Search

This paper investigates the heat transfer of two-phase nanofluid flow between horizontal plates in a rotating system with a magnetic field and external forces. The basic continuity and momentum equations are considered to formulate the governing mathematical model of the problem. Furthermore, certain similarity transformations are used to reduce a governing system of non-linear partial differential equations (PDEs) into a non-linear system of ordinary differential equations. Moreover, an efficient stochastic technique based on feed-forward neural networks (FFNNs) with a back-propagated Levenberg–Marquardt (BLM) algorithm is developed to examine the effect of variations in various parameters on velocity, gravitational acceleration, temperature, and concentration profiles of the nanofluid. To validate the accuracy, efficiency, and computational complexity of the FFNN–BLM algorithm, different performance functions are defined based on mean absolute deviations (MAD), error in Nash–Sutcliffe efficiency (ENSE), and Theil's inequality coefficient (TIC). The approximate solutions achieved by the proposed technique are validated by comparing with the least square method (LSM), machine learning algorithms such as NARX-LM, and numerical solutions by the Runge–Kutta–Fehlberg method (RKFM). The results demonstrate that the mean percentage error in our solutions and values of ENSE, TIC, and MAD is almost zero, showing the design algorithm's robustness and correctness. [ABSTRACT FROM AUTHOR]

The present study investigates the impacts of thermal radiation and inclined magnetic field on the Sutterby fluid by capitalizing Cattaneo-Christov heat flux system. The suitable transformations from PDE into ODE are achieved by capitalizing the strength of similarity conversion system. Well known numerical shooting technique is used along with integrated strength Runge-Kutta method of fourth order. The proposed results are compared with Lobatto 111A method which strengthen the convergence and accuracy of present fluidic system. The skin friction coefficients and Nusselt number are numerically exhibited in tabular form, while the parameter of interests in terms of velocity ratio parameter, power law index, the thermal radiation parameter, Prandtl number, Deborah number, and magnetic parameter. Here in this contemporary investigation, the phenomenon of thermal radiation on an inclined magnetic field using Sutterby capitalizing Cattaneo-Christov heat flux model has been discussed. The resulting complex non-linear ODE are tackled numerically by utilizing a famous shooting technique with the integrated strength of the Runge-Kutta method of fourth order. The obtained numerical results are compared with the MATLAB built-in solver bvp4c. The numerical values of the skin friction coefficient and reduced Nusselt number are narrated in tabular form, while some proficient parameters like velocity ratio parameter, power-law index, Deborah number, magnetic parameter, inclined magnetic angle, the thermal radiation parameter, Reynolds number, and Prandtl number on the velocity and temperature profiles have been discussed numerically as well as graphically. Outcomes of the proposed research show that by increasing the inclined angle, enhancement is seen in the skin-friction coefficient and reduces the Nusselt number. Moreover, by increasing the Reynolds number, the temperature profile declines initially and then moves upward in the channel. The stability and convergence of the proposed methodolgy in validated through residual errors based different tolerances. [ABSTRACT FROM AUTHOR]