A STUDY OF NON-NEWTONIAN FLOW AND HEAT TRANSFER OVER A NON-ISOTHERMAL WEDGE USING THE HOMOTOPY ANALYSIS METHOD

The thermoconvective boundary layer flow of a generalized third-grade viscoelastic power-law non-Newtonian fluid over a porous wedge is studied theoretically. The free stream velocity, the surface temperature variations, and the injection velocity at the surface are assumed variables. A similarity transformation is applied to reduce the governing partial differential equations for mass, momentum, and energy conservation to dimensionless, nonlinear, coupled, ordinary differential equations. The homotopy analysis method (HAM) is employed to generate approximate analytical solutions for the transformed nonlinear equations under the prescribed boundary conditions. The HAM solutions, in comparison with numerical solutions (fourth-order Runge-Kutta shooting quadrature), admit excellent accuracy. The residual errors for dimensionless velocity and dimensionless temperature are also computed. The influence of the “power-law” index on flow characteristics is also studied. The mathematical model finds important applications in polymeric processing and biotechnological manufacture. HAM holds significant promise as an analytical tool for chemical engineering fluid dynamics researchers, providing a robust benchmark for conventional numerical methods.     

HEAT TRANSFER DUE TO MHD SLIP FLOW OF A SECOND-GRADE LIQUID OVER A STRETCHING SHEET THROUGH A POROUS MEDIUM WITH NONUNIFORM HEAT SOURCE/SINK

An analysis is carried out to study the heat transfer characteristics of a second-grade non-Newtonian liquid due to a stretching sheet through a porous medium under the influence of external magnetic field. The stretching sheet is assumed to be impermeable. Partial slip condition is used to study the flow behavior of the liquid. The effects of viscous dissipation, nonuniform heat source/sink on the heat transfer are addressed. The nonlinear partial differential equations governing momentum and heat transfer in the boundary layer are converted into nonlinear ordinary differential equations using similarity transformation. Analytical solutions are obtained for the resulting boundary value problems in the case of two types of boundary heating, namely, constant surface temperature (CST) and prescribed surface temperature (PST). The effects of slip parameter, second-grade liquid parameter, combined (magnetic and porous) parameter, Prandtl number, Eckert number, and nonuniform heat source/sink parameters on the heat transfer are shown in several plots. Analytical expressions for the wall frictional drag coefficient and wall temperature gradient are obtained.     

Entropy generation analysis from the time-dependent quadratic combined convective flow with multiple diffusions and nonlinear thermal radiation

Diffusions of multiple components have numerous applications such as underground water flow, pollutant movement, stratospheric warming, and food processing. Particularly, liquid hydrogen is used in the cooling process of the aeroplane. Further, liquid nitrogen can find applications in cooling equipment or electronic devices, i.e., high temperature superconducting(HTS) cables. So, herein, we have analysed the entropy generation(EG), nonlinear thermal radiation and unsteady(time-dependent) nature ...     

Hydrodynamic behavior of an electrified thin film flowing down an inclined plane at high Reynolds numbers

To answer the questions on the dynamics of thin liquid flow down an inclined plane at high Reynolds numbers subjected to a uniform normal electrostatic field, we have derived evolution equations describing the free-surface behavior by using the von Kármán-Pohlhausen approximation. The integration of the evolution equations is numerically performed to address two-dimensional finite-amplitude surface-wave propagation modes. The growth of a periodic disturbance is first examined to compare with the results linear-stability theory, and then to investigate the nonlinear surface-wave behavior the evolution equations are solved numerically by a Fourier-spectral method. For small evolution time the computed nonlinear modes of instability are well consistent with the results from the linear theory. The effect of an electrostatic field makes the flow system significantly unstable.     

Stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition

The problem of a steady laminar two‐dimensional stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition is studied. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically using the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter and the convective parameter on the fluid flow and heat transfer characteristics are disscussed. It is found that the skin friction coefficient and the heat transfer rate at the surface decrease with increasing values of the material parameter. Moreover, dual solutions are found to exist for the shrinking case, while for the stretching case, the solution is unique. © 2011 Canadian Society for Chemical Engineering     

Data-driven state observation for nonlinear systems based on online learning

For controlling nonlinear processes represented by state-space models, a state observer is needed to estimate the states from the trajectories of measured variables. While model-based observer synthesis is traditionally challenging due to the difficulty of solving pertinent partial differential equations, this article proposes an efficient model-free, data-driven approach for state observation, which is suitable for data-driven nonlinear control without accurate nonlinear models. Specifically, by using a Chen–Fliess series representation of the observer dynamics, state observation is endowed with an online least squares regression formulation that can be solved by gradient flow with performance guarantees. When the target state trajectories for regression are unavailable, by exploiting the Kazantzis–Kravaris/Luenberger observer structure, state observation is reduced to a dimensionality reduction problem amenable to an online implementation of kernel principal component analysis. The proposed approach is demonstrated by a limit cycle dynamics and a chaotic system.     

Water Purification from Heavy Metal Ions in a Packed Column

The process of adsorption from water solutions containing ternary system of Cu(II), Zn(II) and Ni(II) ions in time-variable conditions in a packed column with lyophilized chitosan beads is considered. The system of partial differential equations describing the adsorption column, due to the assumption of a properly defined variable is transformed into a system of ordinary nonlinear equations which enables the identification of object parameters in simple experiments. Analytical solution of that system was possible due to the assumptions made regarding the equation describing sorption kinetics. Using experimental data, the effective diffusion coefficient D_eff and the sorption kinetic constants K in the real environment were identified. The sorption capacity q* was obtained in separate sorption equilibrium experiments. Using a mathematical model the influence of initial concentration and solution flow rate on the breakthrough curve was determined. The approach which is presented provides a new method for modeling of sorption in a packed column.     

The effect of liquid flow distribution on the behaviour of a trickle bed reactor

A mathematical model has been formulated of the effect of flow distribution of the liquid phase carrying a dissolved reactant on the progress of an nth order, irreversible, catalytic reaction with heat effects in an adiabatic trickle bed reactor. The model has been stated in terms of the density of irrigation, temperature and concentration of the reactant in the liquid, all treated as spatially distributed variables. Provisions have been made to account for the existence of the flow down the surface of the wall, which has no catalytic effect.Local concentration and temperature have been proven to be coupled by the invariant T + Uγc = γU. The same invariant governs also local concentration and temperature of the wall flow. Mathematically, the model is represented by a coupled set of nonlinear parabolic partial differential equations enabling concentration and temperature fields to be obtained for an arbitrary type of liquid distribution and intensity of the wall flow.Numerical solutions have been obtained by the finite-difference method simulating reactors irrigated by liquid distributors as central discs of different radii, or a central annulus, and strongly exothermic reactions with the reaction order ranging between 0.1 and 2. Numerical results have shown the effect of liquid distribution on the overall reaction conversion to be very complex. Optimum initial distribution varies depending on the reaction order as well as the required degree of conversion. In general, however, the entrance region flow pattern may play a significant role in affecting especially reactions exhibiting kinetics close to zero order (hydrogenations). The effect of the wall flow has been found unambigously adverse to reaching high conversions and of increasing importance for low order reactions.     

MHD flow and heat transfer of a micropolar fluid over a nonlinear stretching surface with variable surface heat flux and heat generation

An analysis has been carried out to study magnetohydrodynamic boundary layer flow and heat transfer of an electrically conducting micropolar fluid over a nonlinear stretching surface with variable wall heat flux in the presence of heat generation/absorption and a non‐uniform transverse magnetic field. The governing system of partial differential equations is first transformed into a system of ordinary differential equations using similarity transformation. The transformed equations are solved numerically. Results for the dimensionless velocity, micro‐rotation, and temperature profiles are displayed graphically delineating the effects of various parameters characterising the flow. The results show that the velocity profile decreases as the magnetic parameter and the velocity exponent increase, while it increases as the material parameter increases. The results show also that the temperature profile increases as the magnetic parameter, the velocity exponent, and the heat generation parameter increase. Furthermore, the temperature profile decreases as the material parameter, the heat absorption parameter, and the Prandtl number increase.     

FORCED CONVECTION BOUNDARY LAYER FLOW AT A FORWARD STAGNATION POINT WITH NEWTONIAN HEATING

The steady forced convection boundary layer flow near the forward stagnation point of an infinite plane wall generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature is investigated in this study. The governing partial differential equations are first transformed into a system of ordinary differential equations before they are solved numerically by a finite-difference scheme, namely the Keller box method. Numerical solutions are obtained for a large range of values of the Prandtl number.     

Nonlinear vibration and modal analysis of FG nanocomposite sandwich beams reinforced by aggregated CNTs

In the present work, by considering the aggregation effect of single‐walled carbon nanotubes (SWCNT), the nonlinear vibration of functionally graded (FG) nanocomposite sandwich Timoshenko beams resting on Pasternak foundation are presented. The material properties of the FG nanocomposite sandwich beam are estimated using the Eshelby–Mori–Tanaka approach and differential quadrature method (DQM) is used to obtain natural frequency. The nonlinear governing equations and boundary conditions are derived using the Hamilton principle and von Kármán geometric nonlinearity. The higher order nonlinear governing equations and boundary conditions are calculated using the Hamilton principle. A direct iterative method is employed to determine the nonlinear frequencies and mode shapes of the beams. It is shown that the mechanical properties and therefore vibration of functionally graded carbon nanotube reinforced (FG‐CNTR) sandwich beams are severely affected by CNTs aggregation. A detailed parametric study is carried out to investigate the influences of Winkler foundation modulus, shear elastic foundation modulus, length to span ratio, thicknesses of face sheets on the nonlinear vibration of the structure. POLYM. ENG. SCI., 59:1362–1370 2019. © 2019 Society of Plastics Engineers     

Modeling of Liquid Flows in Porous Channels

Liquid flow patterns and features of solving three-dimensional hydrodynamic problems in porous channels are considered. In the limiting cases of Reynolds numbers approaching infinity and zero, a self-similar problem is formulated and a set of partial differential equations in divergence form is derived. It is shown that the flow kinematics is independent of the liquid viscosity and the flow dynamics depends on it.     

HOMOTOPY ANALYSIS OF FREE CONVECTION BOUNDARY LAYER FLOW WITH HEAT AND MASS TRANSFER

A steady two-dimensional laminar boundary layer flow of an incompressible viscous fluid over a semi-infinite surface is considered to investigate the accuracy of the homotopy analysis method. The governing coupled nonlinear system of differential equations is solved by means of the HAM approach. Explicit analytical series solutions are obtained and compared with numerical solutions. Good agreement is observed between the numerical results and HAM analytical solutions.     

Stagnation slip flow and heat transfer on a moving plate

A two-dimensional or axisymmetric stagnation flow impinges on a plate moving in its own plane. The no slip condition on the solid boundary is replaced by the partial slip condition. The Navier-Stokes and energy equations admit exact similarity solutions. The resulting nonlinear differential equations are solved asymptotically and numerically. The flow depends heavily on the velocity slip factor λ. We find drag decreases as 1/λ and heat transfer increases with λ, the Prandtl number, and decreased thermal slip.     

Modeling and numerical analysis of nanoliquid (titanium oxide,graphene oxide) flow viscous fluid with second order velocity slip and entropy generation

The prime objective of the present communication is to examine the entropy-optimized second order velocity slip Darcy–Forchheimer hybrid nanofluid flow of viscous material between two rotating disks.Electrical conducting flow is considered and saturated through Darcy–Forchheimer relation. Both the disks are rotating with different angular frequencies and stretches with different rates. Here graphene oxide and titanium dioxide are considered for hybrid nanoparticles and water as a continuous phase liquid. Joule heating, heat generation/absorption and viscous dissipation effects are incorporated in the mathematical modeling of energy expression. Furthermore, binary chemical reaction with activation energy is considered. The total entropy rate is calculated in the presence of heat transfer irreversibility, fluid friction irreversibility,Joule heating irreversibility, porosity irreversibility and chemical reaction irreversibility through thermodynamics second law. The nonlinear governing equations are first converted into ordinary differential equations through implementation of appropriate similarity transformations and then numerical solutions are calculated through Built-in-Shooting method. Characteristics of sundry flow variables on the entropy generation rate, velocity, concentration, Bejan number, temperature are discussed graphically for both graphene oxide and titanium dioxide hybrid nanoparticles. The engineering interest like skin friction coefficient and Nusselt number are computed numerically and presented through tables. It is noticed from the obtained results that entropy generation rate and Bejan number have similar effects versus diffusion parameter. Also entropy generation rate is more against the higher Brinkman number.     

Nonlinear characterization of oil–gas–water three-phase flow in complex networks

Understanding the dynamics of oil–gas–water three-phase flow has been a challenge in the fields of nonlinear dynamics and fluid mechanics. We systematically carried out oil–gas–water three-phase flow experiments for measuring the time series of flow signals, which is studied in terms of the mapping from time series to complex networks. Two network mapping methods are proposed for the analysis and identification of flow pattern dynamics, i.e. Flow Pattern Complex Network (FPCN) and Fluid Dynamic Complex Network (FDCN). Through detecting the community structure of FPCN based on K-means clustering, distinct flow patterns can be successfully distinguished and identified. A number of FDCN's under different flow conditions are constructed in order to reveal the dynamical characteristics of three-phase flows. The network information entropy of FDCN is sensitive to the transition among different flow patterns, which can be used to characterize nonlinear dynamics of the three-phase flow. These interesting and significant findings suggest that complex networks can be a potentially powerful tool for uncovering the nonlinear dynamics of oil–gas–water three-phase flows.     

MHD flow of a micropolar fluid towards a vertical permeable plate with prescribed surface heat flux

The problem of a steady mixed convection stagnation point flow towards a permeable vertical plate with prescribed surface heat flux immersed in an incompressible micropolar fluid is studied numerically. The governing partial differential equations are first transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by a finite-difference scheme known as the Keller-box method and the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter, buoyancy parameter, suction/injection parameter and the Prandtl number on the fluid flow and heat transfer characteristics are discussed. It is found that dual solutions exist for both assisting and opposing flows. The skin friction coefficient and the local Nusselt number increase in the presence of suction and magnetic field. Moreover, suction as well as fluids with larger Prandtl number widens the range of the buoyancy parameter for which the solution exists.     

Chemically reactive solute transfer in a boundary layer slip flow along a stretching cylinder

This paper presents the distribution of a solute undergoing a first order chemical reaction in an axisymmetric laminar boundary layer flow along a stretching cylinder. Velocity slip condition at the boundary is used instead of no-slip condition. Similarity transformations are used to convert the partial differential equations corresponding to momentum and concentration into highly nonlinear ordinary differential equations. Numerical solutions of these equations are obtained by the shooting method. The velocity decreases with increasing slip parameter. The skin friction as well as the mass transfer rate at the surface is larger for a cylinder than for a flat plate.     

Accuracy in Numerical Solution of the Particle Concentration Field in Laminar Wall-Bounded Flows with Thermophoresis and Diffusion

The accuracy of numerical finite-difference solutions to the one-way-coupled Eulerian partial differential equations for particle concentration in the presence of thermophoresis and diffusion is explored at different Schmidt numbers in laminar boundary-layer flow of a hot gas over a cold wall. Crank-Nicolson and MacCormack space-marching solutions to the coupled partial differential equations are compared with essentially exact solutions to the self-similar ordinary differential equation problem to determine the requirements for achieving accuracy in numerical solutions. When the diffusion sublayer at the wall is to be resolved, in flows laden with nanometer particles, the cell “Peclet” number referenced to the thermophoretic velocity and grid spacing in the wall-normal direction, and particle diffusion coefficient, serves as a criterion for the accuracy of space-marching solutions and determines the required number of wall-normal grid points, which is proportional to the particle Schmidt number. This criterion should be a useful guide in computations of other wall-bounded flows with thermophoresis, for which no accuracy criterion exists. When the diffusion sublayer at the wall is too thin to be resolved, as in flows laden with micron-size or larger particles, outer solutions to the particle concentration equation with no Brownian particle diffusion give excellent predictions of both the particle concentration profile and the flux of particles to the wall.

Copyright 2014 American Association for Aerosol Research     

Hydromagnetic non‐Darcy flow,heat and mass transfer over a stretching sheet in the presence of thermal radiation and Ohmic dissipation

A numerical analysis has been carried out to study magnetohydrodynamic boundary layer flow, heat and mass transfer characteristics on steady two‐dimensional flow of an electrically conducting fluid over a stretching sheet embedded in a non‐Darcy porous medium in the presence of thermal radiation and viscous dissipation. The governing partial differential equations are convected into a system of nonlinear ordinary differential equations by similarity transformation and are solved numerically by using the Successive linearisation method, together with the Chebyshev pseudo‐spectral collocation method. The effects of various parameters on the velocity, temperature, and concentration fields as well as on the skin‐friction coefficient are presented graphically and in tabular forms.