Narrow Results

In this paper, freezing through a cold storage unit is simulated, featuring a container equipped with branch-shaped fins attached to the lower cold surface. Conduction emerges as the primary influencer of the freezing process, leading to the simplification of governing equations and the adoption of the Galerkin method for numerical modeling. Notably, an adaptive grid is introduced to enhance accuracy, and the discretization of unsteady terms is achieved through implicit formulation. Rigorous validation against benchmark data attests to the reasonable accuracy of the numerical procedure. Innovatively, to enhance the efficiency of cold storage, nanoparticles are dispersed within the water, in addition to the strategic use of fins. Both methods contribute to enhancing the system’s performance by amplifying the conduction mode of heat transfer. Two key variables are considered: the volume fraction ($\varphi$) of the nanofluid and its shape factor (m). The study reveals that increasing $\varphi$ and m results in a lower period of freezing, showing reductions of approximately 1.81% and 17.59%, respectively.

A robust and reliable implicit method is proposed for application in data interpolation. The algorithm is based on a recently developed analytic approximation method, namely the distributed approximating functionals (DAFs), which is known to have the "well-tempered" property of UNIFORMLY approximating a function and its derivatives. In comparison with the conventionally used local explicit interpolation algorithms, the implicit method achieves much more accurate interpolation results because it couples all sample values (both known and unknown) in the domain of interest using a set of simultaneous linear algebraic equations. Due to the fact that the well-tempered DAFs also are very good low-pass filters, the performance of the DAF-based implicit method is not affected very much by the high frequency noise in the input signal. As an application, the proposed algorithm is applied to signals that are corrupted with impulse noise.

Local radial basis function-based differential quadrature (RBF-DQ) method is a natural mesh-free approach, in which any derivative of a function at a point is approximated by a weighted linear sum of functional values at its surrounding scattered points. In this paper, the weighting coefficients in the spatial derivative approximation of the Euler equation are determined by using a weighted least-square procedure in the frame of RBFs, which enhances the flexibility of distributing points in the computational domain. An upwind method is further introduced to cope with discontinuities by using Roe's approximate Riemann solver for estimation of the inviscid flux on the virtual mid-point between the reference knot and its surrounding knot. The lower–upper symmetric Gauss–Seidel (LU-SGS) algorithm, which is implemented in a matrix-free form like the one used in the finite-volume method, is introduced in the work to speed up the convergence. The proposed approach is validated by its application to simulate transonic flows over a NACA 0012 airfoil. It was found that the present mesh-free results agree very well with available data in the literature, and the implicit LU-SGS algorithm can greatly save the computational time as compared with explicit time marching methods.

The Duffing oscillator to combined deterministic and narrow-band random excitation, which is a nonlinear equation, is studied and solved numerically using three numerical methods based on finite difference schemes. Method 1, the well-known Euler method, is an explicit method; Method 2 is an implicit first-order method which does not bring contrived chaos into the solution; and Method 3 is based on two first-order methods which is second-order method and is chaos-free. In a series of numerical experiments, it is seen that the proposed methods have superior stability properties to those of the well-known Euler and fourth-order Runge-Kutta methods to which they are compared. When extended to the numerical solution of Duffing oscillator to combined deterministic and narrow-band random excitation, the developed methods give the correct steady-state solutions compared with the literature.

With a numerical method, the discharging process within a container with a double complex cold surface has been scrutinized in this paper. The inherent process makes conduction as the main mechanism and the temperature equation includes three terms and two of them are time-dependent which was discretized by means of implicit technique. Adding nanoparticles within water can enhance the rate of heat release and concentration of powders and their shapes can affect the properties of nanomaterial. Single phases for estimating the features of nanomaterial were applied. The maximum period of process takes 326.95s which is 1.36 times lower than the case of pure water. Increasing the shape factor can enhance the speed of process and its impact is less than concentration of additives.