Chemically Reactive MHD Eyring-Powell Nanofluid Flow past a Stretching Surface with Convergence Test

The motive of this work is to examine the transfer of heat as well as mass phenomena of Eyring-Powell fluid flow on a stretching type of porous medium. The impact of heat absorption and thermal radiation are also considered here to describe the characteristics of the fluid flow. Firstly, a mathematical model of this fluid flow is established which includes time dependent continuity, energy, momentum and concentration formula. Then the fundamental equations are formed to dimensionless format. After that an explicit type finite difference technique is imposed to solve the model by taking the help of FORTRAN. The stability as well as convergence analysis (SCA) is used to develop and check the precession of the overall system. Moreover, the fields of temperature, velocity, concentration, skin friction, Nusselt number and Sherwood number got affected significantly with the influences of various pertinent parameters which are presented in different color diagrams. However, the updated visualization of the fluid flows is also presented by both isotherms and streamlines for the impact of radiation parameter. Moreover, for Eyring-Powell fluid, an interesting observation has been made that the thermophoretic parameter is influencing the temperature field significantly rather than the Brownian parameter. Finally, for the validation of the ongoing investigation, a suitable comparison is also depicted with some published papers and a proper agreement is noticed.

Numerical Simulation Study on the Recovery Process of Autonomous Underwater Vehicle

AUV (Autonomous Underwater Vehicle) recovery is considerably influenced by the nearby flow field and simulations of AUV in different motion paths in the wake of a submarine with a propeller are presented in this paper. A commercial CFD solver STAR CCM+ has been used to research the motion and flow characteristics of AUV, which using the advanced computational continuum mechanics algorithms. The DARPA (Defense Advanced Research Projects Agency) SUBOFF Submarine (L1 = 4.356m) propelled with INSEAN (Italian Ship Model Basin) E1619 propeller is used in this study, and the self-propulsion characteristics of the propeller at an incoming flow velocity of 2.75m/s are obtained through numerical simulation and results are compared with the available experimental data to prove the accuracy of the chosen investigation methodology. A grid/time-step convergence test is performed for verification study. AUV (L2 = 0.4356m) is a smaller-scale SUBOFF without a sail, which approaches the submarine in different motion paths in the submarine wake at a relative speed combined with the dynamic overlapping grid technology. The hydrodynamic performance of the AUV when approaching the submarine and the velocity distribution of the surrounding flow field are analyzed, which provides a useful reference for underwater recovery of the AUV.

Errors In Using Convergence Tests In Infinite Series

The present study aimed to identify the errors made by pre-service elementary mathematics teachers while investigating the convergence of infinite series. A qualitative exploratory case study design was used with a total of 43 undergraduate students. Data were obtained from a test administered in a paper-and-pencil form consisting of seven open-ended questions. The data analysis was done using descriptive and content analysis techniques. Findings were presented as follows: inappropriate test selections; failure to check convergence criteria; incorrect use of a comparison test; limit comparison test error; re-test convergence test results; considering ∑ as a multiplicative function; misunderstanding of special series; considering that series has no character when the convergence test is inconclusive; confusing sequences with series; misunderstanding of the nth-term test; misinterpretation of convergence test results. Findings showed that students with insufficient procedural knowledge had difficulty in solving the given problem even if they understood it, whereas those with insufficient conceptual knowledge could not literally understand what they did even if they solved the problem. Therefore, the establishment of a moderate balance between procedural and conceptual knowledge in the learning of the convergence of series is essential in reducing the errors or learning difficulties for developing deep mathematical understanding

On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence

This paper presents a general formulation of the classical iterative-sweep power flow, which is widely known as the backward–forward method. This formulation is performed by a branch-to-node incidence matrix with the main advantage that this approach can be used with radial and meshed configurations. The convergence test is performed using the Banach fixed-point theorem while considering the dominant diagonal structure of the demand-to-demand admittance matrix. A numerical example is presented in tutorial form using the MATLAB interface, which aids beginners in understanding the basic concepts of power-flow programming in distribution system analysis. Two classical test feeders comprising 33 and 69 nodes are used to validate the proposed formulation in comparison with conventional methods such as the Gauss–Seidel and Newton–Raphson power-flow formulations.

Integrated Software Development and Case Studies for Optimal Operation of Cascade Reservoir within the Environmental Flow Constraints

Reservoir optimal operation considering aquatic ecological protection is a hot topic in current research. This paper proposes an improved minimum monthly average runoff method (IMMR) for calculating environmental flow and an improved invasive weed optimization algorithm (IIWO) for optimizing complex problems. An integrated software consists of three modules, which is developed in this paper, i.e., IIWO convergence test module, environmental flow calculation module, and cascade reservoir operation module. Three test functions are included in the IIWO convergence test module. The minimum monthly average runoff method (MMR), IMMR, Tennant Method, Q90, and Q95 are included in the environmental flow calculation module. The IIWO and invasive weed optimization algorithm (IWO) are included in the cascade reservoir operation module. Wujiang River Basin in China is studied as a case in this paper. The results show that the environmental flow of cascade reservoir calculated by IMMR is 1871 m3/s, the maximum and the minimum are calculated by T-O and T-M, respectively. The power generation of cascade reservoir calculated by IWO is less than IIWO. The conclusions that IIWO has better convergence than IWO in solving cascade reservoir model, and the water volume of environmental flow has no obvious influence on cascade reservoir operation are drawn.