Regression and Artificial Intelligence Models to Predict the Surface Roughness in Additive Manufacturing

In additive manufacturing (AM), it is necessary to study the surface roughness, which affected the building parameters such as layer thickness and building orientation. Some AM machines have minimum layer thickness that doesn't satisfy the desired roughness. Also, it produces a fine surface that isn't required. This increases the building time and cost without any benefits. To overcome these problems and achieve a certain surface roughness, a prediction model is proposed in this chapter. Regression models were used to predict the surface roughness through the building orientation. ANN was used to predict the surface roughness through the building orientation and the layer thickness together. ANN was constructed based on experimental work that study the effect of layer thickness and building orientation on the surface roughness. Some data were used in the training process and others were used in the verification process. The results show that the layer thickness parameter has an effect more than the building orientation parameter on the surface roughness.

Impact of nanoparticle shape on magnetohydrodynamic stagnation-point flow of Carreau nanoliquid: A comparative study

In this paper, a numerical computational work is carried out to investigate the significance of nanoparticle shape on magnetohydrodynamic stagnation-point flow of Carreau nanoliquid caused by a horizontally moving thin needle. The drive and thermal transport nature of Ti6Al4V+Ethylene glycol nanoliquid under the stimulus of space-dependent heat source and magnetized force is discussed numerically. The novelty of this work is to obtain the simultaneous solutions for three different shapes of nanoparticles namely spherical, cylindrical and laminar. The flow governing partial differential equations are transformed into ordinary differential equations with appropriate similarity variables and solved numerically by using Runge–Kutta and Newton's approach. Numerical outcomes of velocity and thermal distributions under the influence of different physical parameters are illustrated via graphical trends, wall friction and rate of heat transfer are interpreted using tabular values. It reveals from results that the thermal transfer performance of the Carreau nanoliquid is advanced when spherical shaped nanoparticles are used as compared with cylindrical and laminar-shaped nanoparticles. Also, it is witnessed that needle thickness parameter plays vital role in augmenting thermal transport rate of the nanoliquid.

B2 Thickness Parameter Response to Equinoctial Geomagnetic Storms

The thickness parameters that most empirical models use are generally defined by empirical relations related to ionogram characteristics. This is the case with the NeQuick model that uses an inflection point below the F2 layer peak to define a thickness parameter of the F2 bottomside of the electron density profile, which is named B2. This study is focused on the effects of geomagnetic storms on the thickness parameter B2. We selected three equinoctial storms, namely 17 March 2013, 2 October 2013 and 17 March 2015. To investigate the behavior of the B2 parameter before, during and after those events, we have analyzed variations of GNSS derived vertical TEC (VTEC) and maximum electron density (NmF2) obtained from manually scaled ionograms over 20 stations at middle and low latitudes of Asian, Euro-African and American longitude sectors. The results show two main kinds of responses after the onset of the geomagnetic events: a peak of B2 parameter prior to the increase in VTEC and NmF2 (in ~60% of the cases) and a fluctuation in B2 associated with a decrease in VTEC and NmF2 (~25% of the cases). The behavior observed has been related to the dominant factor acting after the CME shocks associated with positive and negative storm effects. Investigation into the time delay of the different measurements according to location showed that B2 reacts before NmF2 and VTEC after the onset of the storms in all the cases. The sensitivity shown by B2 during the studied storms might indicate that experimentally derived thickness parameter B2 could be incorporated into the empirical models such as NeQuick in order to adapt them to storm situations that represent extreme cases of ionospheric weather-like conditions.

Spectral computation of reactive bi-directional hydromagnetic non-Newtonian convection flow from a stretching upper parabolic surface in non-Darcyporous medium

This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index [Formula: see text]1, whereas the reverse behavior is observed for stretching rate index [Formula: see text]1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

Boundary Layer Flow and Heat Transfer Analysis by Using the Correlation Coefficient and Regression Model Over a Stretching Bullet-Shaped Object

The boundary layer theory is important when fluid flows over a solid surface that is moving or stationary. In presence of the boundary layer, the effective shape of the body may change leading to changes in pressure distribution, as a result, the overall lift and drag forces change. Therefore, the Boundary layer theory helps in designing aerofoil’s, to compute the lift and drag forces for the aerospace and automobile designers, to control the heat transfer rate from the device, etc. So, the present problem will help design the various types of bullet-shaped objects in the field of automobile engineering. Therefore, the current problem has focused on the two-dimensional axisymmetric BL flow over a stretching bullet-shaped object for the effect of magnetic field strength (M), linear stretching parameter (M), and surface thickness parameter (s). Therefore, the main goal of this work is to determine the relation by applying the correlation coefficient among the physical parameters and velocity field, temperature field, shear stress (τw), Nusselt number (Nux). Hence, the novelty of the current paper is to develop the relationship among the dependent and independent parameters by the correlation coefficient and also developed the numerical method to solve these highly nonlinear equations. The numerical results are discussed for the three different values of the stretching ratio parameter and two values of the surface thickness parameter. The velocity and temperature distribution equations are compressed into a system of ODEs with similarity transformations. These ODEs are then solved using a spectral quasi-linearization method (SQLM) by applying Taylor series expansions that can be used to linearize the non-linear terms in the equations. These resulting linearized systems of equations are determined by the spectral collocation method. The convergence of the numerical solutions was performed by using the residual error of the PDEs. The error analysis is established for the validity of the present model. This error norm is applied to establish the validity and convergence of the numerical solution. The outcome of the mentioned dimensionless parameters over the fluid velocity field, temperature field, skin friction coefficient (Cf), and Nusselt number (Nux) are displayed graphically. It is observed that the parameters M and M are positively correlated with fluid velocity distribution within the BL but the surface thickness parameter(s) are negatively correlated. The rate of temperature increases for the parameter M and Pr but decreases for M and s. Therefore, the boundary layer thickness reduces for increasing the values of M and M but increases for increasing the values of s. The velocity of the fluid is about 80% higher in the case of a thinner surface (s = 0.2) than the thicker surface (s = 2.0) and the heat transfer rate is also igher in the case of a thinner surface comparatively thicker surface. The innovation of this present problem lies in the unification of more physical parameters into the governing equations and an attempt to give a thorough analysis of how the flow properties are affected by these parameters.

Computational Investigations of Arrhenius Activation Energy and Entropy Generation in A Viscoelastic Nanofluid Flow Thin Film Sprayed on A Stretching Cylinder

This paper investigates the two-dimensional and incompressible flow of viscoelastic nano-liquid dynamic and axisymmetric sprayed thin film deposit on a stretched cylinder. It also looked at how activation energy and entropy evaluation affected mass and heat flow. The governing equations are transformed into nonlinear differential equations using similarity transformation techniques, which are then resolved successively using a strong semi-analytical homotopy analysis method (HAM). The velocity decreases as the magnetic field strength and viscoelastic parameters are increased. The temperature rises as the Brownian motion parameter increases, while it falls as the Prandtl number, film thickness parameter, and thermophoresis parameter increase. The greater the Reynolds number and the activation energy parameter, the higher the concentration of nanoparticles. The film size increases nonlinearly with the spray rate. Entropy generation increases as the Brinkmann number, magnetic field, and thermal radiation parameters increase. A nearby agreement is signed after comparing the current investigation with published results. The results obtained, possibly under ideal conditions, could be useful for determining and architecting coating applications.

A novel formulation of 3D Jeffery fluid flow near an irregular permeable surface having chemical reactive species

The main objective of this paper is to offer a comprehensive study regarding solar radiation and MHD effects on 3D boundary layer Jeffery fluid flow over a non-uniform stretched sheet along with variable thickness, porous medium and chemical reaction of first order are assumed. The system of equations representing temperature, velocity and concentration fields are converted into dimensionless form by introducing dimensionless variables. Thereafter, the aforesaid equations are solved with the help of BVP4C in MATLAB. The numerical results obtained through this scheme are more accurate when compared with those in the existing literature. In order to have a pictorial representation, the effects of material and flow parameters on velocity, temperature and concentration profiles are presented through graphs. Moreover, the numerical values of heat and mass transfer rate and skin friction coefficient are given in tabular form. It is evident from the acquired results, that the velocity offers two fold behavior for variable thickness parameter that is, n < 1 close and away from the non-uniform surface. It is also noted that the axial and transverse velocities show an increasing behavior for Deborah number while the fluid temperature and concentration shows opposite behavior at the same time.

Numerical solutions of the flexure equation

The 4th order differential equation describing elastic flexure of the lithosphere is one of the cornerstones of geodynamics, key to understanding topography, gravity, glacial isostatic rebound, foreland basin evolution and a host of other phenomena. Despite being fully formulated in the 1940’s, a number of significant issues concerning the basic equation have remained overlooked to this day. We first explain the different fundamental forms the equation can take and their difference in meaning and solution procedures. We then show how numerical solutions to flexure problems in general as they are currently formulated, are potentially unreliable in an unpredictable manner for cases where the coefficient of rigidity varies in space due to variations of the elastic thickness parameter. This is due to fundamental issues related to the numerical discretisation scheme employed. We demonstrate an alternative discretisation that is stable and accurate across the broadest conceivable range of conditions and variations of elastic thickness, and show how such a scheme can simulate conditions up to and including a completely broken lithosphere more usually modelled as an end loaded, single, continuous plate. Importantly, our scheme will allow breaks in plate interiors, allowing for instance, the creation of separate blocks of lithosphere which can also share the support of loads. The scheme we use has been known for many years, but remains rarely applied or discussed. We show that it is generally the most suitable finite difference discretisation of fourth order, elliptic equations of the kind describing many phenomena in elasticity, including the problem of bending of elastic beams. We compare the earlier discretisation scheme to the new one in 1 dimensional form, and also give the 2 dimensional discretisation based on the new scheme.We also describe a general issue concerning the numerical stability of any second order finite difference discretisation of a fourth order differential equation like that describing flexure where contrasting magnitudes of coefficients of different summed terms lead to round off problems which in turn destroy matrix positivity. We explain the use of 128 bit, floating point storage for variables to mitigate this issue.