Applied Mathematics and Mechanics (English Edition)

Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface

T. HAYAT, S. NAZ, M. WAQAS, A. ALSAEDI

2018, 39(10): 1373-1384. doi:10.1007/s10483-018-2374-8

Abstract ( 589 )

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The effect of nonlinear mixed convection in stretched flows of rate-type nonNewtonian materials is described. The formulation is based upon the Maxwell liquid which elaborates thermal relation time characteristics. Nanofluid properties are studied considering thermophoresis and Brownian movement. Thermal radiation, double stratification, convective conditions, and heat generation are incorporated in energy and nanoparticle concentration expressions. A boundary-layer concept is implemented for the simplification of mathematical expressions. The modeled nonlinear problems are computed with an optimal homotopy scheme. Moreover, the Nusselt and Sherwood numbers as well as the velocity, nanoparticle concentration, and temperature are emphasized. The results show opposite impacts of the Deborah number and the porosity factor on the velocity distribution.

Stability of triple diffusive convection in a viscoelastic fluid-saturated porous layer

K. R. RAGHUNATHA, I. S. SHIVAKUMARA

2018, 39(10): 1385-1410. doi:10.1007/s10483-018-2376-8

Abstract ( 605 )

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The triple diffusive convection in an Oldroyd-B fluid-saturated porous layer is investigated by performing linear and weakly nonlinear stability analyses. The condition for the onset of stationary and oscillatory is derived analytically. Contrary to the observed phenomenon in Newtonian fluids, the presence of viscoelasticity of the fluid is to degenerate the quasiperiodic bifurcation from the steady quiescent state. Under certain conditions, it is found that disconnected closed convex oscillatory neutral curves occur, indicating the requirement of three critical values of the thermal Darcy-Rayleigh number to identify the linear instability criteria instead of the usual single value, which is a novel result enunciated from the present study for an Oldroyd-B fluid saturating a porous medium. The similarities and differences of linear instability characteristics of Oldroyd-B, Maxwell, and Newtonian fluids are also highlighted. The stability of oscillatory finite amplitude convection is discussed by deriving a cubic Landau equation, and the convective heat and mass transfer are analyzed for different values of physical parameters.

Scattering of Tollmien-Schlichting waves as they pass over forward-/backward-facing steps

Ming DONG, Anyong ZHANG

2018, 39(10): 1411-1424. doi:10.1007/s10483-018-2381-8

Abstract ( 613 )

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Forward-/backward-facing steps in boundary-layer flows are often seen in engineering applications, and they have potential impacts on laminar-turbulent transition through scattering of the oncoming instability modes (e.g., Tollmien-Schlichting (T-S) waves). This issue is studied in the present paper by applying a local scattering framework, which is a rather generic mathematical framework on describing the mode scattering process. In this framework, a high-Reynolds-number triple-deck formalism is employed, and a transmission coefficient, defined as the ratio of the asymptotic amplitude of the instability mode downstream of the step to that upstream, is introduced. Through the systematical study, it has been found that both the forward-and backward-facing steps have a destabilizing effect on the oncoming T-S waves in subsonic boundary layers, this effect increases with the height of the step and/or the frequency of the T-S wave, and a backward-facing step (BFS) always has a greater impact than a forward-facing step (FFS). These facts agree with most of the previous investigations. However, one numerical study (WORNER, A., RIST, U., and WAGNER, S. Humps/steps influence on stability characteristics of two-dimensional laminar boundary layer. AIAA Journal, 41, 192-197 (2003)), which was based on an ad-hoc configuration, showed an opposite impact of an FFS. Through the investigation on the specific configuration, it is revealed that the wrong conclusion was drawn by misinterpreting the numerical results.

Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das' nanofluid model

M. A. SHEREMET, R. TRÎMBIŢAŞ, T. GROŞAN, I. POP

2018, 39(10): 1425-1436. doi:10.1007/s10483-018-2377-7

Abstract ( 547 )

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The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls (wavy and undulation numbers) are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.

Control strategy of optimal deployment for spacecraft solar array system with initial state uncertainty

Xinsheng GE, Qijia YAO, Liqun CHEN

2018, 39(10): 1437-1452. doi:10.1007/s10483-018-2378-8

Abstract ( 466 )

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A control strategy combining feedforward control and feedback control is presented for the optimal deployment of a spacecraft solar array system with the initial state uncertainty. A dynamic equation of the spacecraft solar array system is established under the assumption that the initial linear momentum and angular momentum of the system are zero. In the design of feedforward control, the dissipation energy of each revolute joint is selected as the performance index of the system. A Legendre pseudospectral method (LPM) is used to transform the optimal control problem into a nonlinear programming problem. Then, a sequential quadratic programming algorithm is used to solve the nonlinear programming problem and offline generate the optimal reference trajectory of the system. In the design of feedback control, the dynamic equation is linearized along the reference trajectory in the presence of initial state errors. A trajectory tracking problem is converted to a two-point boundary value problem based on Pontryagin's minimum principle. The LPM is used to discretize the two-point boundary value problem and transform it into a set of linear algebraic equations which can be easily calculated. Then, the closed-loop state feedback control law is designed based on the resulting optimal feedback control and achieves good performance in real time. Numerical simulations demonstrate the feasibility and effectiveness of the proposed control strategy.

Effects of stress dependent electrochemical reaction on voltage hysteresis of lithium ion batteries

Haoliang LI, Yicheng SONG, Bo LU, Junqian ZHANG

2018, 39(10): 1453-1464. doi:10.1007/s10483-018-2373-8

Abstract ( 505 )

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Intercalation of lithium ions into the electrodes of lithium ion batteries is affected by the stress of active materials, leading to energy dissipation and stress dependent voltage hysteresis. A reaction-diffusion-stress coupling model is established to investigate the stress effects under galvanostatic and potentiostatic operations. It is found from simulations that the stress hysteresis contributes to the voltage hysteresis and leads to the energy dissipation. In addition, the stress induced voltage hysteresis is small in low rate galvanostatic operations but extraordinarily significant in high rate cases. In potentiostatic operations, the stresses and stress induced overpotentials increase to a peak value very soon after the operation commences and decays all the left time. Therefore, a combined charge-discharge operation is suggested, i.e., first the galvanostatic one and then the potentiostatic one. This combined operation can not only avoid the extreme stress during operations so as to prevent electrodes from failure but also reduce the voltage hysteresis and energy dissipation due to stress effects.

Analytical solution of time fractional Cattaneo heat equation for finite slab under pulse heat flux

Guangying XU, Jinbao WANG

2018, 39(10): 1465-1476. doi:10.1007/s10483-018-2375-8

Abstract ( 429 )

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A fractional Cattaneo model is derived for studying the heat transfer in a finite slab irradiated by a short pulse laser. The analytical solutions for the fractional Cattaneo model, the classical Cattaneo-Vernotte model, and the Fourier model are obtained with finite Fourier and Laplace transforms. The effects of the fractional order parameter and the relaxation time on the temperature fields in the finite slab are investigated. The results show that the larger the fractional order parameter, the slower the thermal wave. Moreover, the higher the relaxation time, the slower the heat flux propagates. By comparing the fractional order Cattaneo model with the classical Cattaneo-Vernotte and Fourier models, it can be found that the heat flux predicted using the fractional Cattaneo model always transports from the high temperature to the low one, which is in accord with the second law of thermodynamics. However, the classical Cattaneo-Vernotte model shows that the unphysical heat flux sometimes transports from the low temperature to the high one.

Fracture mechanics analysis of delamination in a thermoelectric pn-junction sandwiched by an insulating layer

Youjiang CUI, Kaifa WANG, Baoling WANG

2018, 39(10): 1477-1484. doi:10.1007/s10483-018-2379-8

Abstract ( 386 )

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A fracture mechanics analysis is conducted for a delamination problem of a multilayered thermoelectric material (TEM) that consists of an n-type layer and a p-type layer sandwiched by an insulating layer. A time-varying energy release rate is presented when the n-type layer delaminates from the insulating layer. Effects of the temperature difference across the system and the applied electric current on the energy release rate are identified. The influence of the thickness ratio of the insulating layer to the thermoelectric (TE) layer is also examined. Based on the energy release rate criterion, the critical temperature difference for delamination propagation is obtained. Some useful conclusions are given.

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

Libiao XIN, Yanbin LI, Dongmei PAN, Guansuo DUI, Chengjian JU

2018, 39(10): 1485-1498. doi:10.1007/s10483-018-2372-8

Abstract ( 514 )

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In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subject to a uniform magnetic field and inner-pressurized loads are studied. Rather than directly assume the material constants as some specific function forms displayed in pre-studies, we firstly give the volume fractions of different constituents of the functionally graded material (FGM) cylinder and then determine the expressions of the material constants. With the use of the Voigt method, the corresponding analytical solutions of displacements in the radial direction, the strain and stress components, and the perturbation magnetic field vector are derived. In the numerical part, the effects of the volume fraction on the displacement, strain and stress components, and the magnetic perturbation field vector are investigated. Moreover, by some appropriate choices of the material constants, we find that the obtained results in this paper can reduce to some special cases given in the previous studies.

Decay rates of higher-order norms of solutions to the Navier-Stokes-Landau-Lifshitz system

Ruiying WEI, Yin LI, Zheng'an YAO

2018, 39(10): 1499-1528. doi:10.1007/s10483-018-2380-8

Abstract ( 617 )

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In this paper, we investigate a system of the incompressible Navier-Stokes equations coupled with Landau-Lifshitz equations in three spatial dimensions. Under the assumption of small initial data, we establish the global solutions with the help of an energy method. Furthermore, we obtain the time decay rates of the higher-order spatial derivatives of the solutions by applying a Fourier splitting method introduced by Schonbek (SCHONBEK, M. E. L² decay for weak solutions of the Navier-Stokes equations. Archive for Rational Mechanics and Analysis, 88, 209-222 (1985)) under an additional assumption that the initial perturbation is bounded in L¹(R³).

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