Sharif Digital Repository

An index for characterizing wettability of reservoir rocks is presented using slope analysis of spontaneous imbibition recovery data. The slope analysis is performed using the known exact analytical solution to infinite acting period of counter-current spontaneous imbibition. The proposed theoretically based wettability index offers some advantages over existing methods: (1) it is a better measure of the spontaneous imbibition potential of rock (because the magnitude is directly proportional to the imbibition rate); (2) there is no need for forced displacement data; (3) there is no need for waiting until the spontaneous imbibition process ceases completely; and (4) the data needed to run the... 

Particle capture at porous media in cross-flow microfiltration is studied to investigate permeability reduction as a function of membrane pore size and particle size distribution. A new model in pore scale and its pertinent mathematical expressions, which consider pore and particle size distribution, are provided. Permeability reduction of the membrane because of size exclusion during particulate suspension flow was predicted using the developed model. It is assumed that the size exclusion is the dominant mechanism of particle retention causes pore blocking and permeability reduction in the porous media.The exact analytical solution of the stochastic model for size exclusion is used to... 

Functionally graded materials (FGMs) have been introduced to significantly reduce the temperature and thermal stresses on structures at severe thermal loading. Design and development of FGMs as the heat treatable and energy-absorbing materials for high-temperature and thermal protection systems requires understanding of exact temperature and thermal stress distribution, in order to optimize their resistance to failure. In this study, transient temperature and associated thermal stresses in a functionally graded slab symmetrically heated on both sides are determined by separation of the variables scheme. This method is applied to the heat conduction equation in terms of heat flux for... 

The main contribution of this paper is to present a new set of approximate analytical solutions for the parameters of a photovoltaic (PV) five-parameter double-diode model that can be used as initial values for the numerical solutions based on the Newton-Raphson method. The proposed formulations are developed based on only the limited information given by the PV manufacturers, i.e., the open-circuit voltage (V), the short circuit current (I), and the current and voltage at the maximum power point (Im). Compared with the existing techniques that require the entire experimental I-V curve or additional information such as the slope of the I-V curves of the open circuit and the short circuit... 

Ring rolling is one of the most significant methods for producing rings with highly precise dimensions and superior qualities such as high strength uniformity, all accomplished without wasting any materials. In this article, we have achieved analytical formulas for calculating the pressure and shear friction over the contact arcs between the rollers and ring in the ring rolling process for the material in general nonlinear hardening property. We have also asserted the best mathematical model to predict friction for rolling processes. The method we use is based on calculating the analytical stress distribution. In other words, by using of Saint-Venan principal the stress components are... 

Approximate solutions for vibrations of flexible beam-type appendages subjected to tip mass are studied while uniform and exponential profiles for arm deployment are simulated. Applying an equivalent dynamical system and following Lagrangian approach, the equations of motion of the system are derived as nonlinear ordinary differential equations (ODEs) (with time-varying coefficients), in which the effect of the tip mass can be considered as some nonlinearity added to the 'no tip mass' case dynamics. The approximate closed-form solutions are obtained through a novel methodology using a computer algorithm, in which the solutions of the 'no tip mass' case are expanded by imposing quadratic... 

The purpose of this paper is to present efficient and accurate analytical expressions for deflection of a shape memory polymer (SMP) beam employing Euler-Bernoulli beam theory in a thermomechanical SMP cycle. Material behavior is considered using a recently 3D thermodynamically consistent constitutive model available in literature. In different steps of an SMP thermomechanical cycle, closed form expressions for internal variables variations, stresses and beam curvature distribution are presented. We show that during the cooling process, stored strains evolve to fix the temporary shape and then during the heating process they relax to recover the permanent shape. Effects of applying external... 

Non-linear bending analysis of tapered functionally graded (FG) beam subjected to thermal and mechanical load with general boundary condition is studied. The governing equations are derived and a discussion is made about the possibility of obtaining analytical solution. In the case of no axial force along the beam, a closed form solution is presented for the problem. For the general case with axial force, the Galerkin technique is employed to overcome the shortcoming of the analytical solution. Moreover, the Generalized Differential Quadrature (GDQ) method is also implemented to discretize and solve the governing equations in the general form and validate the results obtained from two other... 

The fresh groundwater lenses (FGLs) of small islands can be highly vulnerable to climate change impacts, including sea-level rise (SLR). Many real cases of atoll or sandy islands involve two-layer hydrogeological conceptualizations. In this paper, the influential factors that affect FGLs in two-layer small islands subject to SLR are investigated. An analytical solution describing FGLs in circular islands, composed of two geological layers, is developed for the simplified case of steady-state and sharp-interface conditions. An application of the developed model is demonstrated to estimate the FGL thickness of some real-world islands by comparison with existing FGL thickness data. Furthermore,... 

In this paper, an analytical solution is presented for free vibration and dynamic behavior of doubly curved laminated shell consisting of a functionally graded core layer and surface attached functionally graded piezoelectric layers. Shell through-thickness kinematics is based on higher order shear deformation theory of shells, whereas a quadratic variation is assumed for electric potential. Using Hamilton's principle and Maxwell's equation, the governing equations of motion under mechanical loads are derived as seven highly coupled partial differential equations. Implementing Laplace transformation, doing few mathematical operations and using Laplace inverse method, time dependencies of... 

An index for characterizing wettability of reservoir rocks is presented using slope analysis of spontaneous imbibition recovery data. The slope analysis is performed using the known exact analytical solution to infinite acting period of counter-current spontaneous imbibition. The proposed theoretically based wettability index offers some advantages over existing methods: (1) it is a better measure of the spontaneous imbibition potential of rock (because the magnitude is directly proportional to the imbibition rate); (2) there is no need for forced displacement data; (3) there is no need for waiting until the spontaneous imbibition process ceases completely; and (4) the data needed to run the... 

Tunnels constructed using New Austrian Tunnelling Method (NATM) are always based on certain round (unsupported) advance lengths, after which, the temporary lining is placed. The settlement of the ground surface resulting from such construction is of high significance in design and practice. The existing data in this respect, however, is scarce. It is the aim of this paper to propose a semi-analytical procedure based on three-dimensional finite element analyses to predict the maximum surface settlement of the ground in NATM tunnels under different combinations of tunnel diameter, overburden depth, round length and soil and lining properties. The comparison of the results with three case... 

The biomicrofluidic devices utilizing electrophoresis for sample manipulation are usually encountered with non-Newtonian behavior of working fluids. Hence, developing theoretical models capable of predicting the electrophoretic velocity of colloidal particles in non-Newtonian fluids is of high importance for accurate design and active control of these devices. The present investigation is dealing with the electrophoresis of a spherical particle in a biofluid obeying the Quemada rheological model. The sphere radius is considered to be significantly larger than the Debye length. Moreover, it is assumed that the particle zeta potential is small so that the Debye-Hückel linearization is... 

Particle capture at porous media in cross-flow microfiltration is studied to investigate permeability reduction as a function of membrane pore size and particle size distribution. A new model in pore scale and its pertinent mathematical expressions, which consider pore and particle size distribution, are provided. Permeability reduction of the membrane because of size exclusion during particulate suspension flow was predicted using the developed model. It is assumed that the size exclusion is the dominant mechanism of particle retention causes pore blocking and permeability reduction in the porous media.The exact analytical solution of the stochastic model for size exclusion is used to... 

Free vibration analysis of moderately thick rectangular FG plates on elastic foundation with various combinations of simply supported and clamped boundary conditions are studied. Winkler model is considered to describe the reaction of elastic foundation on the plate. Governing equations of motion are obtained based on the Mindlin plate theory. A semi-analytical solution is presented for the governing equations using the extended Kantorovich method together with infinite power series solution. Results are compared and validated with available results in the literature. Effects of elastic foundation, boundary conditions, material, and geometrical parameters on natural frequencies of the FG... 

A rather new semi-analytical method towards investigating the free vibration analysis of generally laminated composite beam (LCB) with a delamination is presented. For the first time the combined effects of material couplings (bending-tension, bending-twist, and tension-twist couplings) with the effects of shear deformation, rotary inertia and Poisson's effect are taken into account. The semi-analytical solution for the natural frequencies and mode shapes are presented by incorporating the constraint conditions using the method of Lagrange multipliers. To verify the validity and the accuracy of the obtained results, they were compared with the results from other available references. Very... 

An analytical solution for obtaining steady-state eddy-current-based force on a levitated permanent magnet above a plate with linear conductivity in the field of an electromagnet having cylindrical symmetry is presented in this paper. In literature, the force due to eddy current in this levitation system have been used for high precision positioning of a levitated permanent magnet without providing an explicit analytical model. In this system, a change in the coil's current and also the motion of the levitated permanent magnet in 3-D space generate eddy current in the plate. A novel explicit solution for obtaining damping forces due to these eddy currents is obtained as a function of... 

Rectangular plates on distributed elastic foundations are widely employed in footings and raft foundations of variety of structures. In particular, mounted columns and single footings may partially occupy the rectangular plate of any kind. This study deals with free vibration problem of thin rectangular plates on Winkler and Pasternak elastic foundation model which is distributed over a particular arbitrary area of the plate. Closed form solutions are developed through solving the governing differential equations of plates. Moreover, a novel mathematical approach is proposed to find the exact analytical solution of free vibration of plates with mixed or fully-clamped boundary conditions.... 

The equilibrium equations of the first-order nonlinear von Karman theory for FG circular plates under asymmetric transverse loading and heat conduction through the plate thickness are reformulated into those describing the interior and edge-zone problems of the plate. A two parameter perturbation technique, in conjunction with Fourier series method is used to obtain analytical solutions for nonlinear behavior of functionally graded circular plates with various clamped and simply-supported boundary conditions. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified with known... 

In this article, mixed-convective heat transfer of nanofluids in a vertical channel partially filled with highly porous medium was studied. In the porous region, the Brinkman-Forchheimer extended Darcy model was used to describe the fluid flow pattern. Different viscous dissipation models were also applied to account for viscous heating. At the porous medium-fluid interface, interfacial coupling conditions for the fluid velocity and temperature were used to derive the analytical solution using a two-parameter perturbation method. The model used for the nanofluids incorporates the effects of Brownian motion and thermophoresis. With constant wall temperature, velocity and temperature profiles...