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This paper seeks to investigate the effect of a heat conducting vertical partition in an enclosure on natural convection heat transfer and fluid flow using the polynomial‐based differential quadrature (PDQ) method.

The PDQ method with the non‐uniform Chebyshev‐Gauss‐Lobatto grid point distribution given below is used to transform the governing equations into a set of algebraic equations. After numerical discretization, the resulting algebraic equations are solved by the successive over‐relaxation iteration method.

It is found that the average Nusselt number decreases towards a constant value as the partition is distanced from the hot wall towards the middle of the enclosure. Furthermore, with decreasing thermal conductivity ratio, the average Nusselt number first increases and passes a peak point and then begins to decrease. The average heat transfer rate exhibits little dependence on the width of the partition in the range taken into consideration in this study for the thickness of the partition.

This study offers more knowledge on natural convection in partitioned enclosures.

The purpose of this paper is to study the generalized Couette flow of Eyring-Powell fluid. The paper aims to discuss diverse issues befell for the heat transfer, magnetohydrodynamics and slip.

A hybrid technique based on pseudo-spectral collocation is applied for the solution of nonlinear resulting system.

Viscous fluid results which are yet not available can be taken as a limiting case of presented problem. The results for the case of Hartmann flow can be obtained as a special case when plate velocity is zero, i.e. pressure gradient induced flow. The results for the zero fluid slip and no thermal slip also become special cases of this work, and the results can be recovered by setting, and to zero. These solutions are valid not only for small but also for large values of all emerging parameters.

This model is investigated for the first time, as the authors know.

The low Mach number approximation of the Navier—Stokes equations is of similar nature to the equations for incompressible flow. A major difference, however, is the appearance of a space‐ and time‐varying density that introduces a supplementary non‐linearity. In order to solve these equations with spectral space discretization, an iterative solution method has been constructed and successfully applied in former work to two‐dimensional natural convection and isobaric combustion with one direction of periodicity. For the extension to other geometries efficiency is an important point, and it is therefore desirable to devise a direct method which would have, in the best case, the same stability properties as the iterative method. The present paper discusses in a systematic way different approaches to this aim. It turns out that direct methods avoiding the diffusive time step limit are possible, indeed. Although we focus for discussion and numerical investigation on natural convection flows, the results carry over for other problems such as variable viscosity flows, isobaric combustion, or non‐homogeneous flows.

The purpose of this paper is to propose a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions of two-space-dimensional quasilinear hyperbolic partial differential equations subject to appropriate Dirichlet and Neumann boundary conditions.

The PDQM reduced the equations into a system of second order linear differential equation. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations.

The accuracy of the proposed method is demonstrated by several test examples. The numerical results are found to be in good agreement with the exact solutions. The proposed technique can be applied easily for multidimensional problems.

The main advantage of the present scheme is that the scheme gives very accurate and similar results to the exact solutions by choosing less number of grid points and the problem can be solved up to big time. The good thing of the present technique is that it is easy to apply and gives us better accuracy in less numbers of grid points as comparison to the other numerical techniques.

The purpose of this paper is to focus on the application of Chebyshev spectral collocation methodology with Gauss Lobatto grid points to micropolar fluid over a stretching or shrinking surface. Radiation, thermophoresis and nanoparticle Brownian motion are considered. The results have attainable scientific and technological applications in systems involving stretchable materials.

The model equations governing the flow are transformed into non-linear ordinary differential equations which are then reworked into linear form using the Newton-based quasilinearization method (SQLM). Spectral collocation is then used to solve the resulting linearised system of equations.

The validity of the model is established using error analysis. The velocity, temperature, micro-rotation, skin friction and couple stress parameters are conferred diagrammatically and analysed in detail.

The study obtains numerical explanations for rapidly convergent solutions using the spectral quasilinearization method. Convergence of the numerical solutions was monitored using the residual error analysis. The influence of radiation, heat and mass parameters on the flow are depicted graphically and analysed. The study is an extension on the work by Zheng et al. (2012) and therefore the novelty is that the authors tend to take into account nanoparticles, Brownian motion and thermophoresis in the flow of a micropolar fluid.

The purpose of this paper is to propose a new approach to determine the aeroelastic instability of truncated conical shells. In the proposed approach the governing equation of flutter for a truncated conical shell is established using Love's thin shell theory and the quasi-steady first-order piston theory.

The derivatives in both the governing equations and the boundary conditions are discretized with the differential quadrature method, and the critical flutter chamber pressure is obtained by eigenvalue analysis.

The influence of the shell geometry parameters, such as semi-cone angle, radius-thickness ratio and length-radius ratio, on the critical flutter chamber pressure is studied. Results are also presented to indicate the stabilizing effects of aerodynamic damping and the destabilizing effects of the curvature correction term of piston theory on flutter of truncated conical shell.

The present approach is an efficient method for the free vibration and flutter analysis of truncated conical shells due to its high order of accuracy and less requirement of virtual storage and computational effort.

This paper aims to reconstruct the spatially varying orthotropic conductivity based on a two-dimensional inverse heat conduction problem described by a partial differential equation (PDE) model with mixed boundary conditions. The proposed discretization uses a highly accurate technique and allows simple implementations. Also, the authors solve the related inverse problem in such a way that smoothness is enforced on the iterations, showing promising results in synthetic examples and real problems with moving heat source.

The discretization procedure applied to the model for the direct problem uses a pseudospectral collocation strategy in the spatial variables and Crank–Nicolson method for the time-dependent variable. Then, the related inverse problem of recovering the conductivity from temperature measurements is solved by a modified version of Levenberg–Marquardt method (LMM) which uses singular scaling matrices. Problems where data availability is limited are also considered, motivated by a face milling operation problem. Numerical examples are presented to indicate the accuracy and efficiency of the proposed method.

The paper presents a discretization for the PDEs model aiming on simple implementations and numerical performance. The modified version of LMM introduced using singular scaling matrices shows the capabilities on recovering quantities with precision at a low number of iterations. Numerical results showed good fit between exact and approximate solutions for synthetic noisy data and quite acceptable inverse solutions when experimental data are inverted.

The paper is significant because of the pseudospectral approach, known for its high precision and easy implementation, and usage of singular regularization matrices on LMM iterations, unlike classic implementations of the method, impacting positively on the reconstruction process.

The purpose of this paper is to propose a semi‐analytical method for studying the interaction between reservoir and concrete gravity dams.

The reservoir is assumed to be unbounded at the far end and the solution is sought for incompressible and in‐viscid fluid. A concrete gravity dam is assumed to behave as a cantilever beam of variable section, and the inclination of the neutral axis is ignored.

It is shown that use of the differential quadrature method (DQM), with a few grid points in conjunction with the finite difference method (FDM), yields an acceptable convergence of results. Comparing the results of the proposed method with those of the literature shows the competency of the method.

DQM for space derivatives and FDM for time derivatives are used to discretize the partial differential equation of motion.

Mathematical and numerical models are developed to study the melting of a Phase Change Material (PCM) inside a 2D cavity. The bottom of the cell is heated at constant and uniform temperature or heat flux, assuming that the rest of the cavity is completely adiabatic. The paper used suitable numerical methods to follow the interface temporal evolution with a good accuracy. The purpose of this paper is to show how the evolution of the latent energy absorbed to melt the PCM depends on the temperature imposed on the lower wall of the cavity.

The problem is written with non-homogeneous boundary conditions. Momentum and energy equations are numerically solved in space by a spectral collocation method especially oriented to this situation. A Crank-Nicolson scheme permits the resolution in time.

The results clearly show the evolution of multicellular regime during the process of fusion and the kinetics of phase change depends on the boundary condition imposed on the bottom cell wall. Thus the charge and discharge processes in energy storage cells can be controlled by varying the temperature in the cell PCM. Substantial modifications of the thermal convective heat and mass transfer are highlighted during the transient regime. This model is particularly suitable to follow with a good accuracy the evolution of the solid/liquid interface in the process of storage/release energy.

The time-dependent physical properties that induce non-linear coupled unsteady terms in Navier-Stokes and energy equations are not taken into account in the present model. The present model is actually extended to these coupled situations. This problem requires smoother geometries. One can try to palliate this disadvantage by constructing smoother approximations of non-smooth geometries. The augmentation of polynomials developments orders increases strongly the computing time. When the external heat flux or temperature imposed at the PCM is much greater than the temperature of the PCM fusion, one must choose carefully some data to assume the algorithms convergence.

Among the areas where this work can be used, are: buildings where the PCM are used in insulation and passive cooling; thermal energy storage, the PCM stores energy by changing phase, solid to liquid (fusion); cooling and transport of foodstuffs or pharmaceutical or medical sensitive products, the PCM is used in the food industry, pharmaceutical and medical, to minimize temperature variations of food, drug or sensitive materials; and the textile industry, PCM materials in the textile industry are used in microcapsules placed inside textile fibres. The PCM intervene to regulate heat transfer between the body and the outside.

The paper's originality is reflected in the precision of its results, due to the use of a high-accuracy numerical approximation based on collocation spectral methods, and the choice of Chebyshev polynomials basis in both axial and radial directions.

The focus of the paper is only on the contributions toward the use of entropy generation of non-Newtonian Casson fluid over an exponential stretching sheet. The purpose of this paper is to investigate the entropy generation and homogeneous–heterogeneous reaction. Velocity and thermal slips are considered instead of no-slip conditions at the boundary.

Basic equations in form of partial differential equations are converted into a system of ordinary differential equations and then solved using the spectral quasi-linearization method (SQLM).

The validity of the model is established using error analysis. Variation of the velocity, temperature, concentration profiles and entropy generation against some of the governing parameters are presented graphically. It is to be noted that the increase in entropy generation due to increase in heterogeneous reaction parameter is due to the increase in heat transfer irreversibility. It is further noted that the Bejan number decreases with Brinkman number because increase in Brinkman number reduces the total entropy generation.

This paper acquires realistic numerical explanations for rapidly convergent temperature and concentration profiles using the SQLM. Convergence of the numerical solutions was monitored using the residual error of the PDEs. The resulting equations are then integrated using the SQLM. The influence of emergent flow, heat and mass transfer parameters effects are shown graphically.