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The study of the blood flow through arterial walls is an important subject due to different chemical reactions and magnetohydrodynamic having an impact on the arterial walls during the treatment of cancer, malignant tumors, drug targeting and endoscopy. So, this paper aims to present a comprehensive investigation of the blood bioconvective flow of Carreau–Yasuda (C–Y) nanofluids in an arterial. Variable velocity conditions near the walls are considered. The flow domain is filled by a porous medium and a time-dependent magnetic field is assumed. The impacts of an exponential chemical reaction are considered and the viscous dissipation in the case of the C–Y model is formulated and examined. The fully implicit finite difference method is applied to solve the dimensionless governing system. The case of the shear thinning $(n=0.5)$ and shear thickening $(n=1.5)$ are analyzed for the variations of the governing parameters such as Weissenberg $(0.001\le \mathrm{\text{We}}\le 0.1)$ and parameter of the porous medium $(0\le \beta \le 2)$. The major outcomes revealed that the friction coefficient is improved as the C–Y parameter is raised. Also, values of heat and mass transfer are higher in the case of the shear thinning compared to the shear thickening.

In computational fluid dynamics (CFD), there is a transformation of methods over the years for building commercially coded software. Each method has predicted its own set of importance, but the exportation and prediction of data are some of the crucial elements for post-processing and validating results. In the present investigation, a detailed comparative analysis is performed over finite difference method (FDM) and finite volume method (FVM) method for the 1D steady-state heat conduction problem over a 1-m-long plate. The comparison was made between solution creation and validation between FDM and FVM for the analytical and computational scheme. The convergence-dependent study is performed as multi-objective optimization to predict how artificial neural network (ANN) can be used to verify and validate the solution of CFD.

Anomalous Reaction-Sub-diffusion equations play an important role transferred in a lot of our daily applications in our life, especially in applied chemistry. In the presented work, a modified type of these models is considered which is the Reaction-Sub-diffusion equation of variable order, the linear and nonlinear models and we will refer to it by VORSDE. An accurate technique depends on a mix of the finite difference methods (FDM) together with Hermite formula is introduced to study these important types of anomalous equations. Regarding the analysis of the stability for the mentioned, it is done using the variable Von-Neumann technique; also the convergent analysis is introduced. As a result of the previous steps, we derived a stability condition which will be held for many discretization schemes of the variable order derivative and some other parameters and we checked it numerically.

In this paper, FD formulations in cylindrical coordinates are used to model the field radiated, by a circular source, in fluid and solid media.

The stability of the used schemes is controlled by a proper choice of time and space steps. Absorbing boundary conditions are introduced to satisfy the assumption of a propagation in a half space medium. In order to minimize the CPU time, calculations are limited for regions disturbed by the propagating ultrasonic pulse then the calculus zone is incremented.

Some numerical results are presented to illustrate the effect of the medium nature, source vibration profiles and eventually the presence of targets in the acoustic field. A spatio-temporal description of the diffraction phenomena is given. The radiated field is interpreted in terms of plane and edge waves. For solid media, this interpretation allows the determination of the arrival times which are compared with those numerically predicted. Numerical results corresponding to fluid media are compared to those obtained by the Impulse Response Method. The good agreement obtained justifies the choice of the FDM for the modeling of the wave propagation problems.

Three-dimensional printers (3DP), which are often heard with additive manufacturing, are widely used in part production. Sensitive and custom-made products in different designs can be produced more easily and quickly, but waste specimen formed after the failed three-dimensional (3D) prints cause waste and environmental pollution from the expensive filament material. It is thought that such problems can be prevented by minimizing the waste when the scrap materials generated as a result of each production are recovered. This study investigated the benefits of recycling all possible waste filament specimens, including the supports removed from the part after the defective products or supported production, by granulating and reusing in the production of new parts in the next 3D production process. Mechanical differences between the 3D specimens produced with virgin filaments to be printed with recycled filaments are investigated and it has been determined that most of the countries cause environmental pollution due to the waste of materials including additive manufacturing and 3DP processes. The use of the filament material, which takes a long time to procure from abroad and is mainly procured externally, will be increased from one time to twice or thrice, thus facilitating the availability and preventing environmental pollution.

One of the most widely used 3D printing techniques is fused deposition modeling (FDM) which builds things layer by layer by dispensing molten materials through a heated nozzle. To showcase the flexibility of 3D printing, test samples were made using polylactic acid (PLA). Trial runs with Taguchi’s (L27) orthogonal array were performed. Layer thickness, printing speed, and carbon deposition (C-deposition) were the three input parameters that were improved. This was accomplished by combining principal component analysis (PCA) with multi-objective optimization based on ratio analysis (MOORA) in an integrated approach to multi-criteria optimization. The main goal of this study is to maximize the input parameters for the Industry 4.0 technological production process of embossing components. The MOORA-PCA technique finds the best combinations of process variables; for example, printing at a speed of 75mm/s, layer thickness of 0.1mm, and carbon content of 15mg yield the required results. The results of this study will help production managers and researchers choose the best FDM 3D printing methods for improving mechanical qualities and surface roughness. The economic feasibility of the 3D printing businesses may be strengthened by these research findings, which will benefit customers looking for ecologically friendly items.

This paper presents a blood-perfused skin model as implemented in a spreadsheet software application for accessing burn injuries resulting from exposure of skin surface to flowing hot fluids or constant heat sources. Finite-difference analysis of heat transfer in skin burns provides an accurate prediction of tissue time–temperature relationships throughout the duration of thermal insult. The Henriques theory of skin burns is used for determining the spatial and temporal extent of tissue damage. The epidermis, dermis, and subcutaneous fat were modeled as uniform elements with distinct thermal properties. Method for implementing finite-difference solution in spreadsheet software has been described. A comparison of the injury threshold computed by this model against Henriques's result has been done and the results are in good agreement.

This paper analyzes the interaction of high Rayleigh number flow with conjugate heat transfer. The two-relaxation time lattice Boltzmann is used as a turbulent buoyancy-driven flow solver whereas the implicit finite difference technique is applied as a heat transfer solver. An in-house numerical code is developed and successfully validated on typical CFD problems. The impact of the Biot number, heat diffusivity ratio and the Rayleigh number on turbulent fluid flow and heat transfer patterns is studied. It is revealed that the thermally-conductive walls of finite thickness reduce the heat transfer rate. The temperature of the cooled wall slightly depends on the value of the buoyancy force. The heat diffusivity ratio has a significant effect on thermal and flow behavior. The Biot number significantly affects the mean Nusselt number at the right solid–fluid interface whereas the mean Nusselt number at the left interface is almost insensible to the Biot number variation.

This paper provides an analysis of the numerical performance of a hybrid computational fluid dynamics (CFD) solver for 3D natural convection. We propose to use the lattice Boltzmann equations with the two-relaxation time approximation for the fluid flow, whereas thermodynamics is described by the macroscopic energy equation with the finite difference solution. An in-house parallel graphics processing unit (GPU) code is written in MATLAB. The execution time of every single step of the algorithm is studied. It is found that the explicit finite difference scheme is not as stable as the implicit one for high Rayleigh numbers. The most time-consuming steps are energy and collide, while stream, boundary conditions, and macroscopic parameters recovery are executed in no time, despite the grid size under consideration. GPU code is more than 30 times faster than a typical low-end central processing unit-based code. The proposed hybrid model can be used for real-time simulation of physical systems under laminar flow behavior and on mid-range segment GPUs.

This paper aims to look into the determination of effective area-average concentration and dispersion coefficient associated with unsteady flow through a small-diameter tube where a solute undergoes first-order chemical reaction both within the fluid and at the boundary. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer, and an irreversible component due to absorption into the wall. To understand the dispersion, the governing equations along with the reactive boundary conditions are solved numerically using the Finite Difference Method. The resultant equation shows how the dispersion coefficient is influenced by the first-order chemical reaction. The effects of various dimensionless parameters e.g. Da (the Damkohler number), α (phase partitioning number) and Γ (dimensionless absorption number) on dispersion are discussed. One of the results exposes that the dispersion coefficient may approach its steady-state limit in a short time at a high value of Damkohler number (say Da ≥ 10) and a small but nonzero value of absorption rate (say Γ ≤ 0.5).

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials of the third kind are used to reduce the proposed problem to a system of ODEs, which is solved by the finite difference method (FDM). Some theorems about the convergence analysis are stated and proved. A numerical simulation is given and the results are compared with the exact solution.

The present study carries out the comparison of the water level associated with the numerical methods: Finite Difference Method (FDM) and Finite Volume Method (FVM) and the simulation considered on the present climate condition along the coast of Bangladesh. The governing equations of the first model are discretized through FDM and solved by a conditionally stable semi implicit manner on an Arakawa C-grid system. For the second model, α-coordinate is used for the irrational bottom slope representation and the mesh grid of the study domain is generated by the unstructured triangular cells. The feasible study domain with coast and island boundaries are approximated through proper stair steps for the FDM and the unstructured mesh representation for FVM. A one-way nested scheme technique is applied to the first model to include coastal intricacies as well as to preserve computational cost. Both the models are applied to extrapolate sea-surface elevation associated with the catastrophic cyclone 1991(BOB 01) along the seashore of Bangladesh. The simulation results from both the models are statistically copacetic and make a good acquiescent with some observed and reported data. In the statistical viewpoint, both the method has a good acceptance in storm surge simulation, but this study ensures the strong positive reconciliation with observed data and FVM simulation data. In Bangladesh region, it will be wise decision to use Finite Volume Methods for simulating the storm surge.

Numerical simulation of thermal stress during casting solidification process can predict crack, residual stress concentration, deformation. Though stress simulation involves too many complex problems such as numerical model, mechanical boundary condition and high thermo-mechanical parameters, it still retains as a difficult hotspot of macro-simulation of casting nowadays. Based on finite difference method (FDM), a 3D FDM/FDM numerical simulation system for temperature and stress analysis during casting solidification process was developed. To verify the system, a standard stress frame model and a practical casting were simulated. Pouring experiments have been carried out in the laboratory. The results of simulation coincided with those obtained from experiment and practical results. When adopting FDM to calculate casting thermal stress, thermal analysis and stress analysis can use the same FD model, which can avoid matching between different models and reduce the errors of temperature load transferring. It makes the simulation of fluid-flow, temperature and stress unify into one model.