Passive Boundary Conditions Research Articles

Multiple solutions and stability analysis in MHD non‐Newtonian nanofluid slip flow with convective and passive boundary condition: Heat transfer optimization using RSM‐CCD

AbstractThis study explores the effect of Williamson nanofluid in the presence of radiation and chemical reaction caused by stretching or shrinking a surface with convective boundary conditions. After implementing two‐component model and Lie group theory, the transformed ODEs are solved using the Runge–Kutta Dormand–Prince (RKDP) shooting approach technique. The dual solutions are predicted for certain range of physical nanofluid parameters, such as Williamson parameter (), stretching/shrinking parameter (), and suction parameter () with different slip and magnetic M parameters. Contour plots are generated for the stable branch of the Nusselt number () for different combinations, providing insights into the heat transfer characteristics. The eigenvalue problem is solved in order to predict flow stability. The optimization of heat transfer in nanoliquid is conducted by RSM‐CCD. The resulting quadratic correlation enables the prediction of the optimal Nusselt number for , , and . This investigation is motivated by various applications including manufacturing processes, thermal management systems, energy conversion devices, and other engineering systems where efficient heat transfer is crucial.

Model test of a hydroelastic truncated floating bridge with a stay-cable tower

Experimental studies of long offshore and coastal structures such as very long floating bridges are challenged by the combination of coastal wave environments with relatively small design waves and excessive structural dimensions. It is often not possible to fit the entire model into the limited available space while at the same time being able to properly model the incoming waves. The sensible choice when deciding between such opposing model scale requirements, is to allow for a proper physical representation of the wave environment while finding alternatives to circumvent the space limitations. One way to do this is by truncating the original model design at carefully selected locations along the bridge and inserting passive or active boundary conditions so as to maintain similar static and dynamic properties as the prototype. The present study gives an in-depth description of the as-build experimental model of a truncated section of the Bjørnafjord phase 5 K12 concept, with simplified passive boundary conditions. The truncated section includes a complex double-curved geometry of the bridge girder connecting a cable-stayed tower at the southern end with ten floating pontoons at the northern end. The truncation points coincide with the tower column and the first moored pontoon of the full bridge. The boundary conditions in the bridge girder at the truncation points are simplified as fixed while allowing for free rotation around the vertical and longitudinal axes at the end with the otherwise moored pontoon. The truncated model is extensively instrumented in order to capture three degrees of freedom (DOF) motions at 13 locations along the bridge girder as well as six DOF motions of each pontoon. Force transducers capture the bridge girder and stay-cable axial forces, while strain gauges measure shear forces, bending moments and torque at 12 locations along the bridge girder and at each pontoon column.The present study aims at documenting fundamental properties of the as-build model in order to act as a base for future verification and calibration of design tools used for similar floating bridge concepts. This encompasses a detailed description of the complex geometry, mass and stiffness properties of the structural parts and important responses from static documentation tests. Natural periods and corresponding modal response of the first two structural modes are captured from a horizontal decay test and finally the responses from pure current tests are discussed. The present study is focused on documenting the as-build experimental model while a separate paper is to be published later on focusing on results from tests with combinations of waves and current.

Modeling and Simulations of Buongiorno's Model for Nanofluid in a Microchannel with Electro-Osmotic Effects and an Exothermal Chemical Reaction.

The article presents a mathematical model for the magnetized nanofluid flow and heat transfer with an exothermic chemical reaction controlled by Arrhenius kinetics. Buongiorno’s model with passive boundary condition is employed to formulate the governing equation for nanoparticles concentration. The momentum equation with slip boundary conditions is modelled with the inclusion of electroosmotic effects which remain inattentive in the study of microchannel flows with electric double layer (EDL) effects. Conclusions are based on graphical and numerical results for the dimensionless numbers representing the features of heat transfer and fluid flow. Frank-Kamenetskii parameter resulting from the chemical reaction showed significant effects on the optimization of heat transfer, leading to increased heat exchangers’ effectiveness. The Hartmann number and slip parameter significantly affect skin friction, demonstrating the notable effects of electroosmotic flow and the exothermic chemical reaction on heat transfer in microchannels. This analysis contributes to prognosticating the convective heat transfer of nanofluids on a micro-scale for accomplishing successful thermal designs.

A Bio-Thermal Convection in Water-Based Nanofluid Containing Gyrotactic Microorganisms: Effect of Vertical Throughflow

The effect of vertical throughflow on the onset of bio-thermal convection in a water-based nanofluid containing gyrotactic microorganisms is investigated using more realistic boundary conditions. The Galerkin weighted residual method is used to obtain numerical solutions of the mathematical model. The effects of bioconvection Rayleigh number, gyrotaxis number, bioconvection Péclet number, Lewis number, Péclet number, particle density increment number, modified diffusitivity ratio, and nanoparticle Rayleigh number on thermal Rayleigh number are examined.The combined effect of Brownian motion and thermophoresis of nanoparticles, vertical throughflow, and gyrotactic microorganisms on the thermal Rayleigh number is found to be destabilizing and its value is decreased by first to third orders of magnitude as compared to regular fluids. Critical wave number is dependent on bioconvection parameters, nanofluid parameters as well as throughflow parameter. The results obtained using passive boundary conditions are compared with those of active boundary conditions. The present study may find applications in seawater convection at the ocean crust.

Extension of the divide-and-conquer algorithm for the efficient inverse dynamics analysis of multibody systems

This paper presents a new mathematical framework to extend the Generalized Divide-and-Conquer Algorithm (GDCA) for the inverse dynamics analysis of fully actuated constrained multibody systems. Inverse-GDCA (iGDCA) is a highly parallelizable method which does not create the mass and Jacobian matrices of the entire system. In this technique, generalized driving forces and constraint loads due to kinematic pairs are clearly and separately differentiated from each other in the equations of motion. As such, it can be easily used for control scheme purposes. iGDCA works based on a series of recursive assembly and disassembly passes to form and solve the equations governing the inverse dynamics of the system. Herein, the mathematical formulations to efficiently combine the dynamics of consecutive bodies in the assembly pass for the purpose of inverse dynamics analysis are presented. This is followed by generating the disassembly pass algorithm to efficiently compute generalized actuating forces. Furthermore, this paper presents necessary mathematical formulations to efficiently treat the inverse dynamics of multibody systems involving kinematic loops with various active and passive boundary conditions. This is followed by the design of a new strategy to efficiently perform the assembly–disassembly pass in these complex systems while avoiding unnecessary computations. Finally, the presented method is applied to selected open-chain and closed-chain multibody systems.

Bioconvection nanofluid slip flow past a wavy surface with applications in nano-biofuel cells

A theoretical study is presented to examine free convective boundary layer flow of water-based bio-nanofluid containing gyrotactic microorganisms past a wavy surface. Buongiorno's nanofluid model with passively controlled boundary condition is applied to investigate the effects of the emerging parameters on the physical quantities namely, skin friction, Nusselt numbers and density number of motile microorganisms. The effects of the both hydrodynamic and thermal slips are also incorporated. Local similarity and non-similarity solutions are obtained using the seventh-order Runge–Kutta–Fehlberg method (RKF7) coupled with shooting quadrature. In order to compare our numerical results with the existing data, the active mass flux boundary condition is also used to benchmark MAPLE numerical solutions with earlier similar and non-similar solutions for a smooth stationary surface. It is found that the passive boundary condition reduces the skin friction and enhances local Nusselt numbers. Also the wavy surface is found to result in higher skin friction and higher local Nusselt numbers compared with a stationary surface. It is found that motile micro-organism density number is elevated with increasing bioconvection Péclet number whereas the motile micro-organism species boundary layer thickness is reduced with increasing bioconvection Lewis number. The work finds applications in heat transfer enhancement in bio-inspired nanoparticle-doped fuel cells.

Estimation of boundary-layer flow of a nanofluid past a stretching sheet: A revised model

The previous model for the boundary layer nanofluid flow past a stretching surface with a specified nanoparticle volume fraction on the surface is revisited. The major limitation of the previous model is the active control of the nanoparticle volume fraction on the surface. In a revised model proposed in this paper, the nanoparticle volume fraction on the surface is passively controlled, which accounts for the effects of both the Brownian motion and the thermophoresis under the boundary condition, whereas the Buongiorno's model considers both effects in the governing equations. The assumption of zero nanoparticle flux on the surface makes the model physically more realistic. In the revised model, the dimensionless heat transfer rates are found to be higher whereas the dimensionless mass transfer rates are identically zero due to the passive boundary condition. It is also found that the Brownian motion parameter has a negligible effect on the Nusselt number.

Solution of model equation of completely passive natural convection by improved differential transform method

In this paper we investigate the natural convection which exists under the Boussinesq approximation and completely passive boundary conditions. This phenomenon is applicable to the cooling of a heated body and heating and cooling of rooms and buildings and etc. The model equations of momentum and energy are solved by using improved differential transform method. This method is an iterative way for obtaining Taylor series coefficients. The convergence of the Taylor series is obtained by combining the method with the Least Square method for the problem first time here. The combination of these two powerful methods yields semi analytical solutions in the form of a polynomial through a straightforward manner. The efficiency and applicability of the algorithm are assessed and tested and error calculations have been presented.

Capillary-mediated dendritic branching

We consider the Gibbs-Thomson temperature distribution as an active interface energy field with gradients and fluxes. Capillarity in conventional dendritic growth theories acts only as a passive boundary condition on the transport field that conducts latent heat into the melt to drive the solidification. Instead, we find the vector divergence of capillary-mediated interface fluxes autonomously releases or withdraws energy along a curved solid-liquid interface. Local energy conservation (a Stefan balance) shows that capillary-mediated energy slightly retards, or enhances, the local freezing rate. At special points near the tip where the capillary-mediated energy release changes sign, the surface Laplacian of the Gibbs-Thomson potential vanishes. Locally adjacent freezing rates develop opposed biases from the added or subtracted capillary energies, which 'curl', or rotate, the solid-liquid interface. A noise-free Greens function dynamic solver confirms that the rotation points induce dendritic branching. Moreover, capillary-induced rotations occur precisely at points that may be calculated exactly for different initial shapes with different interface energy anisotropies. This mechanism appears to provide a deterministic process capable of inducing branching and evolving material-specific dendritic patterns. Noise and stability play no direct roles in dendritic morphogenesis.

Completely passive natural convection

AbstractWe show that a unique, nontrivial, natural convection state exists under the Boussinesq approximation and completely passive boundary conditions.

Boundary value problems for linear stochastic differential equations

This paper deals with methods for the solution of boundary value problems for linear systems of stochastic differential equations. We investigate numerical algorithms, the problem of existence and uniqueness of solutions and other specific problems (including stationary boundary value problems, reduction of a boundary value problem to a Cauchy problem, extended boundary value problems, active and passive boundary conditions, etc.).

An eddy‐permitting model of the Atlantic circulation: Evaluating open boundary conditions

As part of the French CLIPPER project, an eddy permitting model of the Atlantic circulation has been run for 22 years. The domain has open boundaries at Drake passage and at 30°E, from Africa to Antarctica. The simulated mean circulation, as well as the eddy activity, is satisfactory for a 1/3° model resolution, and the meridional heat transport at 30°S is within the range estimated from observations. We use the “mixed” open boundary algorithm of Barnier et al. [1998], which has both a radiation condition and a relaxation to climatology. The climatological boundary forcing strongly constrains the solution in the whole domain. The model heat balance adjusts through the surface (heat flux retroaction term) more than the open boundaries. The radiation phase velocities calculated within the algorithm are analyzed. This shows, quite surprisingly, that both the eastern and western boundaries have a similar behavior, regardless of the preferred directions for advection (mainly eastward) and wave propagation (mainly westward). Our results confirm that open boundary algorithms behave differently according to the dynamics of the region considered. The passive boundary condition that Penduff et al. [2000] applied successfully in the north eastern Atlantic does not work in the present South Atlantic model. We emphasize the need for a careful prescription of the climatology at the open boundary, for which a new approach based on synoptic sections is implemented.

Diffraction by a wedge with higher‐order boundary conditions

This paper presents a powerful analytical procedure that combines the higherorder boundary condition approximation and the modified Malyuzhinets technique to treat electromagnetic scattering from arbitrarily angled wedge‐like composite configurations with penetrable faces. The configuration may be either a perfectly conducting wedge covered with a dielectric/ferrite material or a composite wedge with strongly absorbing faces, so that the field transmitted directly through the configuration can be neglected. With special emphasis on retaining the passivity of the media interfaces, boundary conditions on the wedge faces are approximated using impedance conditions with higher‐order field derivatives. To close the formulation of the diffraction problem, a class of contact conditions is described that ensures the uniqueness and reciprocity. A general solution which is valid for passive boundary conditions of arbitrary odd orders is derived in an explicit form as the Sommerfeld integral involving arbitrary constants. By choosing these constants in such a way as to fit its analytical behavior for kr ≪ 1 to the exact one obtained by directly integrating the Maxwell equations, a specific form of the contact conditions can be deduced that reflects the design features of the configurations near their edges and forces the solution to be an asymptotic one for vanishing thicknesses of the coatings or skin layers. As a result, the unique and reciprocal closed‐form solution associated with third‐order boundary conditions is presented which uniformly describes the diffraction of an H‐ polarized plane electromagnetic wave by a variety of the composite wedge‐like structures with penetrable faces, extending thereby Malyuzhinets' solution for an impedance wedge to more sophisticated boundary conditions.

A Noise Source Identification Technique Using an Inverse Helmholtz Integral Equation Method

A technique is developed which utilizes numerical models and field pressure information to characterize acoustic fields and identify acoustic sources. The numerical models are based on boundary element numerical procedures. Either pressure, velocity, or passive boundary conditions, in the form of impedance boundary conditions, may be imposed on the numerical model. Alternatively, if no boundary information is known, a boundary condition can be left unspecified. Field pressure data may be specified to overdetermine the numerical problem. The problem is solved numerically for the complete sound field from which the acoustic sources may be determined. The model can then be used to identify acoustic intensity paths in the field. The solution can be modified and the model used to evaluate design alternatives. In this investigation the method is tested analytical and verified. In addition, the sensitivity of the method to random and bias error in the input data is demonstrated.