Vertical Wavy Surface Research Articles

Initially reactive and concentrated generalized fluid wavy flow with the applications of disorder theory and magnetic field: A computational study

The wavy flow of generalized fluid namely, Cross fluid is mathematically formulated on a gravitationally affected vertical wavy surface with significant physical effects which is the main theme of this work. This particular dynamics of chemically reactive materials is further explored with an irreversible process. A significant heat transfer is measured through thermal resistance during the consideration of entropy optimization. Since entropy generation is associated with the mechanical systemenergy loss is more helpful in monitoring the entropy production in different engineering and industrial processes. Specifically, such irreversibility process appearance causing a noticeable low efficiency in the relevant practical sectors. For better performance in the minimization of friction on the wavy surface, flow is dissipated in terms of heat. However, the measure of loss in terms of work is introduced in the form of thermal radiation, viscous dissipation, magnetic field, and first-order chemical reaction. Additionally, the expected pressure drooping on the wavy surface is another goal of the entire study. The non-linear mathematical equations are determined by following the maximum viscosity approach. Relevant and important results are portrayed to show the various features of the newly developed work. The significant findings are approximated via one of the collocation methods while using MATLAB software. The Richardson number and buoyancy parameter enhanced the flow speed of the materials. The heat transfer rate is decreased by both Eckert number and wavy amplitude and the chemical reaction factor enhanced the mass transfer rate. The heat energy of the materials is escalated with the help of electromagnetic wave radiation and temperature ratio factor. Strengthening the chemical reaction factor declined the mass flow during the typical motion of the liquid. In the last, a comparison is provided to show the accuracy of the numerical approach.

Magnetohydrodynamics thermosolutal convection of hybrid MWCNT-Fe[formula omitted]O[formula omitted]-water nanofluid along a vertical wavy surface with wall heat and mass flux

This numerical analysis investigates the behavior of magnetohydrodynamics (MHD) thermosolutal convection in a hybrid nanofluid made up of multi-wall carbon nanotube (MWCNT)-Fe3O4 and water along a vertical wavy surface with wall heat and mass flux conditions. The mathematical model is developed using the conservation equations of mass, momentum, energy, and energy. The governing equations are converted into a non-dimensional form using the appropriate transformation, and the implicit finite difference technique is used to solve them. The effects of various parameters, such as the Schmidt number (Sc), nanoparticles volume fraction (ϕ), wavy amplitude (a), magnetic parameter (M), buoyancy ratio (Br), on the velocity, temperature, concentration distribution (Φ), streamlines, isotherms, local skin friction coefficient (Cf), local Nusselt (Nu) number, local Sherwood number (Sh) are investigated. Results show that higher amplitude and the addition of hybrid nanofluids volume fraction slow down the heat and mass transport rate, as indicated by declining local Nusselt and Sherwood numbers. However, enhancing the buoyancy ratio increases the fluid flow’s skin friction, heat, and mass transport. The velocity, temperature, concentration distribution, skin friction, and convective heat transport within the wavy surface is weakened by the addition of the magnetic parameter M.

Finite Element Analysis for Magneto-Convection Heat Transfer Performance in Vertical Wavy Surface Enclosure: Fin Size Impact

Finite Element Analysis for Magneto-Convection Heat Transfer Performance in Vertical Wavy Surface Enclosure: Fin Size Impact

Magnetic Field Effect and Heat Transfer of Nanofluids within Waveform Microchannel

In this research, a numerical study of mixed convection of non-Newtonian fluid and magnetic field effect along a vertical wavy surface was investigated. A simple coordinate transformation to transform wavy surface to a flat surface is employed. A cubic spline collocation numerical method is employed to analyze transformed equations. The effect of various parameters such as Reynolds number, volume fraction 0-, Hartmann number, and amplitude of wave length was evaluated in improving the performance of a wavy microchannel. According to the presented results, the sinusoidal shape of the microchannel has a direct impact on heat transfer. By increasing the microchannel wave amplitude, the Nusselt number has risen. On the other hand, increasing the heat transfer in the higher wavelength ratio corrugated channel is seen as an effective method of increasing the heat transfer, especially at higher Reynolds numbers. The results showed that with increasing Hartmann numbers, the flow line near the wall becomes more regular and, according to the temperature gradient created, the Nusselt number growth.

Numerical investigation on steady natural convective flow past a perpendicular wavy surface with heat absorption/generation

The controlling of heat transport procedures through external energy source effects is one of the mainly significant problems in modern applied physical sciences. Major strong research in thermal sciences, mechanical engineering and including energy modeling, planning and energy supervisions, energy conservations, energy efficiencies, biomass and bio-energy, renewable energy, energy storage, energy in buildings. In the current existing paper, the consequences of thermal conductivity on temperature, this is inversely proportionally by the linear function of temperature on free convective movement of an incompressible viscous fluid through the heated uniform and vertical wavy surface is examined. Associated with boundary conditions, the governing boundary layer equations be translated into the non-dimensional structure for phenomenon by utilizing an appropriate transformation. In the domain of vertical plate that is flat, the resulting method of nonlinear partial differentiated equations are mapped and then numerically by applying the implicit finite difference technique with Keller-box technique. The rate of heat transfer, the skin friction coefficient, the isotherms and streamlines throughout the boundary layer are exhibited graphically.

Analysis of Reciprocal Thermal Conductivity on Free Convection Flow along a Wavy Vertical Surface

The effects of thermal conductivity which depend on temperature are conversely proportional with the linear function of temperature on free convective flow where the fluid is viscous and incompressible along a heated uniform and the vertical wavy surface has been examined in this study. The boundary layer equations with the associated boundary conditions that govern the flow are converted into a nondimensional form by using an appropriate transformation. In the domain of a vertical plate that is flat, the resulting method of nonlinear PDEs is mapped and then worked out numerically by applying the implicit central finite difference technique with Newton’s quasilinearization method, and the block Thomas algorithm is well known as the Keller-box method. The outputs are obtained in the terms of the heat transferring rate, the frictional coefficient of skin, the isotherms, and streamlines. The outcomes showed that the local heat transferring rate, the local skin friction coefficient, the temperature, and the velocity all are decreasing, and both the thermal layer of boundary and velocity become narrower with the rising values of reciprocal variation of temperature-dependent thermal conductivity. On the other hand, the friction coefficient of skin, the velocity, and the temperature decrease where the friction coefficient of skin and velocity decrease by 43% and 64%, respectively, but the heat transfer rate increases by 61% approximately, and both the boundary layer thermal and velocity become thinner when the Prandtl number increases.

Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium

Abstract A mathematical model is developed to analyze the free convection flow induced by catalytic surface reaction on a vertical wavy surface embedded in a non-Darcy porous medium. The governing equations are transformed using a generalized transformation which are valid near to and far from the leading edge. We then solve the resulting equations employing finite difference method. A comparison between the present solutions and the results of a past study is made which provides a good agreement. Numerical results reveal that the wall temperature and the surface concentration are enhanced for higher heat release parameter. An increase in the amplitude of the wavy surface and the reactant consumption parameter causes a decrease in the wall temperature and the surface concentration. Due to the increase of the reduced Darcy number the wall temperature substantially becomes higher whereas the surface concentration diminishes. However, a converse characteristic is observed in the case of the activation energy parameter. The momentum, thermal and concentration boundary layers are significantly increased for higher values of the reduced Darcy number and the consumption reactant parameter. Contrary to this, the larger heat release parameter reduces the thicknesses of the momentum, thermal and concentration boundary layers.

Natural Convection of MHD over a Vertical Wavy Surface in Presence of Porous Media

This paper shows the natural convective heat transfer in porous media over the vertical wavy surface and it assumes that the fluid is viscous and in-compressible. This model shows the effects of the inverse of Darcy number. The dimensional partial differential equations are converted into a dimensionless form. The non-linear system of equations is obtained and these equations are solved numerically by the finite difference method. The results are obtained for inverse Darcy number, magnetic parameter, Prandtl number, amplitude of surface, parameter of heat generation and parameter of thermal conductivity, and their effects on the velocity, temperature of the fluid and Nusselt number.

Viscous Dissipation Effect in the Free Convection of Non-Newtonian Fluid with Heat Generation or Absorption Effect on the Vertical Wavy Surface

The present article analyzes the effect of viscous dissipations on natural convection heat transfer. The power law model for non-Newtonian fluid with heat generation or absorption effect along a sinusoidal wavy surface with isothermal boundary condition is investigated. A simple coordinate transform is employed to map the wavy surface into a flat surface, and also, the fully implicit finite difference method is incorporated for the numerical solution. The findings of this study can help better understand the effect of parameters such as the Brinkman number, heat generation/absorption, wave amplitude magnitude, and generalized Prandtl number on convective heat transfer in dilatant and pseudoplastic non-Newtonian. Results show that as the Brinkman number increases, the amount of heat transfer decreases. This is physically justifiable considering that the fluid becomes warmer due to the viscous dissipation, decreasing its temperature difference with the constant temperature surface. Also, the effect of the power law viscosity index is surveyed. It is demonstrated that the magnitude of the local Nusselt number in the plane leading edge has the smallest quantity for pseudoplastic fluids compared to dilatant Newtonian fluids. Additionally, as the distance from the plane leading edge increases, the heat transfer declines.

Bejan's flow visualization of buoyancy-driven flow of a hydromagnetic Casson fluid from an isothermal wavy surface

The proposed work numerically investigates the buoyancy-driven flow of Casson fluid from a vertical wavy surface under the influence of a magnetic field and evaluates the underlying transport of heat in the free convective regime both quantitatively and qualitatively. Pertaining to this analysis, the primitive forms of coupled non-linear partial differential equations are evaluated with the help of an efficient and straightforward Crank–Nicolson implicit finite difference technique. By representing the graphical plots of flow velocity, temperature, and friction-factor coefficients, obtained for different physical parametric values pertinent to this analysis, we discuss the influence of the Hartmann number, surface waviness parameter, and rheological parameter of the fluid on the underlying thermohydrodynamics. In addition to the isotherm and streamline plots, by demonstrating the functional form, we discuss an extensive flow visualization technique that provides unique heat flow visualization for the wavy surface based on Bejan's heat function concept. The results indicate that for increasing the magnitude of the magnetic parameter, the evolution of isotherms, streamlines, and heatlines deviates periodically with a higher amplitude, which signifies the transfer of high heat energy as well as the efficient transport of heat in the convective regime.

A computational analysis of dissipation effects on the hydromagnetic convective flow of hybrid nanofluids along a vertical wavy surface

AbstractHybrid nanofluids (HNFs) are innovative nanofluids produced by adding various types of nanoparticles to the base fluid. A mathematical analysis of flow and heat transfer of hydromagnetic HNF along a vertical wavy texture is performed in this article. The effects of viscous dissipation are also encountered in the present study. The considered HNF was composed of two nanoparticles, copper and titania. The mathematical modeled partial differential equations are transformed into dimensionless nonsimilar forms. The results obtained for the HNF were compared with those for the ‐ and ‐based nanofluid with the help of a well‐known numerical procedure, the Keller‐box scheme. On nonflat (wavy) texture, the Nusselt number is higher as compared with a flat sheet. The Nusselt number is higher for Cu nanoparticles relative to Ti nanoparticles. For increased wavy amplitude and magnetic parameter Mg values, a reduction in the coefficient of skin friction and Nusselt number is expected.

Numerical investigation of MHD radiative heat and mass transfer of nanofluid flow towards a vertical wavy surface with viscous dissipation and Joule heating effects using Keller-box method

In this paper, the effect of viscous dissipation and Joule heating on magneto-hydrodynamic (MHD) nanofluid flow towards a vertical sinusoidal wavy surface has been investigated numerically. The wavy surface is considered to be heated with uniform flux. Effects of radiation and nanoparticle volume concentration are also considered. The fluid flow over the surface geometry is designed through the highly non-linear partial differential equations, and governing equations must be transformed into a dimensionless non-similar system of equations to get a better solution by applying the highly efficient well-known Keller-box scheme. In this regard, the numerical solutions are obtained for a concentration of mass fluid, velocity profile, temperature profile, local skin friction number coefficient, local Nusselt number, and Sherwood number shown graphically. Connected parameters involve in the modelled problem such as heat generation parameter, radiative conduction flow parameter, the amplitude of the waviness of the surface, Prandtl number, Brownian motion parameter, Buoyancy ratio, magnetic parameter, Thermophoresis parameter and the Lewis number for momentum, temperature profile, and concentration profile of the fluid through different graphs are explained. In this process, certain iterations were performed for different step sizes in the direction of η=0.01 and x=0.005, respectively. So, keeping this in view to get the more accurate results with all parameters considered, 0≤M≤1, 0≤Rd≤1,0≤Q≤1,0.01≤α≤0.04, 0≤Le≤40, 0.1≤Nb≤0.7,0.1≤Nt≤0.7,0.1≤Nr≤0.7,0.1≤Ec≤0.4,0.1≤J≤0.4,. The obtained results illustrate that Nusselt number, Sherwood number, and velocity profile decreases respectively with the increase of waviness amplitude, but skin friction changes its behaviour to wavier. Also, temperature and concentration profiles increase respectively with enhancing the value of the amplitude of waviness. Finally, it is noted that Nusselt number and Sherwood number decrease for higher values of the Brownian parameter. But after a specific value of x, the trend of Sherwood number increases. However, the behaviour of skin friction decreases, but in a precise manner, it remains almost unchanged.

Natural convection of fluid with variable viscosity and viscous dissipation from a heated vertical wavy surface in presence of magnetic field

ABSTRACT
 
 The present numerical work describes the effect of the temperature dependent variable viscosity and viscous dissipation on natural convection heat transfer boundary layer flow of a viscous incompressible electrically conducting fluid along a vertical wavy surface in presence of a transverse magnetic field. The wavy surface is maintained at uniform wall temperature that is higher than that of the ambient. A simple coordinate transformation is employed to transform the wavy surface into a flat plate. A marching finite difference scheme is used for present analysis. The numerical results, including the developments of the skin friction coefficients, the local Nusselt number, the streamlines as well as the isotherms are presented and discussed in detail. The results of this investigation illustrated that the skin friction coefficient increase with an increase of the variable viscosity and viscous dissipation parameter, while the local Nusselt number at the heated surface decrease with increasing values of variable viscosity, intensity of magnetic field and viscous dissipation parameter.

Effect of Nanofluid on Heat Transfer Enhancement for Mixed Convection Flow Over a Corrugated Surface

Abstract A mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al2O3-water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of Ri = 1.0 \mathrm{Ri}=1.0 , the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic.

Numerical Examination of Thermophysical Properties of Cobalt Ferroparticles over a Wavy Surface Saturated in Non-Darcian Porous Medium

Abstract In this study, the effect of magnetic field on an incompressible ferrofluid flow along a vertical wavy surface saturated in a porous medium is investigated. Ferrofluid is made by incorporating magnetic particles, in this case cobalt, at the nanoscale level into a base fluid. For the study of porous medium two well-known models, namely, Darcy and non-Darcy, are used. The mathematical model in terms of governing partial differential equations which are based on conservation laws in mechanics according to the assumption is developed, and this model is converted into a dimensionless form by suitable transformations. Due to the complex non-linear partial differential equations, the numerical solution is calculated by using an implicit finite difference scheme. The impact of involved parameters, namely, magnetic parameter, nanoparticle volume fraction parameter, the amplitude of the wavy surface, and the Grashof number, on Nusselt and average Nusselt numbers are studied through graphs and tables. The results show that for large values of the magnetic parameter, both the Nusselt number and the average Nusselt number decrease in ferrofluid flow. The value of the Nusselt number in the Darcy model is higher than the value of the Nusselt number in the non-Darcy model.

Entropy generation in mixed convection flow past a vertical wavy surface

Irreversibility phenomenon is numerically investigated for mixed convection flow along a uniformly heated vertical wavy surface. Surface texture of the plate does not allow for a self-similar solution due to which the nature of the problem is non-similar. The numerical solution of the governing non-similar equations has been achieved by utilizing the implicit finite difference scheme commonly known as Keller-Box method and the outputs are shown through graphical pictures. The influence of various physical parameters of interest (mixed convection parameter, wavy amplitude, Prandtl number) on entropy generation and Bejan number has been discussed in detail. It is observed that entropy production enhances with an increment in mixed convection parameter.

Influence of nonlinear radiation on natural convection flow of carbon nanotubes suspended in water-based fluid along a vertical wavy surface

In this study, we have investigated that how thermal efficiency of the base fluid (water) can be enhanced by incorporating single and multi-walled carbon nanotubes in the presence of nonlinear thermal radiation along a vertical wavy surface. The mixture of carbon nanotubes with the base fluid enhances the convection process and this process can speed up by increasing the radiation effects. Due to the enhancement in the convection process of the nanofluid, the fluid particles disperse more rapidly, and consequently the fluid motion also increases. The proposed mathematical model of the natural convection flow of carbon nanotubes suspended in a water-based fluid along a vertical wavy surface under the radiation effect is developed in the form of partial differential equations and then further reduced to a dimensionless nonsimilar system. A numerical procedure is adopted to obtain the result for emerging dimensionless parameters. The outcomes of this study are presented in the form of numerical data and graphs.

Analysis of Heat Transfer Enrichment in Hydromagnetic Flow of Hybrid Nanofluid Along Vertical Wavy Surface

The hybrid nanofluids are novel nanofluids and can be made by adding different types of nanoparticles in the plain fluid. The mathematical modeling of hybrid nanofluid under the magnetic influence over a vertical wavy surface is developed in the present theoretical investigation. The analysis is performed for hybrid nanofluid consisting of Al₂O₃-SiO₂ nanoparticles and compared with SiO₂ nanoparticle. The theoretical results also indicate that Al₂O₃-SiO₂ water hybrid nanofluid have higher heat transfer rate when compared with SiO₂- water nanofluid. In hybrid nanofluid, the choice of a suitable mixture of nanoparticles can lead to desire heat transfer phenomena. The implicit finite difference scheme is utilized for solution purposes. Results are presented in tabular and graphical form for the choice of suitable parameters.

Numerical Investigation on Convective Flow of Two-Phase MHD Dusty Nanofluids over a Wavy Surface with Brownian Motion and Thermophoresis Effects

The emergence of dusty nanofluids as a area of nanoscale heat transfer in fluids is directly correlated to miniaturization trends and nano technology. So, the prime focus of this analyzation is to describe the model of heat and mass transfer phenomenons of two-phase magnetohydrodynamic dusty nanofluids over a vertical sinusoidal wavy surface. The significances of Brownian motion and thermophoresis effects have been considered in the model. The three various nanofluids namely Aluminium oxide ( $$\hbox {Al}_2\hbox {O}_3$$ )-water, Copper (Cu)-water and Titanium oxide ( $$\hbox {TiO}_2$$ )-water immersed with conducting dust particles are taken into consideration for flow analysis. Novel governing equations involving conservation of momentum, mass and thermal energy are subjected to irregular region and converted into non-dimensional form. The resultant equations are numerically approached by developing a finite difference technique with Newton’s quasilinearization method using mathematical software MATLAB. Dynamic characteristics of the flow with the effect of physical parameters associated with velocity, temperature and concentration distributions are interpreted through graphs to get some physical view into the flow patterns. Also, skin-friction coefficient, heat and mass transfer rate are calculated at the boundaries and the outcomes obtained are compared with existing literature.

Heat transfer in natural convection flow of nanofluid along a vertical wavy plate with variable heat flux

The present analysis is concerned to examine the enhancement of heat transfer in natural convection flow of nanofluid through a vertical wavy plate assumed at variable heat flux. The rate of heat transfer in nanofluid flow as compared to pure water can be increased due to increase the density of nanofluid which depends on the density and concentration of nanoparticles. For this analysis, Tiwari and Das model is used by considering two nanoparticles i. e. Al2O3 and Cu are suspended in a base fluid (water). A very efficient implicit finite difference technique converges quadratically is applied on the concerning PDE for numerical solution. The effects of pertinent parameters namely, volume fraction parameter of nanoparticle, wavy surface amplitude, Prandtl number and exponent of variable heat flux on streamlines, isothermal lines, local skin friction coefficient and local Nusselt number are shown through graphs. In this analysis, a maximum heat transfer rate is noted in Cu-water nanofluid through a vertical wavy surface as compared to Al2O3-water and pure water.