An analysis for magnetic dipole with stagnation point flow of micropolar nanofluids is modeled for numerical computation subject to thermophoresis, multi buoyancy, injection/suction, and thermal radiation. The partial derivative is involved in physical consideration, which is transformed to format of ordinary differential form with the aid of similarity functions. The variational finite element procedure is harnessed and coded in Matlab script to obtain the numerical solution of the coupled non-linear ordinary differential problem. The fluid temperature, velocity, tiny particles concentration, and vector of micromotion are studied for two case of buoyancy (assisting 0<λ, and opposing 0>λ) through finite-element scheme. The velocity shows decline against the rising of ferromagnetic interaction parameter (β) (assisting 0<λ and opposing 0>λ), while the inverse behaviour is noted in micro rotation profile. Growing the thermo-phoresis and microrotation parameters receded the rate of heat transfer remarkable, and micromotion and fluid velocity enhance directly against buoyancy ratio. Additionally, the rate of couple stress increased against rising of thermal buoyancy (λ) and boundary concentration (m) in assisting case, but opposing case shows inverse behavior. The finite element scheme convergency was tested by changing the mesh size, and also test the validity with available literature.
Summary
An accurate estimate of the battery state of charge and state of health is critical to ensure the lithium‐ion battery's efficiency and safety. The equivalent circuit model‐based methods and data‐driven models show the potential for robust estimation. However, the state of charge and state of health estimation system's performance with a parallel comparison has been rarely investigated. In this study, the performances of state of charge and state of health with equivalent circuit model‐based methods and data‐driven estimations are analyzed by different aged and capacity batteries through methods including extended Kalman filters, fully connected deep network with drop methods, and the combination (extended Kalman filters—fully connected deep network with drop methods). Besides the battery state of the voltage and current, the relationship between inner resistance, temperature, and capacity are also considered. Finally, a suggested method is promising for online state estimation of battery working at different temperatures and initial working state. The results indicate that the maximum state of charge estimation errors of the fully connected deep network with drop methods is 0.56% for the fully charged battery. Simultaneously, with an uncertain initial state of charge, the extended Kalman filter shows the lowest maximum state of charge estimation errors (1.4%). For the state of health estimation, the optimized method uses extended Kalman filters to do the monitor first; after 5 testing points, if the state of health drops to lower than 0.95, extended Kalman filters—fully connected deep network with drop methods is suggested. And finally, estimation errors for this method decreased from 30% to 2%.
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