Transformation Magnetohydrodynamics in Presence of a Channel Filled with Porous Medium and Heat Transfer of Non-Newtonian Fluid by Using Lie Group Transformations

In this paper, the numerical results are presented by using Lie group transformations, to be more efficient and sophisticated. To solve various fluid dynamic problems numerically, we present the numerical results in a field of velocity and distribution of temperature for different parameters regarding the problem of radiative heat, a magnetohydrodynamics, and non-Newtonian viscoelasticity for the unstable flow of optically thin fluid inside a channel filled with nonuniform wall temperature and saturated porous medium, including Hartmann number, porous medium and frequency parameter, and radiation parameter, with a comparison of the corresponding flow problems for a Newtonian fluid. Moreover, the effects of the pertinent parameters on the friction coefficient of skin and local Nusselt number were discussed numerically and also illustrate that graphically

Numerical and Scientific Investigation of Some Molecular Structures Based on the Criterion of Super Classical Average Assignments

Numbering a graph is a very practical and effective technique in science and engineering. Numerous graph assignment techniques, including distance-based labeling, topological indices, and spectral graph theory, can be used to investigate molecule structures. Consider the graph G, with the injection Ω from the node set to 1,2,…,∆, where ∆ is the sum of the number of nodes and links. Assume that the induced link assignment Ω∗ is the ceiling function of the average of root square, harmonic, geometric, and arithmetic means of the vertex labels of the end vertices of each edge. If the union of range of Ω of the node set and the range of Ω of the link set is the set 1,2,…,∆, then Ω is called a super classical average assignment (SCAA). This is known as the SCAA criterion. In this study, the graphical structures corresponding to chemical structures based on the SCAA criterion are demonstrated. The graphical depiction of chemical substances was first defined and second, the union of any number of cycles Cn, the tadpole graph, the graph extracted by identifying a line of any two cycles Cm and Cn, and the graph extracted by joining any two cycles by a path are all examined in this work

Comparative Analysis of Darcy–Forchheimer Radiative Flow of a Water-Based Al₂O₃-Ag/TiO₂ Hybrid Nanofluid over a Riga Plate with Heat Sink/Source

The behavior of the Darcy–Forchheimer flow of a double-hybrid nanofluid toward a Riga plate with radiation and heat source/sink effects is investigated. The two different hybrid nanofluids, (Al2O3 and Ag) and (Al2O3 and TiO2) with a base fluid (H2O), are considered. The governing flow models with accompanying boundary constraints are reshaped into non-linear ODEs by applying the symmetry variables. The reshaped ODEs are numerically computed using Bvp4c in Matlab and the ND solver in Mathematica. The impact of the emerging parameters on the heat transfer, surface shear stress, temperature and velocity profile is scrutinized and expressed in a tabular and graphical structure. It is noticed that the upsurge of the Hartmann number leads to an improvement in the velocity profile. The velocity declines when enriching the porosity parameter. The radiation and Biot number lead to strengthening the temperature profile. The surface shear stress exalts due to a larger modified Hartman number. The radiation and unsteady parameters are downturns in the heat transfer gradient

A Novel Approach for Solving Fuzzy Differential Equations Using Cubic Spline Method

Ambiguity in real-world problems can be modeled into fuzzy differential equations. The main objective of this work is to introduce a new class of cubic spline function approach to solve fuzzy initial value problems efficiently. Further, the convergence of this method is shown. As it is a single-step method that converges faster, the complexity of the proposed method is too low. Finally, a numerical example is illustrated in order to validate the effectiveness and feasibility of the proposed method, and the results are compared with the exact as well as Taylor’s method of order two

Comparative Study on Thermal Transmission Aspects of Nano and Ferrofluid in Enclosures Holding Heat-Generating Body

The heat-transmission characteristics of Co ferrofluid and SiO2−water nanofluid are compared numerically inside enclosures including a heat-generating body. Using the finite-volume method, a steady laminar incompressible flow in two dimensions is solved. The numerical study is conducted to determine the impacts of the solid volume fraction (φ=0.02,0.1 and 0.2), the temperature-difference ratio (ΔT*=0,4 and 20), and the Rayleigh number (Ra=105,106 and 107) on both SiO2−water nanofluid and Co ferrofluid, respectively. In consideration of isothermal and streamlines contours, the aspects of temperature transmission and fluid flow are addressed. It is shown that there is no remarkable difference in the convection rate for both the fluids while increasing the Rayleigh number and temperature difference ratio

A Green Approach—Cost Optimization for a Manufacturing Supply Chain with MFIFO Warehouse Dispatching Policy and Inspection Policy

The present paper considers a manufacturing supply chain of deteriorating type inventories. The problem addresses the extra rented warehouse (RW) to store extra inventories if the manufacturer is producing more inventories than their owned warehouse (OW) capacity. Now, the problem is which inventories should be used first with minimum cost and minimum deterioration. To solve this problem, we have assumed a MFIFO (mixed first in first out) dispatching policy and constant demand rate over a finite time horizon. Along with these we have also assumed an inspection policy during the supply chain to separate deteriorated items and a carbon tax policy is also considered to control carbon emissions. The rate of deterioration depends on the number of inspections. If the number of inspections increases, it minimizes the rate of the decaying process. Due to the adoption of the inspection policy, the supply chain moves toward a green supply chain as it removes deteriorated inventories that minimize further decay by contact, and simultaneously separated deteriorated products can be utilized for other purposes that solve the problem of the disposal of deteriorating inventories and reduce emission generation. We have also established the uniqueness of the established model. The motto of solving the mathematical model is to find the values of the optimum value of N, the number of cycles, and n, the number of inspections that helps to minimize total cost. At last, we illustrate the result with the help of a numerical example

Hyers–Ulam Stability of Additive Functional Equation Using Direct and Fixed-Point Methods

In this present work, we obtain the solution of the generalized additive functional equation and also establish Hyers–Ulam stability results by using alternative fixed point for a generalized additive functional equation χ∑g=1lvg=∑1≤g<h<i≤lχvg+vh+vi−∑1≤g<h≤lχvg+vh−l2−5l+2/2∑g=1lχvg−χ−vg/2. where l is a nonnegative integer with ℕ−0,1,2,3,4 in Banach spaces

Thermal Behavior of the Time-Dependent Radiative Flow of Water-Based CNTs/Au Nanoparticles Past a Riga Plate with Entropy Optimization and Multiple Slip Conditions

This communication deliberates the time-reliant and Darcy–Forchheimer flow of water-based CNTs/gold nanoparticles past a Riga plate. In addition, nonlinear radiation, heat consumption and multiple slip conditions are considered. Entropy generation is computed through various flow parameters. A suitable transformation with symmetry variables is invoked to remodel the governing mathematical flow models into the ODE equations. The homotopy analysis scheme and MATLAB bvp4c method are imposed to solve the reduced ODE equations analytically and numerically. The impact of sundry flow variables on nanofluid velocity, nanofluid temperature, skin friction coefficient, local Nusselt number, entropy profile and Bejan number are computed and analyzed through graphs and tables. It is found that the nanofluid velocity is reduced by greater porosity and slip factors. The thickness of the thermal boundary layer increases with increasing radiation, temperature ratio, and heat consumption/generation parameters. The surface drag force is reduced when there is a higher Forchheimer number, unsteadiness parameter and porosity parameter. The amount of entropy created is proportional to the radiation parameter, porosity parameter and Reynolds number. The Bejan number profile increases with radiation parameter, heat consumption/generation parameter and the Forchheimer number

Thermally Radiative Darcy–Forchheimer Flow of <i>Cu</i>/<i>Ag</i> Nanoliquid in Water Past a Heated Stretchy Sheet with Magnetic and Viscous Dissipation Impacts

This communication predominately discusses the rheological attributes of the Darcy–Forchheimer flow of a nanoliquid over a stretchy sheet with a magnetic impact. The present model considers the two diverse nanoparticles, such as Cu and Ag, and water as a base liquid. The heat equation accounts for the consequences of thermal radiation and a nonlinear heat sink/source when evaluating heat transmission phenomena. The current mechanical system is represented by higher-order PDEs, which are then remodeled into nonlinear higher-order ODEs that employ appropriate symmetry variables. The current mathematical systems are numerically computed by implementing the bvp4c technique. The characteristic attitudes of the related pertinent factors on the non-dimensional profiles are sketched via the figures, tables, and charts. The analysis predicts that the speed of the nanoliquid particles becomes slower when there is more presence of a magnetic field and injection/suction parameters. The growing amount of radiation is also pointed out, and the Eckert number corresponds to enriching the thermal profile

Dynamics of a Novel IVRD Pandemic Model of a Large Population over a Long Time with Efficient Numerical Methods

The model of any epidemic illness is evolved from the current susceptibility. We aim to construct a model, based on the literature, different to the conventional examinations in epidemiology, i.e., what will occur depends on the susceptible cases, which is not always the case; one must consider a model with aspects such as infections, recoveries, deaths, and vaccinated populations. Much of this information may not be available. So without artificially assuming the unknown aspects, we frame a new model known as IVRD. Apart from qualitative evaluation, numerical evaluation has been completed to aid the results. A novel approach of calculating the fundamental reproduction/transmission range is presented, with a view to estimating the largest number of aspects possible, with minimal restrictions on the spread of any disease. An additional novel aspect of this model is that we include vaccines with the actively infected cases, which is not common. A few infections such as rabies, ebola, etc., can apply this model. In general, the concept of symmetry or asymmetry will exist in every epidemic model. This model and method can be applied in scientific research in the fields of epidemic modeling, the medical sciences, virology, and other areas, particularly concerning rabies, ebola, and similar diseases, to show how immunity develops after being infected by these viruses