and accurate.

Reduction of Flow-Induced Trailing Edge Noise of Semi-Infinite Flat Plate by Structural Resonance

A unique method for the reduction in flow-induced trailing edge noise scattering for a semi-infinite thin plate is proposed by utilizing short flexible panels mounted on the surface of the plate. The proposed configuration differs from conventional cantilevered elastic trailing edges due to the limitations of their structural integrity and applicability. The key idea is to design short panels that vibrate in structural resonance under the fluid loading for absorbing the energy from the flow to sustain their vibration. A time-domain direct aeroacoustic simulation coupled with structural dynamics is carried out at a low Reynolds number of 50,000 to explore the aeroacoustic-structural interactions. The effectiveness of noise reduction of the designed configuration is analyzed by comprehensive aeroacoustic analysis where a significant noise reduction is observed for the plate mounted with three flexible panels without any adverse effects on the plate aerodynamics. The structural analysis shows a systematic vibration pattern for all the panels which clearly indicates the presence of complex fluid-structural interaction under resonance conditions. Design strategy of the proposed configuration along with its limitations are also discussed.

Revisiting the frozen gust assumption through the aeroacoustic scattering of wavepackets by a semi-infinite plate

This paper presents an analytic solution for the aerodynamic noise generated by a traveling wavepacket passing near the edge of a rigid semi-infinite flat plate. The solution is derived in the time domain for a wavepacket of either constant or spatially-varying wavenumber, for which novel closed-form expressions are obtained for the incident and scattered sound fields. The case of a varying wavepacket constitutes a surrogate model for turbulent flow distortions caused by the edge region and its geometry. This modeling approach permits a relaxation of the frozen gust assumption that is commonly used in the analytical prediction of trailing-edge noise, whereby the local vorticity is assumed to be unaffected by the edge. Our results shed light on the role that spatial variations of the vortical field near the trailing edge have on the incident and scattered sound contributions to the acoustic far field. In particular, we find that the wavenumber modification has a significant effect on the incident field but not on the scattered field amplitude. However, the phase difference between the incident and scattered fields depends strongly on the spatial variation in the wavepacket wavenumber, which leads to a variation in the sound level and directivity of the total pressure field.

Insight into free convection of an unsteady flow of kerosene conveying copper nanoparticles subject to thermal radiation

The present article deals with the analysis of the enhanced heat transport phenomenon due to the interaction between radiative heat and heat absorption in the time-dependent flow of nanofluid past a semi-infinite flat plate embedding within a permeable medium. The inclusion of a magnetic field also strengthens the profiles. Because of today’s need in several industries and biological fluids such as radiotherapy, peristaltic flow of blood pumping, drug delivery system, etc. the application of nanofluid is vital. Therefore, the implementation of thermal radiation and heat absorption plays an important role. The transformation of the dimensional governing equations needs various non-dimensional quantities and variables and the perturbation technique is deployed with the suitable choice of perturbation parameter. These transformed equations are handled analytically and the variation of the characterising parameters is illustrated graphically for the different values setting their range as cited in the literature. Furthermore, the important outcomes are thinning in the velocity bounding surface thickness is obtained for the augmentation in the resistive force of magnetic field within a permeable medium; , nanoparticle concentration and the magnetic parameter enhance the shear rate coefficient.

Linear stability analysis of hypersonic boundary layers computed by a kinetic approach: a semi-infinite flat plate at $$\varvec{4.5\le \mathrm{M}_\infty \le 9}$$

Linear stability analysis is performed using a combination of two-dimensional Direct Simulation Monte Carlo (DSMC) method for the computation of the basic state and solution of the pertinent eigenvalue problem, as applied to the canonical boundary layer on a semi-infinite flat plate. Three different gases are monitored, namely nitrogen, argon and air, the latter as a mixture of 79\% Nitrogen and 21\% Oxygen at a range of free-stream Mach numbers corresponding to flight at an altitude of 55km. A neural network has been utilised to predict and smooth the raw DSMC data; the steady laminar profiles obtained are in very good agreement with those computed by (self-similar) boundary layer theory, under isothermal or adiabatic wall conditions, subject to the appropriate slip corrections computed in the DSMC method. The leading eigenmode results pertaining to the unsmoothed DSMC profiles are compared against those of the classic boundary layer theory. Small quantitative, but no significant qualitative differences between the results of the two classes of steady base flows have been found at all parameters examined. The frequencies of the leading eigenmodes at all conditions examined are practically identical, while perturbations corresponding to the DSMC profiles are found to be systematically more damped than their counterparts arising in the boundary layer at the conditions examined, when the correct velocity slip and temperature jump boundary conditions are imposed in the base flow profiles; by contrast, when the classic no-slip boundary conditions are used, less damped/more unstable profiles are obtained, which would lead the flow to earlier transition. On the other hand, the DSMC profiles smoothed by the neural network are marginally more stable than their unsmoothed counterparts.

Numerical investigation of mixed convection boundary layer flow for nanofluids under quasilinearization technique

The study of boundary layer flow under mixed convection has been investigated numerically for various nanofluids over a semi-infinite flat plate which has been placed vertically upward for both buoyancy-induced assisting and buoyancy-induced opposing flow cases. To facilitate numerical calculations, a suitable transformation has been made for the governing partial differential equations (PDEs). Then, similarity method has been applied locally to approximate the nonlinear PDEs into a coupled nonlinear ordinary differential equations (ODEs). Then, quasilinearization method has been taken for linearizing the nonlinear terms which are present in the governing equations. Thereafter, implicit trapezoidal rule has been taken for integration numerically along with principle of superposition. The effect of physical parameters which are involved in the study are analyzed on the flow and heat transfer characteristics. This study reveals the presence of dual solutions in case of opposing flow. Further, this study shows that with increasing phi and Pr, the range of existence of dual solutions becomes wider. Also, it has been noted that nanofluids enhance the process of heat transfer for buoyancy assisting flow and it delays the separation point in case of opposing flow.

Unsteady MHD free convection flow past a vertical permeable flat plate in a rotating frame of reference with constant heat source and variable thermal boundary condition in a nanofluid

Abstract The problem of unsteady magnetohydrodynamics (MHD) free convection flow of nano-fluid past an oscillation moving vertical semi-infinite permeable flat plate with constant heat source and vertical variable thermal boundary condition in a rotating frame of reference is studied theoretically. The boundary layer has the oscillatory type of solution because slip velocity is assumed to oscillate in time with constant frequency. The governing equations are solved using small perturbation approximation. For this investigation, we use two types of nano-particles in base fluid, namely Cu (copper) and Al2O3 (aluminium oxide). The effect of various types of suspended metallic nano-particles and non-dimensional physical parameters on the fluid flow and heat transfer rate are presented and discussed through the graphs.

Spectral relaxation computation of electroconductive nanofluid convection flow from a moving surface with radiative flux and magnetic induction

Abstract A theoretical model is developed for steady magnetohydrodynamic viscous flow resulting from a moving semi-infinite flat plate in an electrically conducting nanofluid. Thermal radiation and magnetic induction effects are included in addition to thermal convective boundary conditions. Buongiorno’s two-component nanoscale model is deployed, which features Brownian motion and thermophoresis effects. The governing nonlinear boundary layer equations are converted to nonlinear ordinary differential equations by using suitable similarity transformations. The transformed system of differential equations is solved numerically, employing the spectral relaxation method (SRM) via the MATLAB R2018a software. SRM is a simple iteration scheme that does not require any evaluation of derivatives, perturbation, and linearization for solving a nonlinear system of equations. Effects of embedded parameters such as sheet velocity parameter$\lambda$, magnetic field parameter$\beta$, Prandtl number$Pr$, magnetic Prandtl number$Prm$, thermal radiation parameter$Rd$, Lewis number$Le$, Brownian motion parameter$Nb$, and thermophoresis parameter$Nt$ on velocity, induced magnetic field, temperature, and nanoparticle concentration profiles are investigated. The skin-friction results, local Nusselt number, and Sherwood number are also discussed for various values of governing physical parameters. To show the convergence rate against iteration, residual error analysis has also been performed. The flow is strongly decelerated, and magnetic induction is suppressed with greater magnetic body force parameter, whereas temperature is elevated due to extra work expended as heat in dragging the magnetic nanofluid. Temperatures are also boosted with increment in nanoscale thermophoresis parameter and radiative parameter, whereas they are reduced with higher wall velocity, Brownian motion, and Prandtl numbers. Both hydrodynamic and magnetic boundary layer thicknesses are reduced with greater reciprocal values of the magnetic Prandtl number Prm. Nanoparticle (concentration) boundary layer thickness is boosted with higher values of thermophoresis and Prandtl number, whereas it is diminished with increasing wall velocity, nanoscale Brownian motion parameter, radiative parameter, and Lewis number. The simulations are relevant to electroconductive nanomaterial processing.

Application of Gyarmati’s principle to study active boundary layer control of ionic fluid past a Riga plate

Similarity solutions of laminar electromagnetohydrodynamic boundary layer flows in forced convection are investigated aiming at the evaluation of irreversible momentum, heat and mass transport balance equations by a variational principle. The transportation fields inside the boundary layer are approximated as trial polynomial functions, and the functionals of variational principle are formulated. The Euler–Lagrange equations of variational principle are constructed as algebraic equations in terms of momentum, thermal and concentration boundary layer thicknesses. Electrically conductive fluid flow over a semi-infinite flat plate controlled by electromagnetic force (Z) is considered. The effects of viscous dissipation (Ec), thermophoretic particle deposition (Nt) and thermal diffusion (Sr) in the presence of heat source/sink (Q) on skin friction, heat and mass transfer rates have been examined in this work. To demonstrate the efficiency of the present technique, some specific obtained results are compared with the known numerical results in literature and the accuracy is ensured. Further, the regression analysis is performed to state the dependency of these parameters on heat and mass transfer rates.

Analysis of Forced Convection Boundary Layer Flow and Heat Transfer Past a Semi-Infinite Static and Moving Flat Plate Using Nanofluids-by Haar Wavelets

The paper presents, the steady state two-dimensional forced convection boundary layer flow of heat transfer past a semi-infinite static flat plate (Blasius problem) and moving flat plate (Sakiadis problem) in the water based nanofluid with various nanoparticles. The self-similar solution exists for the boundary layer equations and using suitable similarity variables, the governing equations have been converted into coupled nonlinear ordinary differential equations (NODEs) with an infinite domain. The governing problems over an infinite interval were solved using semi-numerical technique which makes the use of power of Haar wavelets coupled with collocation method. The solutions obtained using wavelet methods have been confirmed to be more accurate as compared to other previously published results. The several physical interesting results of the problem are concentrated and verified through numerical schemes. Three different types of nonmetallic or metallic nanoparticles such as alumina (Al2O3), copper (Cu) and titania (TiO2) in the base fluid of water with Prandtl number Pr = 6.2, to study the effect of solid volume fraction parameter Φ of the nanofluids. The effect of local skin friction coefficients, Nusselt number, velocity and temperature profiles are plotted for various values of nanoparticle volume fractions and for different nanoparticles are analyzed in detail, the numerical results are presented in terms of Tables. It predicts that, the solid volume fraction affects the fluid flow and heat transfer characteristics.

Розрахунок взаємодії надзвукового струменя з плоскою перешкодою, відхиленою відносно вісі струменя

This paper presents results of a numerical solution of the model problem of the interaction of a plane supersonic jet with a semiinfinite flat plate inclinable off the jet axis. The paper is devoted to the study of the flow parameters in the jet flow field and the pressure distribution over the plate surface as a function of the plate inclination. The aim of the paper is to obtain the flow parameters in the jet flow field and the pressure distribution over the plate surface as a function of the plate inclination angle and front edge position. To obtain numerical results, marching algorithms in the inviscid gas and viscous layer approximation were used. At specified values of the supersonic underexpanded/overexpanded jet parameters, calculations were conducted in the plate inclination angle range of 0 to 20?. The position of the plate front edge was specified by two coordinates: a longitudinal and a transversal one, and in the parametric calculations the transversal coordinate was varied at a fixed longitudinal one. The cross-section at which the nonuniform jet field starts to interact with the plate was determined as a function of both the plate front edge position and the plate inclination. The numerical study showed the following: with increasing plate inclination angle, the oscillation frequencies of the flow parameters in the jet flow field and on the plate surface decrease, while their oscillation amplitudes increase, and the position of the maximum pressure point on the plate surface depends on the initial position of the plate front edge and may not coincide with the cross-section at which the jet–plate interaction starts. The results obtained may be used in qualitative estimation of the effect of different parameters in the jet flow field.

Unsteady boundary layer flow and heat transfer of a viscous fluid over a semi-infinite stationary flat plate: Blasius flow problem

In this paper, a class of similarity solution for the unsteady Navier–Stokes equations which describe the two-dimensional unsteady laminar boundary layer flow of a viscous incompressible fluid over a semi-infinite flat stationary plate surface has been derived. Here, the boundary layer is formed owing to an uniform free stream flow over this plate surface and the unsteadiness in this flow dynamics comes only from the similarity solution which is not yet available in the open literature. For this similarity solution the governing boundary layer equations (momentum and thermal) transform into a set of non-linear ordinary differential equations which conceive two physical parameters, namely, unsteadiness parameter γ and Prandtl number Pr. The impact of these two parameters on the unsteady boundary layer flows as well as on the heat transfer analysis have been discussed in detailed. The present analysis confirms the non-existence of the boundary layer solutions after a certain negative value of γ, while it continues for a large positive value of γ and specifically for the value of γ = 0, we get the steady boundary layer solution for the Blasius flow problem. Here, we have considered the whole range of the Pr values, which includes both the limiting cases Pr → 0 and Pr → ∞, in the discussion of the heat transfer analysis. For these two limiting cases, two approximated separate mathematical formulae for the heat transfer solutions have been derived in terms of the well-known bessel, error and hypergeometric functions, whose results for any given value of γ within the solution domain are well fitted with the corresponding numerical results.

Receptivity to Freestream Periodic Vorticity Disturbance on a Flat Plate with an Elliptic Leading Edge

The receptivity of the Blasius boundary layer over a semi-infinite flat plate with an elliptic leading edge and of aspect ratio five was investigated using a direct numerical solution of two-dimensional Navier-Stokes equations. The result of the computation where the slip condition is applied to the fluctuating component of velocity at the wall surface is compared with that of an ordinary computation using a nonslip condition. Another numerical experiment is performed where no vorticity fluctuation is supplied from a freestream while prerecorded values of vorticities at the wall in response to the passage of convecting fluctuations are used as the wall vorticity boundary condition. It is shown that vorticity fluctuations in the boundary layer can be classified according to their wavelengths. Waves with longer wavelengths originate from the freestream, whereas waves with shorter wavelengths close to T-S waves originate from the surface of the plate. In another numerical experiment, the slip boundary condition against the fluctuation component of vorticity is applied to the limited area of the wall surface. The aim of the study is to determine the part of the elliptic leading edge or flat plate that induces vorticity fluctuations, thereby resulting in the creation of T-S waves. The numerical results show that the contribution of vorticity fluctuations originating from the juncture is the most crucial, whereas the vorticities supplied in the elliptic leading-edge surface negatively affect the amplitude of vorticity fluctuations inside the boundary layer. And, the stagnation section did not show positive contribution.

Effects of free stream excitation on the boundary layer over a semi-infinite flat plate

Transition to turbulence for flow over a semi-infinite flat plate can occur due to disturbances convecting in the free stream, and various routes have been studied in the literature. Specifically, this has been discussed in great detail as a global receptivity problem [Sengupta et al., “Nonmodal nonlinear route of transition to two-dimensional turbulence,” Phys. Rev. Res. 2, 012033(R) (2020)]. Here, the same is studied for the deterministic excitation of a vortex translating with a fixed speed at a fixed height outside the boundary layer. The study aims to capture the fundamental differences in the mechanisms followed by linear and nonlinear global formulations, the existence of the nonmodal spatio-temporal wave front (STWF), onset of nonlinearity, and nonlinear saturation of the STWF by dispersion and phase effects. Other issues related to the initial location of the vortex and its strength are addressed in the present work. The main finding of the investigation is that the onset of the STWF is captured by both formulations, but it occurs at different locations and times. The nonlinear global receptivity study shows earlier onset and saturation of the STWF, while the corresponding linear study shows a delayed onset and no saturation. Overall, it is essential to operate within a nonlinear framework to capture the later stages of transition, phase shift due to nonlinear dispersion and saturation, which depend strictly on nonlinearity.

Effect of suction/blowing on heat-absorbing unsteady radiative Casson fluid past a semi-infinite flat plate with conjugate heating and inclined magnetic field

This article studies the effect of suction/blowing, inclined magnetic field, and chemical reaction on heat-absorbing unsteady radiative Casson fluid past a semi-infinite flat plate in porous medium incorporating the oscillatory plate movement as a linear combination of ‘cosine’ and ‘sine’ functions in time. Further, the mass and heat transfer characteristics are examined under the influence of conjugate mass and heat transfer phenomena at the boundary. The governing equations of the model, viz. the energy, mass transfer, and momentum, are transformed into the non-dimensional form adopting suitable non-dimensional variables and parameters. The exact analytic solutions of the model for species concentration and fluid temperature are obtained using Laplace transform technique whilst, the solution for the fluid velocity has been obtained numerically with the help of the INVLAP routine of MATLAB. The expressions for fluid temperature, species concentration, and velocity are obtained and studied graphically for various physical parameters influencing the fluid flow model taking into account the case of both suction and blowing. Further, the solutions when the Casson fluid parameter $$\alpha \rightarrow \infty $$ are also obtained as special cases. Results for the skin friction coefficient, Sherwood number, and Nusselt number are numerically calculated and put in tabular form. An increment for the inclination angle of the magnetic field enhances the fluid velocity while it has a reverse effect on skin friction. Increasing the Schmidt number Sc leads to a reduction in fluid concentration and increasing the value of thermal radiation accelerates fluid temperature. This fluid flow model has several industrial applications in the field of chemical, polymer, medical sciences, etc.