Convective and absolute instability of viscoelastic liquid jets

The instability, and subsequent disintegration, of a column of fluid is of interest in a wide variety of growing applications. Despite over 200 years of scientific scrutiny, the instability of a liquid jet remains an active area of study for many researchers from a wide range of scientific disciplines. The last few decades have seen a growth in novel techniques for examining the absolute instability of liquid jets, in many such cases, these methods are intractable. In this thesis, the convective and absolute instability of a viscoelastic liquid jet falling under gravity is examined for axisymmetrical disturbances. We use the upper-convected Maxwell model to provide a mathematical description of the dynamics of a viscoelastic liquid jet. An asymptotic approach, based on the slenderness of the jet, is used to obtain the steady-state solutions. By considering traveling wave modes, we derive a dispersion relationship relating the frequency to the wavenumber of disturbances which is then solved numerically using the Newton-Raphson method. We show the effect of changing a number of dimensionless parameters on convective and absolute instability. In this work, we use a mapping technique developed by Kupfer et al. (1987) to find the cusp point in the complex frequency plane and its corresponding saddle point (the pinch point) in the complex wavenumber plane for absolute instability. The convective/absolute instability boundary is identified for various parameter regimes. We then extend this by including the effect of the surrounding gas, using insoluble surfactants, and immersing the viscoelastic jet into another viscoelastic fluid

Investigation of Mixed Convection in Spinning Nanofluid over Rotating Cone Using Artificial Neural Networks and BVP-4C Technique

The significance of back-propagated intelligent neural networks (BINs) to investigate the transmission of heat in spinning nanofluid over a rotating system is analyzed in this study. The buoyancy effect is incorporated along with the constant thermophysical properties of nanofluids. Levenberg–Marquardt intelligent networks (ANNLMBs) are employed to study heat transmission by using a trained artificial neural network. The system of highly non-linear flow governing partial differential equations (PDEs) is transformed into ordinary differential equations (ODEs) which is taken as a system model. This achieved system model is utilized to generate data set using the “Adams” method for distinct scenarios of heat transmission investigation in a spinning nanofluid over a rotating system for the implementation of the proposed ANNLMB. Additionally, with the help of training, testing, and validation, the approximate solution of heat transmission in a spinning nanofluid in a rotating system is obtained using a BNN-based solver. The generated reference data achieved employing the proposed artificial neural network based on a Levenberg–Marquardt intelligent network is distributed in the following manner: training at 82%, testing at 9%, and validation at 9%. Furthermore, MSE, histograms, and regression analyses are performed to depict and discuss the impact of the varying influence of key parameters, such as unsteadiness “s” in spinning flow, Prandtl number effect “pr”, the rotational ratio of nanofluid and cone α1 and buoyancy effect γ1 on velocities F′G and temperature Θ profiles. The mean square error confirms the accuracy of the achieved results. Prandtl number and unsteadiness decrease the temperature profile and thermal boundary layer of the rotating nanofluid

Investigation of Mixed Convection in Spinning Nanofluid over Rotating Cone Using Artificial Neural Networks and BVP-4C Technique

The significance of back-propagated intelligent neural networks (BINs) to investigate the transmission of heat in spinning nanofluid over a rotating system is analyzed in this study. The buoyancy effect is incorporated along with the constant thermophysical properties of nanofluids. Levenberg–Marquardt intelligent networks (ANNLMBs) are employed to study heat transmission by using a trained artificial neural network. The system of highly non-linear flow governing partial differential equations (PDEs) is transformed into ordinary differential equations (ODEs) which is taken as a system model. This achieved system model is utilized to generate data set using the “Adams” method for distinct scenarios of heat transmission investigation in a spinning nanofluid over a rotating system for the implementation of the proposed ANNLMB. Additionally, with the help of training, testing, and validation, the approximate solution of heat transmission in a spinning nanofluid in a rotating system is obtained using a BNN-based solver. The generated reference data achieved employing the proposed artificial neural network based on a Levenberg–Marquardt intelligent network is distributed in the following manner: training at 82%, testing at 9%, and validation at 9%. Furthermore, MSE, histograms, and regression analyses are performed to depict and discuss the impact of the varying influence of key parameters, such as unsteadiness “s” in spinning flow, Prandtl number effect “pr”, the rotational ratio of nanofluid and cone α1 and buoyancy effect γ1 on velocities F′G and temperature Θ profiles. The mean square error confirms the accuracy of the achieved results. Prandtl number and unsteadiness decrease the temperature profile and thermal boundary layer of the rotating nanofluid

Galerkin finite element analysis for buoyancy driven copper-water nanofluid flow and heat transfer through fins enclosed inside a horizontal annulus: Applications to thermal engineering

The hydrothermal significance of natural convection flow through the horizontal annulus reveal most important implication and those geometrical shapes are introduced in enormous industrial and engineering implementations related to superheaters, heat exchangers, hydrogen fuel cells, gas turbines, solar collectors, vehicle engines, and turbomachinery etc. With this motivation, the current advance study enlightens the natural convection heat transfer impacts of Cu−water nanofluid flow through horizontal annulus with inserting Fins at the inner cylinder. Different fins numbers (0, 2 and 4) are inserted at inner cylinder wall are heated. The outer cylinder kept at cooled temperature. The significance nanoparticles fraction (Φ=1%−5%), Rayleigh number (1000,10000and100000) and different fin numbers (0,2and4) on fluid flow, thermal field, and local Nusselt number investigated. The Galerkin finite element method has been employed to carry out the numerical solution for different values of flow controlling parameters. The impacts of prominent parameter on streamlines, isotherms and 2d graphs are analyzed. The analysis concluded that velocity and thermal outcomes upsurges for Rayleigh number. It is conclude that important thermal transfer increment can be observed due to the occurrence of solid nanoparticles and that is boosted by growing the solid particle fraction. The velocity is reduced by increasing the values of nanoparticle volume fraction. Additionally larger heat transfer for nanoparticles Volume fraction Φ=5% as compare to Φ=1%

Thermally radiative bioconvective nanofluid flow on a wavy cylinder with buongiorno model: A sensitivity analysis using response surface methodology

The significant impact of nanotechnology has turned the ordinary into the excellent in the ever-changing environment of science and technology. Recent times have seen a dramatic transformation as advances in science and technology continue to push us into the domain of nanoscale innovation. Fluid flow over a range of geometries is involved in the physical processes of heat and mass transfer subject to the constraints. These phase change systems are also converted into the latest technology by improving the thermal conductivity of the fluids through the mixing of nanoparticles in the ordinary base fluid. This approach makes things finer and quicker from the perspective of efficiency and structure. It has many applications in various domains especially in nano-medicines, chemotherapy, microprocessors, refrigeration, and biotechnology. In this work, nanofluid flow through a wavy cylinder is considered in the existence of thermal radiation, activation energy, and motile microorganisms. The physical model is computationally solved by developing a system of PDE's (partial differential equations) and then transformed into ODE's (ordinary differential equations) by the smooth implementation of similarity variables. The resultant ODE's numerically treated by the bvp4c built package of MATLAB and get the required results. These results are discussed and graphically visualized in the analysis section. For the validation of results, the statistical approach is implemented on the acquired results and shows the fitted model, contour plots, surface plots, residual plots, and streamlines of the involved parameters and their impacts on the model. The impact of involving physical quantities on flow velocity, thermal, concentration, and microorganism's density profiles also discussed. From the results, it is noted that the velocity profile increases by increasing the counts of mixed convection. Thermal distribution enhanced due to boosting the values of thermophoresis and Brownian motion. The concentration of nanoparticles increased by increasing the magnetic field strength. The larger values of peclet number minimize the density of microorganisms. Skin friction coefficient is increased by around 28% and mass transport going to be increased by 36% due to the existence of microorganisms. The analysis of variance shows that our model is significant and the fitted summary also shows the fitness of model

Entropy optimized Ferro-copper/blood based nanofluid flow between double stretchable disks: Application to brain dynamic

Researchers and scientists were inspired by the enormous reactions from industry about heat transformation enhancements due to the entropy generation. The entropy generation shows as a extremes for complex mechanisms like solid state physics, two-phase flows, electro-magnetic air conditioning, and economic evaluation of manufacturing processes, as well as biological technologies chemistry, including biochemistry. We note here that many thermal mechanisms are related to the irreversibility system. The current work focused on the entropy generation impacts in viscous magnetized mono-nanofluids flow between stretchable rotating disks. Ferro and copper are considered as nanoparticles and Blood as a base fluid. The Darcy-Forchheimer porous medium and joule heating effects are considered. For simplifying the current analysis, suitable transformation were introduced in the mathematical description to renovate the partial differential equations (PDE’s) into coupled ordinary ones. To solve the resulting ODEs well-known numerical algorithm bvp4c is used in Matlab in the light of Lobatto-IIIA formula. The consequence of sundry parameters against velocity components, pressure field, temperature distribution and entropy generation are described graphically

Some Novel Results Involving Prototypical Computation of Zagreb Polynomials and Indices for SiO4 Embedded in a Chain of Silicates

A topological index as a graph parameter was obtained mathematically from the graph’s topological structure. These indices are useful for measuring the various chemical characteristics of chemical compounds in the chemical graph theory. The number of atoms that surround an atom in the molecular structure of a chemical compound determines its valency. A significant number of valency-based molecular invariants have been proposed, which connect various physicochemical aspects of chemical compounds, such as vapour pressure, stability, elastic energy, and numerous others. Molecules are linked with numerical values in a molecular network, and topological indices are a term for these values. In theoretical chemistry, topological indices are frequently used to simulate the physicochemical characteristics of chemical molecules. Zagreb indices are commonly employed by mathematicians to determine the strain energy, melting point, boiling temperature, distortion, and stability of a chemical compound. The purpose of this study is to look at valency-based molecular invariants for SiO4 embedded in a silicate chain under various conditions. To obtain the outcomes, the approach of atom–bond partitioning according to atom valences was applied by using the application of spectral graph theory, and we obtained different tables of atom—bond partitions of SiO4. We obtained exact values of valency-based molecular invariants, notably the first Zagreb, the second Zagreb, the hyper-Zagreb, the modified Zagreb, the enhanced Zagreb, and the redefined Zagreb (first, second, and third). We also provide a graphical depiction of the results that explains the reliance of topological indices on the specified polynomial structure parameters

Convective Heat Transfer in Magneto-Hydrodynamic Carreau Fluid with Temperature Dependent Viscosity and Thermal Conductivity

This study is aimed to explore the magneto-hydrodynamic Carreau fluid flow over a stretching/shrinking surface with a convectively heated boundary. Temperature-dependent variable thermophysical properties are utilized to formulate the problem. The flow governing equations are obtained with boundary layer approximation and constitutive relation of the Carreau fluid. The shooting method is utilized to obtain graphical and numeric outcomes. Additionally, initial guesses are generated with the help of Newton’s method. The effect of Weissenberg number, Magnetization, stretching ratio, Prandtl number, suction/blowing parameter, and Lewis number is obtained on velocity, temperature and species continuity profile and analyzed. Shear stress rates and Nusselt number outcomes under body forces influences are present in tabulated data and discussed. It is observed that in absence of magnetization force, B = 0 and strong mass suction 5≤S≤7.5 effect high rates of Nusselt number is obtained. It is concluded that under the influence of power law index and non-linearity parameter maximum heat transfer and reduced shear stress rates are obtained