Search

We study the bacterial respiration through the numerical solution of the Fairen–Velarde coupled nonlinear differential equations. The instantaneous concentrations of the oxygen and the nutrients are computed. The fixed point solution and the stable limit cycle are found in different parameter ranges as predicted by the linearized differential equations. In a specified range of parameters, it is observed that the system spends some time near the stable limit cycle and eventually reaches the stable fixed point. This metastability has been investigated systematically. Interestingly, it is observed that the system exhibits two distinctly different time scales in reaching the stable fixed points. The slow time scale of the metastable lifetime near the stable limit cycle and a fast time scale (after leaving the zone of limit cycle) in rushing towards the stable fixed point. The gross residence time, near the limit cycle (described by a slow time scale), can be reduced by varying the concentrations of nutrients. This idea can be used to control the harmful metastable lifespan of active bacteria. [ABSTRACT FROM AUTHOR]

The present exploration discusses the combined effect of non-linear thermal radiation along with viscous dissipation and magnetic field through a porous medium. A distinctive aspect of our work is the simultaneous use of porous wall and a porous material. The impact of thermal rays is essential in space technology and high temperature processes. At the point when the temperature variation is very high, the linear thermal radiation causes a noticeable error. To overcome such errors, nonlinear thermal radiation is taken into account. The coupled system of ordinary differential equations are derived from the partial differential equation. The dimensional model equations are transformed into non-dimensional forms using some appropriate non-dimensional transformation and the resulting nonlinear equations are solved numerically by executing persuasive numerical technique R-K integration procedure with the shooting method. Graphical analysis were used to assess the consequences of engineering factors for the momentum, angular velocity, concentration and temperature profiles. The skin friction values, local Sherwood and Nusselt number are the fascinating physical quantities whose numerical data are computed and validated against different parametric values. The vortex viscosity parameter and spin gradient viscosity parameter shows the reverse phenomenon on micro-rotation profile. The thermal radiation phenomena flattens the temperature and speeds up the heat transfer rate in the lower wall and a peak in the concentration is observed for the P e m > > 1 due to the inertial force. The Variational Iteration Method (VIM) and Adomian Decomposition Method (ADM) are the two analytical approach which have been incorporated here to decipher the non linear equations for showing better approximity. Comparisons with existing studies are scrutinized very closely and they are determined to be in good accord. [ABSTRACT FROM AUTHOR]

In the present study, heat transfer and fluid flow of a pseudo-plastic non-Newtonian nanofluid over permeable surface has been solved in the presence of injection and suction. Similarity solution method is utilized to convert the governing partial differential equations into ordinary differential equations, which then is solved numerically using Runge-Kutta-Fehlberg fourth-fifth order (RKF45) method. The Cu, CuO, TiO2 and Al2O3 nanoparticles are considered in this study along with sodium carboxymethyl cellulose (CMC)/water as base fluid. Validation has been done with former numerical results. The influence of power-law index, volume fraction of nanoparticles, nanoparticles type and permeability parameter on nanofluid flow and heat transfer was investigated. The results of the study illustrated that the flow and heat transfer of non-Newtonian nanofluid in the presence of suction and injection has different behaviors. For injection and the impermeable plate, the non-Newtonian nanofluid shows a better heat transfer performance compared to Newtonian nanofluid. However, changing the type of nanoparticles has a more intense influence on heat transfer process during suction. It was also observed that in injection, contrary to the other two cases, the usage of non-Newtonian nanofluid can decrease heat transfer in all cases. [ABSTRACT FROM AUTHOR]

• The combined effects of hybrid nanoparticles and the mixture base fluid are analyzed. • The hybrid phase (Al 2 O 3 – Cu) presents lower Skin friction coefficient to that obtained for the nano-phase (Cu). • The mixture base fluid (H 2 O − C 2 H 6 O 2) predicts lower Skin friction coefficient C f than base fluid (H 2 O). • DRA analytical solutions match perfectly with numerical results and those available in literature. • This comparison shows an excellent agreement is observed between the analytical and numerical solutions. The most important objective of this research-work is to investigate the impacts of velocity-slip boundary conditions and shape factor of solid nanoparticles on the hydrodynamic behavior of the nonlinear problem of MHD Jeffery–Hamel hybrid nanofluid flow where the mixture H 2 O - C 2 H 6 O 2 (50 % - 50 %) was utilized as a base fluid. Using appropriate velocity transformations, the basic partial differential equations arising from mathematical modeling are transformed into non-linear ordinary differential equations. Afterwards, the determined nonlinear equation was numerically solved utilizing Runge-Kutta-Fehlberg 4th–5th order approach featuring shooting technique and analytically with the help of Duan–Rach Approach (DRA). The impact of active factors like Reynolds number, channel half-angle, Hartman number, base fluids nature, hybrid nanoparticles, velocity-slip boundary conditions, shape and Geometry of solid nanoparticles on hybrid nanofluid velocity and skin friction coefficient are visualized and investigated. The minimal local skin friction is found to be obtainable with the nanoparticles of Platelet form and second-order slip model where a reduction of 70% is gained compared to the local skin friction coefficient with spherical nanoparticles when the Hartmann number is higher. Results obtained also reveal that a higher reduction of 69% in local skin friction coefficient intensity is observed for both hybrid phase Al 2 O 3 - C u and mixture base fluid H 2 O - C 2 H 6 O 2 with second-order slip boundary condition model when Knudsen number Kn = 0,08. A comparison was made between the results obtained from this investigation in particular cases and the results obtained via the HAM-based Mathematica package for validation. Also, the obtained analytical DRA data are compared with numerical RKF45 data and the ones represented in the literature. The comparison revealed that the results match perfectly which justifies applicability, validity, and the higher exactness of the adopted Duan-Rach approach. [ABSTRACT FROM AUTHOR]

Here formulation and computations are presented to introduce the novel concept of activation energy in chemically reacting stagnation point flow towards a stretching sheet. Constitutive expression for Cross liquid is taken into account. Magnetic field is utilised in the transverse direction. Application of suitable variables generates the non-linear differential systems. Numerical solution by Runge-Kutta-Fehlberg approach is presented. Characteristics for the significant variables like Weissenberg number, Hartmann number, Schmidt number, activation energy chemical reaction parameter, velocity ratio parameter and Prandtl number on the physical quantities are addressed through graphs and tables. Our computations reveal that species concentration rises via larger activation energy parameter whereas it decays when Schmidt number is incremented. The Weissenberg number has opposite characteristics for local Nusselt and Sherwood numbers when compared with surface drag force. [ABSTRACT FROM AUTHOR]

An analysis on the subject of “induced magnetic field effect on stagnation flow of a TiO2-Cu/water hybrid nanofluid over a stretching sheet” has been carried out in this paper. It should be noted that hybrid nanofluid consists of two or more types of nanoparticles along with a base fluid and it is used to increase the heat transfer. Furthermore, the non-linear differential equations modeling this issue are included in this article. In order to solve these equations numerically, Runge-Kutta Fehlberg method is used as a numerical method in this problem. The main objective of this paper is to investigate the effects of change in parameters of stretching ratio parameter (A ∗ ), nanoparticles volumetric fractions (∅ 2 ), magnetic parameter (β) and reciprocal magnetic Prandtl number (λ) on the functions including velocity, induced magnetic field and temperature for both Cu-water nanofluid and TiO2-Cu/water hybrid nanofluid. Also Lorentz force which is derived from magnetic field is mentioned in this section. In addition, the impacts of (∅ 2 ), (β) and (λ) on the profiles of nanofluid and hybrid nanofluid temperature for three categories of nanoparticle shapes named brick, cylinders, and platelets are analyzed. At the end, the influences of (∅ 2 ), (β) and (λ) on skin friction coefficient (C f ) and Nusselt number (Nu x ) for Cu-water nanofluid and TiO2-Cu/water hybrid fluid for different nanoparticles shapes are discussed. In all of these studies it can be seen that applying platelets shaped nanoparticles is more effective. [ABSTRACT FROM AUTHOR]

Abstract: The present work investigates an appropriate way to calculate the variations of nuclides composition in the reactor core during operations. Specific Software has been designed for this purpose using C#. The mathematical approach is based on the solution of Bateman differential equations using a Runge–Kutta–Fehlberg method. Material depletion at constant flux and constant power can be calculated with this software. The inputs include reactor power, time step, initial and final times, order of Taylor Series to calculate time dependent flux, time unit, core material composition at initial condition (consists of light and heavy radioactive materials), acceptable error criterion, decay constants library, cross sections database and calculation type (constant flux or constant power). The atomic density of light and heavy fission products during reactor operation is obtained with high accuracy as the program outputs. The results from this method compared with analytical solution show good agreements. [Copyright &y& Elsevier]

The main purpose of this article is to examine the flow and heat transfer of a squeezing unsteady nanofluid (F e 3 O 4 –water) between two parallel plates in the case where the thermal conductivity is a function of temperature and under a presence of the inclined magnetic field. The effects of the variable thermal conductivity and inclined magnetic field are conceived in ordinary nonlinear differential equations, which characterize the velocity and temperature distributions of the problem considered, this solved numerically via Runge–Kutta–Fehlberg based shooting method and analytically by analytical technique namely DTM method. On the other hand, as well as the influence of varying physical parameters such as: the volume fraction of the nanoparticles of the type magnetite (F e 3 O 4 ), Hartmann number, squeeze number, the angle of inclination of the applied magnetic field and conductivity parameter, the results obtained to highlight the effectiveness of the analytical technique adopted. The results found that F e 3 O 4 nanoparticles in (H 2 O) as base fluid enhances considerably the heat transfer features. The existence of variable thermal conductivity and an inclined magnetic field realize a decrease in heat transfer. • DTM is used to stimulate a squeezing unsteady nanofluid between two plates. • Variable thermal conductivity and magnetic field on F e 3 O 4 –water are considered. • DTM and RKF45 are compared. • F e 3 O 4 NPs in (H 2 O) enhances significantly the heat transfer characteristics. • Inclined magnetic field and the variable thermal conductivity decrease heat transfer. [ABSTRACT FROM AUTHOR]

On the basis of the error correction method developed recently, an algorithm, so-called error embedded error correction method, is proposed for initial value problems. Two deferred equations are used to approximate the solution and the error, respectively, at each integration step. For the solution, the deferred equation, which is based on a modified Euler’s polygon including the information of both the solution and its estimated error at the previous integration step, is solved with the classical fourth-order Runge-Kutta method. For the error, the deferred equation, which is based on a local Hermite cubic polynomial with three pieces of information—the solution, its estimated error at the previous step, and the constructed solution—is solved by the seventh-order Runge-Kutta-Fehlberg method. The constructed algorithm controls the error and possesses a good behavior of error bound in a long time simulation. Numerical experiments are presented to validate the proposed algorithm. [ABSTRACT FROM AUTHOR]