Effects of Heat Generation/Absorption on Magnetohydrodynamics Flow Over a Vertical Plate with Convective Boundary Condition

Heat generation effect in a steady two-dimensional magnetohydrodynamics (MHD) flow over a moving vertical plate with a medium porosity has been studied. By similarity transformation variables, the coupled non-linear ordinary differential equations describing the model are obtained. The resulting equation is then solved, using Galerkin Weighted Residual Method (GWRM), where the effect of heat generation, Magnetic Parameter as well as other physical parameters encountered were examined and discussed. Some of the major findings were that increase in heat generation and convective heat parameter enhances the plate surface temperature as well as temperature field which allows the thermal effect to penetrate deeper into the quiescent fluid.

Fluid relaxation and retardation time properties in the flow of Burgers fluid subject to modified heat and mass flux theory

In this study, the heat transport is scrutinized in the flow of magnetized Burgers fluid accelerated by stretching cylinder. Rather than, classical Fourier's and Fick's laws, the Cattaneo-Christov theory featuring the improved heat and mass conduction is utilized to investigate the energy transport. Further, the transport of thermal and solutal energy is controlled by the significant influence of heat generation/absorption and chemical reaction. The physical flow problem is modelled in the form of partial differential equations (PDEs) which are then transformed into the non-linear ordinary differential equations (ODEs) by invoking appropriate similarity variables. The numerical simulation to the system of ODE's is tackled by employing BVP-Midrich scheme in Maple. The numerical results for flow field, thermal and concentration distributions are exhibited graphically. The impact of fluid relaxation and retardation time parameters on the velocity field are observed in growing and decaying way, respectively. Both the thermal and solutal energy transport decline with higher values of retardation time parameter. The rise in Burgers fluid parameter enhances the transport of energy during the fluid motion. The effect of thermal and solutal relaxation time parameters on heat and mass transport in the fluid are noticed in the declining manner.

A mathematical model for the dependence of keratin aggregate formation on the quantity of mutant keratin expressed in EGFP-K14 R125P keratinocytes

We examined keratin aggregate formation and the possible mechanisms involved. With this aim, we observed the effect that different ratios between mutant and wild-type keratins expressed in cultured keratinocytes may have on aggregate formation in vitro, as well as how keratin aggregate formation affects the mechanical properties of cells at the cell cortex. To this end we prepared clones with expression rates as close as possible to 25%, 50% and 100% of the EGFP-K14 proteins (either WT or R125P and V270M mutants). Our results showed that only in the case of the 25% EGFP-K14 R125P mutant significant differences could be seen. Namely, we observed in this case the largest accumulation of keratin aggregates and a significant reduction in cell stiffness. To gain insight into the possible mechanisms behind this observation, we extended our previous mathematical model of keratin dynamics by implementing a more complex reaction network that considers the coexistence of wild-type and mutant keratins in the cell. The new model, consisting of a set of coupled, non-linear, ordinary differential equations, allowed us to draw conclusions regarding the relative amounts of intermediate filaments and aggregates in cells, and suggested that aggregate formation by asymmetric binding between wild-type and mutant keratins could explain the data obtained on cells grown in culture.

Heat Transfer Exploration of MHD Flow Stream with Changing Viscosity and Thermal Conductivity due to Expandable Surface

In this paper an examination is completed to explore the influence of variable thickness and variable thermal conductivity on MHD stream. We have considered the governing stream and heat transfer conditions as partial differential equations. These non-linear partial differential equations are changed to non-linear ordinary differential equations at that point explained numerically utilizing fourth order RK strategy with shooting procedure. The influence of governing factors on velocity and temperature is concentrated through diagrams and numerical estimations of skin frictions and wall temperature inclination are determined, classified and examined.

Calculation of special functions arising in the problem of diffraction by a dielectric ball

To apply the incomplete Galerkin method to the problem of the scattering of electromagnetic waves by lenses, it is necessary to study the differential equations for the field amplitudes. These equations belong to the class of linear ordinary differential equations with Fuchsian singularities and, in the case of the Lneburg lens, are integrated in special functions of mathematical physics, namely, the Whittaker and Heun functions. The Maple computer algebra system has tools for working with Whittaker and Heun functions, but in some cases this system gives very large values for these functions, and their plots contain various kinds of artifacts. Therefore, the results of calculations in the Maple11 and Maple2019 systems of special functions related to the problem of scattering by a Lneburg lens need additional verification. For this purpose, an algorithm for finding solutions to linear ordinary differential equations with Fuchsian singular points by the method of Frobenius series was implemented, designed as a software package Fucsh for Sage. The problem of scattering by a Lneburg lens is used as a test case. The calculation results are compared with similar results obtained in different versions of CAS Maple. Fuchs for Sage allows computing solutions to other linear differential equations that cannot be expressed in terms of known special functions.

Guaranteed Estimation of Solutions to the Cauchy Problem When the Restrictions on Unknown Initial Data Are Not Posed

The paper deals with Cauchy problems for first-order systems of linear ordinary differential equations with unknown data. It is assumed that the right-hand sides of equations belong to certain bounded sets in the space of square-integrable vector-functions, and the information about the initial conditions is absent. From indirect noisy observations of solutions to the Cauchy problems on a finite system of points and intervals, the guaranteed mean square estimates of linear functionals on unknown solutions of the problems under consideration are obtained. Under an assumption that the statistical characteristics of noise in observations are not known exactly, it is proved that such estimates can be expressed in terms of solutions to well-defined boundary value problems for linear systems of impulsive ordinary differential equations.

A Comparison Study of Numerical Techniques for Solving Ordinary Differential Equations Defined on a Semi-Infinite Domain Using Rational Chebyshev Functions

A rational Chebyshev (RC) spectral collocation technique is considered in this paper to solve high-order linear ordinary differential equations (ODEs) defined on a semi-infinite domain. Two definitions of the derivative of the RC functions are introduced as operational matrices. Also, a theoretical study carried on the RC functions shows that the RC approximation has an exponential convergence. Due to the two definitions, two schemes are presented for solving the proposed linear ODEs on the semi-infinite interval with the collocation approach. According to the convergence of the RC functions at the infinity, the proposed technique deals with the boundary value problem which is defined on semi-infinite domains easily. The main goal of this paper is to present a comparison study for differential equations defined on semi-infinite intervals using the proposed two schemes. To demonstrate the validity of the comparisons, three numerical examples are provided. The obtained numerical results are compared with the exact solutions of the proposed problems.

Flow and Heat Transfer of MHD Dusty Nanofluid Toward Moving Plate with Convective Boundary Condition

This paper considers the flow and heat transfer characteristics of dusty nanofluid over a moving plate in the presence of magnetohydrodynamic (MHD) with convective boundary condition. Two types of nanofluid namely CuO-water and Al2O3-water permeated with dust particles are considered. The governing partial differential equations are converted into a system of non-linear ordinary differential equations using similarity transformation, then the non-linear ordinary differential equations are solved using shooting method with fourth-fifth order Runge-Kutta Fehlberg method (RKF45). The influence of non-dimensional governing parameters such as velocity ratio parameter, magnetic field parameter, volume fraction of the nanoparticle, volume fraction of the dust particle, mass concentration of the dust particle, fluid particle interaction parameter for velocity, fluid particle interaction parameter for temperature and Biot number on the velocity and temperature profiles for fluid and dust phases of CuO-water and Al2O3-water dusty nanofluids are discussed and presented through graphs. The skin friction coefficient and Nusselt number are discussed and presented in tabular form.