Sinusoidal Boundary Research Articles

Mathematical Models on Mechanics of Biofluids

In this work, we study the mathematical models of flows for some biofluids. In biomechanics, peristaltic flow plays an important role in which the motion generated in the fluid contained in a distensible tube when a progressive wave of area contraction and expansion travels along the wall of the tube. We consider the effect of elasticity of the tube wall in the flow through the progressive wave travelling along its length without its direct calculation. Since the no – slip condition has used on a moving undulating wall surface, it determines the sinusoidal boundary conditions on the upper and lower wall of the tube. The wide occurrence of peristaltic motion gives its result physiologically from neuro-muscular properties of any tubular smooth muscle.

Comparison between shear-driven and pressure-driven oscillatory flows over ripples

Direct numerical simulations of oscillatory flow over a bed made of ripples have been performed. Two oscillatory flow forcing mechanisms have been compared: (i) a sinusoidal external pressure gradient (pressure-driven flow); and (ii) a sinusoidal velocity boundary conditions on the rippled bed (shear-driven flow). In the second case, the oscillations of the bed are such that when observed from a reference frame fixed with the bed, the free stream follows the same harmonic oscillation as in the pressure-driven case. While the outer layers have the same dynamics in the two cases, close to the bed differences are observed during the cycle, mostly because the large form drag across the ripples cannot be reproduced in the shear-driven case. A comparison against experimental data from an oscillating tray apparatus provides a relatively good agreement for the phase-averaged flow when the same forcing is considered (i.e. a shear-driven flow). The pressure-driven case has a comparable error to the shear-driven numerical results over the crest of the ripples, whereas the discrepancy is larger at the troughs. The discrepancies between the two cases are more limited for time-averaged flow quantities, such as the mean flow pattern and the time-averaged Reynolds stress distribution. This suggests that numerical or experimental shear-driven configurations may capture well the net effects of coastal transport processes (which occur in pressure-driven oscillatory flow), but care should be exercised in interpreting phase-dependent dynamics near the troughs. More work is needed to fully assess the sensitivity to the forcing mechanisms in different flow regimes.

Multi-objective optimization of porous fins in closed cavity with heat source of sinusoidal periodic temperature boundary condition

Multi-objective optimization of porous fins in closed cavity with heat source of sinusoidal periodic temperature boundary condition

Periodic driving shape controls energy transmission.

In the early 2000s, Geniet and Leon [Phys. Rev. Lett. 89, 134102 (2002)0031-900710.1103/PhysRevLett.89.134102] discovered the nonlinear supratransmission (NST) in a medium with a forbidden frequency band gap. It is a process in which nonlinear structures are created by a sinusoidal harmonic boundary condition imposed at a frequency in the band gap. The present study extends this concept and shows that an optimal shape of a periodic nonsinusoidal excitation may induce (or inhibit) energy flow through the lattice below (or above) the NST threshold, demonstrating that nonlinear supratransmission is reliant not only on the driving amplitude but also on its shape. This is evidenced through numerical simulations and mathematical calculations varying the excitation signal shape in the Fermi-Pasta-Ulam case study. Setting the shape parameter to zero recovers the results of the literature in relation to the sinusoidal signal.

Comparing sensitivities of groundwater head to variations in hydraulic parameters under boundary conditions of river stage rise and tidal variation

The sensitivity of hydraulic head responses to spatially distributed hydraulic parameters is essential for uncertainty analysis, inverse modeling, and parameter estimation and interpretation. This study formulates the Fréchet sensitivity kernel of hydraulic head responses to a suddenly rising boundary and a sinusoidal head fluctuation boundary to variation of spatially distributed hydraulic parameters in a semi-infinite, one-dimensional (1-D), confined aquifer, and it then derives analytical solutions. Different from previous studies that derived expressions for Fréchet kernels in the time domain for a 2-D pumping test, this study is the first to derive the closed-form Fréchet kernels in time and frequency domains for a semi-infinite, 1-D, confined aquifer. This study uses the Fréchet kernels to investigate the nature of singularities in the spatial sensitivity functions around the observation location and boundary. The information content revealed by observation of head change or head fluctuation amplitude at a given specified location and time (or frequency) under the above two boundary conditions is different. When comparing Fréchet sensitivity kernels across various times or periods, multi-frequency information, much like multi-time information, can be instrumental for hydrogeological parameter inversion. The explicit-form Fréchet sensitivity kernels also identify the optimal time or period for obtaining measurements.

Natural convective heat transfer of Al2O3-Cu/water hybrid nanofluid in a rectotrapezoidal enclosure under the influence of periodic magnetic field

This study seeks to examine quantitatively the two-dimensional unsteady free convective heat transfer enhancement of Al2O3-Cu/H2O hybrid nanofluid within a rectotrapezoidal-shaped structure. The lower wall is both uniformly and non-uniformly heated with different thermal boundary conditions, the top horizontal wall is adiabatic, and the vertical and inclined walls are assumed chilly. The enclosure is penetrated by a periodic magnetic field. A set of variable transformations is used to render the governing equations dimensionless, which makes it possible to identify the model parameters that control it. The finite element method is then used to numerically solve these equations. To verify the code's numerical precision, comparisons with formerly available works are performed and, a high level of agreement is obtained among the results. The generated outcomes are shown for the principal parameters that control the flow in the context of streamlines, heat lines, isotherms, average Nusselt number, friction factor, and thermal efficiency index. The findings demonstrated that the efficiency index, friction factor, and heat transmission are all considerably influenced by the Rayleigh number (Ra). The lowest Ra yields the maximum thermal efficiency. The results also revealed that the hybrid nanoparticle volume fraction and period of the magnetic field amplified the heat transfer rate and efficiency index due to the increased pumping force. It is observed that when the percentage of the mixing ratios for Cu nanoparticles rises from 0% to 100%, the heat transport in Al2O3-Cu/H2O hybrid nanofluid increases for a fixed volume fraction of hybrid nanoparticles. As compared to parabolic and sinusoidal boundary conditions, the uniform temperature boundary setting for Ra = 105 exhibits the highest average rate of heat transport of 10.04. The average Nusselt number increases by 25.12% at Ra = 103 with a 3% volume fraction of hybrid nanofluid as compared to pure water and the mixing ratios of Al2O3:Cu = 0:300 gives the highest increased rate of 16.30%. The results further illustrate that Al2O3-Cu/H2O hybrid nanofluid has the highest heat transfer rate compared to the pure water and Al2O3– H2O nanofluid.

Time-periodic natural convection in a pentagonal house with pitched roof during one day

A numerical investigation of unsteady natural convective flow and heat transfer in a pentagonal house is performed. We set a sinusoidal periodic heat flux boundary condition for the pitched roof. Local radial basis function method and Fourier spectral method are adopted to solve the governing equations. The Rayleigh number varies from 103 to 105, the period of the roof heat flux ranges from 10 to 1,000, and the amplitude is set as 0.1, 0.3, and 0.5, respectively. It is found that all the control parameters significantly impact the fluid flow and heat transfer. The temperature and flow fields exhibit periodic behavior due to the sinusoidal heat source. The increasing Rayleigh number leads to a larger periodic average Nusselt number of the top and right walls and a smaller value of the bottom wall. Moreover, an obvious hysteresis phenomenon of heat transfer occurs especially for high Rayleigh number and large period.

A phase change material based annular thermoelectric energy harvester from ambient temperature fluctuations: Transient modeling and critical characteristics

Annular thermoelectric power generator has been increasingly considered in application of ambient energy harvesting owing to the advantages of simple structure and no pollution. To improve thermal stability and energy harvesting performance of this system, the latent heat of phase change materials to improve thermal management and the high thermal conductivity of the heat sink to enhance heat transfer with the ambient are harness to annular thermoelectric power generator. Motivated by this, a phase change material based annular thermoelectric energy harvester (PCM-ATEH) with fins is developed for ambient energy harvesting and its three-dimensional transient model is also built up through jointly with thermo-electric and phase change processes. This paper considers the influence of key parameters such as temperature fluctuation amplitude, temperature fluctuation period, height ratio of PCM and thermoelectric generator (TEG) and melting temperature on liquid fraction, temperature difference, voltage and power density. Moreover, the comparison of PCM-ATEH and PCM based thermoelectric energy harvester (PCM-TEH) with/without fins is further conducted in this study to explore thermal management and energy harvesting performance. The energy harvesting characteristics of PCM-ATEH with fins is developed concerning the combination of power generation of TEG and melting process of PCM. Based on the results, it is found that the temperature difference and power density of PCM-ATEH with fins vary periodically with the sinusoidal temperature boundary, and results show that increasing temperature fluctuation period is not always feasible. Additionally, the comparative results indicate that the peak power density and energy efficiency of PCM-ATEH with fins are increased by 0.126 W/m2 and 0.02 % compared with PCM-TEH with fins, and increased by 0.195 W/m2 and 0.041 % compared with PCM-ATEH without fins. The results of energy harvesting characteristics show that a maximum of 0.77$ per watt can be reached to power generation cost of PCM-ATEH with fins. This paper can provide theoretical guidance for thermal management and energy conversion of energy harvesting system.

Prabhakar fractional approach for enhancement of heat transfer due to hybrid nanomaterial with sinusoidal heat conditions

The thermal improvement in heat transfer investigation using a hybrid nanofluid model is investigated. In a class of hybrid nanofluid, aluminum oxide, and titanium oxide nanoparticles are used. Kerosene oil and water decomposition are used in hybrid nanoparticles. The analysis is carried out for sinusoidal boundary constraints. Moreover, the current phenomenon's gravitational impact and magnetic force features are disclosed. The porous inclined surface, which moves with a sinusoidal pattern, endorsed the flow. The dimensionless system with suitable variables is achieved. The fractional framework with generalized Prabhakar model is used for the solution procedure. The basic concept of the fractional approach is presented. The physical contribution of parameters is observed for analyzing the thermal phenomenon.

Numerical simulation of mass and heat transport phenomena of hydromagnetic flow of Casson fluid with sinusoidal boundary conditions

AbstractA magnetic field might interact with its surroundings, influencing chemical and physical processes in materials processing, heat exchangers, and other scientific study. Therefore, a computational study of non‐Newtonian (Casson) free convective MHD unsteady fluid flow has been highlighted in this article with mass and heat transit property through a vertical infinite porous plate. A sinusoidal boundary conditions as well as chemical reaction and thermal radiation have been considered. Using a collection of nondimensional variables, the flow related equations are also turned into nondimensional form. The EFDM algorithm is employed in order to arrive at a numerical solution via Compaq Visual Fortran. The reliability of the numerical solution has been confirmed using stability testing and convergence analysis. The whole system is convergent when the values of Prandtl number and Lewis number are greater than or equals to 0.075 and 0.025, respectively. A visual depiction of the impact of the pertinent factors on dimensionless velocity, temperature, and concentration profiles are displayed through graphical representation as well as with tabular representation. It has been inspected that when the magnetic component is regarded, it greatly affects the heat transfer factors of Casson nanofluid and the heat also rises when Eckert number, heat source and radiation parameter accelerate. It is also found that the Sherwood number is increased as the impact of chemical reaction parameter and the Lewis number, also the skin friction is decreased as the influence of porosity term got accelerated. The comparison of the current findings with the data that were previously published serves as the final stage in validating the present study.

Solution of Water and Sodium Alginate-Based Casson Type Hybrid Nanofluid with Slip and Sinusoidal Heat Conditions: A Prabhakar Fractional Derivative Approach

This paper aims to investigate free convection heat transmission in hybrid nanofluids across an inclined pours plate, which characterizes an asymmetrical hybrid nanofluid flow and heat transfer behavior. With an angled magnetic field applied, sliding on the border of walls is also considered with sinusoidal heat transfer boundary conditions. The non-dimensional leading equations are converted into a fractional model using an effective mathematical fractional approach known as the Prabhakar time fractional derivative. Silver (Ag) and titanium dioxide (TiO2) are both considered nanoparticles, with water (H2O) and sodium alginate (C6H9NaO7) serving as the base fluids. The solution of the momentum, concentration, and energy equation is found by utilizing the Laplace scheme, and different numerical algorithms are considered for the inverse of Laplace, i.e., Stehfest and Tzou’s. The graphical analysis investigates the impact and symmetry of significant physical and fractional parameters. Consequently, we surmise that water-based hybrid nanofluid has a somewhat higher velocity than sodium alginate-based hybrid nanofluid. Furthermore, the Casson parameter has a dual effect on the momentum profile. Furthermore, the memory effect reduces as fractional restriction increases for both the velocity and temperature layers. The results demonstrate that increasing the heat transmission in the solid nanoparticle volume fractions enhanced the heat transmission. In addition, the numerical assessment examined the increase in mass and heat transmission, while shear stress was increased with an increase in the Prabhakar fractional parameter α.

Numerical Study on Heat-Transfer Characteristics of Convection Melting in Metal Foam under Sinusoidal Temperature Boundary Conditions.

Convection melting in metal foam under sinusoidal temperature boundary conditions is numerically studied in the present study. A multiple-relaxation-time lattice Boltzmann method, in conjunction with the enthalpy approach, is constructed to model the melting process without iteration steps. The effects of the porosity, phase deviation, and periodicity parameter on the heat-transfer characteristics are investigated. For the cases considered in this work, it is found that the effects of the phase deviation and periodicity parameter on the melting rate are weak, but the melting front can be significantly affected by the sinusoidal temperature boundary conditions.

Fluid–Structure Interaction Model for Assessing Aneurysm Initiation at the Circle of Willis

Abstract Hemodynamics associated with the arteries of the circle of Willis (CoW) is analyzed to identify possible cerebral aneurysm initiation locations using computational methods. A numerical fluid–structure interaction model is developed using an idealized geometry with the linear elastic, isotropic arterial wall. Blood flow is assumed to be laminar, incompressible, and modeled using Navier–Stokes equations, non-Newtonian viscosity, and sinusoidal boundary conditions. Available analytical and experimental results are used for the validation of the model. The highest wall shear stress (WSS) and von Mises stress (VMS) are identified for understanding the most vulnerable sites. The WSS distribution in the entire CoW region shows that ACoA junction has the highest value and risk of aneurysm initiation. The flow patterns created due to the geometrical features of the CoW seem to be the significant factor in the distribution of WSS. It is noticed that a decrease in wall elasticity will reduce the magnitude of WSS, both the temporal and spatial averaged value. The wall weakening effects are more pronounced for the posterior communicating artery. The wall weakening creates changes in core velocity and WSS. Changes in Von Mises stress are also noticed due to wall weakening effects. Highly localized VMS is noticed at ACoA and could possess a higher risk for aneurysm initiation and rupture. Despite the simplifications involved in developing the fluid–structure interaction model, this work demonstrates the critical locations at the CoW region regarding aneurysm initiation.

Eigenfunction-based solution for solid-liquid phase change heat transfer problems with time-dependent boundary conditions

Solid-liquid phase change heat transfer problems appear in a broad variety of engineering systems, such as thermal management and latent energy storage. Boundary conditions in such systems often vary with time, for example, due to sinusoidal heating, or step changes in externally applied temperature or heat flux. Unfortunately, phase change problems with time-dependent boundary conditions do not generally admit an exact solution, and therefore, approximate analytical solutions are of much interest. This paper presents an eigenfunction expansion based technique for solving one-dimensional phase change heat transfer problems with time-dependent temperature or heat flux boundary conditions. The temperature field is expressed as a series solution of appropriate eigenfunctions, and with time-dependent coefficients, which are determined by deriving and solving an ordinary differential equation that accounts for the time-dependent nature of the boundary condition. Solutions for Cartesian, cylindrical and spherical problems are derived. Results are found to be in excellent agreement with past work and numerical simulations. The effect of Stefan problem on the nature of phase change propagation is studied. Two practical problems involving sinusoidal and step function boundary conditions are also solved and analyzed in detail. In addition to improving the fundamental understanding of phase change heat transfer, this work may also contribute towards design and optimization of practical engineering problems involving phase change heat transfer.

Thermal analysis of simultaneously evolving laminar pulsatile flow through two large parallel plates with time-dependent heat flux boundary conditions

Understanding unsteady convective heat transfer (UCHT) behavior of simultaneously evolving laminar pulsatile flow between two large parallel plates exposed to time-dependent thermal boundary conditions is the goal of this research. The time-dependent sinusoidal velocity waveform is applied at the entrance of the two large parallel plates exposed to time-dependent sinusoidal heat flux boundary conditions (TSHBC). The finite volume technique is used in the present work. The current results have been compared to the literature data under the same operating conditions and found to be in good concurrence. The influence of various parameters, for instance, amplitude, frequency, phase difference, heat flux ratio, and the Reynolds number on the transient Nusselt number, is investigated. An improvement in energy transfer is observed when the pulsatile flow between two large parallel plates with TSHBC than the non-pulsatile flow with a fixed heat flux type boundary. Furthermore, the energy transfer improvement is observed once the velocity and heat flux waveform frequency is equal. The applicability of the present work could be found in the solar heating system, cooling of electronic devices, etc., whereby a more robust understanding of the unsteady convective heat transfer could facilitate the design and develop an efficient system.

Time-periodic thermal rectification in heterojunction thermal diodes

Thermal diodes that rectify time-periodic temperature (T) fields have been proposed for applications in waste heat scavenging and thermal control. Although these applications involve transient temperatures, prior analytical solutions for heat conduction in thermal diodes have focused on the steady-state response. We use analytical perturbation methods supported by finite-element method (FEM) calculations to study time-periodic rectification in a one-dimensional heterojunction diode consisting of two materials with thermal conductivity k and heat capacity c that each scale linearly with T. One boundary of the diode experiences a sinusoidal boundary condition with an average temperature T0, an angular frequency ω, and a temperature amplitude ΔT, while the other boundary is maintained at a constant T0. The analytical perturbation solution shows that the nonlinear response has frequency components at direct current (dc) and at the second harmonic of ω for small ΔT/T0. We introduce a rectification asymmetry metric φ as the difference in the forward and reverse diode orientation dc heat fluxes and find that φ can be enhanced at large ω by a factor of two compared to the quasi-steady φ at small ω. We identify the optimal dimensionless parameters to maximize φ and find that φ is independent of the heat capacity temperature coefficient for all ω. We use FEM calculations to validate the perturbation solution and to study the effects of larger ΔT oscillations, interface thermal contact resistances, and heat losses. Our modeling results can be used to design heterojunction thermal diodes for applications and experiments involving time-periodic thermal rectification.

Convection Inside Nanofluid Cavity with Mixed Partially Boundary Conditions

In recent decades, research utilizing numerical schemes dealing with fluid and nanoparticle interaction has been relatively intensive. It is known that CuO nanofluid with a volume fraction of 0.1 and a special thermal boundary condition with heat supplied to part of the wall increases the average Nusselt number for different aspect ratios ranges and for high Rayleigh numbers. Due to its simplicity, stability, accuracy, efficiency, and ease of parallelization, we use the thermal single relaxation time Bhatnagar-Gross-Krook (SRT BGK) mesoscopic approach D2Q9 scheme lattice Boltzmann method in order to solve the coupled Navier–Stokes equations. Convection of CuO nanofluid in a square enclosure with a moderate Rayleigh number of 105 and with new boundary conditions is highlighted. After a successful validation with a simple partial Dirichlet boundary condition, this paper extends the study to deal with linear and sinusoidal thermal boundary conditions applied to part of the wall.

Acoustic tweezing of microparticles in microchannels with sinusoidal cross sections

Acoustic tweezing of bioparticles has distinct advantages over other manipulation methods such as electrophoresis or magnetophoresis in biotechnological applications. This manipulation method guarantees the viability of the bio-particles during and after the process. In this paper, the effects of sinusoidal boundaries of a microchannel on acoustophoretic manipulation of microparticles are studied. Our results show that while top and bottom walls are vertically actuated at the horizontal half-wave resonance frequency, a large mono-vortex appears, which is never achievable in a rectangular geometry with flat walls and one-dimensional oscillations. The drag force caused by such a vortex in combination with the tilted acoustic radiation force leads to trapping and micromixing of microparticles with diameters larger and smaller than the critical size, respectively. Simulation results in this paper show that efficient particle trapping occurs at the intermediate sinusoidal boundary amplitudes. It is also indicated that in a square-sinusoidal geometry there are two strong vortices, instead of one vortex. Sub-micrometer particles tend to be trapped dramatically faster in such a geometry than in the rectangular-sinusoidal ones.

Automation of the heated floor system in a room under the influence of ambient conditions

Energy consumption for cooling and heating buildings should be reduced in the future to maintain suitable indoor thermal comfort at a lower cost. Numerical simulation of heat transfer within building systems can help to design the energy-efficient buildings. This article presents a fundamental theoretical research done to understand the effect of automation of the underfloor heating system in a room under the influence of ambient conditions on heat transfer. The considered physical process has been described mathematically taking into account the turbulent natural convection and thermal surface radiation within an air filled enclosure having a panoramic window. Sinusoidal boundary condition has been applied to the external surface of panoramic window to model the possible diurnal ambient temperature oscillation. An automation of the underfloor heating system is determined by the heater volumetric heat flux that magnitude depends on the ambient conditions. The governing equations with boundary conditions have been solved numerically by the finite-difference method. The influence of the relevant parameters, viz., surface emissivity, length of underfloor heating system and ambient boundary conditions has been investigated in detail. Distributions of integral and local characteristics illustrating flow and thermal structures in the large-scale enclosure have been studied. The contribution of the thermal radiative mechanism to the overall heat transfer is close in magnitude to the convective heat transfer even under normal room conditions.

Bénard-Taylor ferroconvection with time-dependent sinusoidal boundary temperatures

The combined effect of centrifugal acceleration and time-varying boundary temperatures on the onset of convective instability of a rotating magnetic fluid layer is investigated by means of the regular perturbation method. A perturbation expansion in terms of the amplitude of applied temperature field is implemented to effectively deal with the effects of temperature modulation. The criterion for the threshold is established based on the condition of stationary instability manifesting prior to oscillatory convection. The modulated critical Rayleigh number is computed in terms of Prandtl number, magnetic parameters, Taylor number and the frequency of thermal modulation. It is shown that subcritical motion exists only for symmetric excitation and the destabilizing effect of magnetic mechanism is perceived only for asymmetric and bottom wall excitations. It is also delineated that, for bottom wall modulation, rotation tends to stabilize the system at low frequencies and the opposite is true for moderate and large frequencies. Furthermore, it is established that, notwithstanding the type of thermal excitation, the modulation mechanism attenuates the influences of both magnetic stresses and rotation for moderate and large frequencies.