This analysis focuses on extending and developing some previous studies of energy transport through nanofluids to include the states of combined convection flow of a Williamson hybrid nanofluid that flows around a cylinder. Mathematical models that simulate the behavior of these upgraded nanofluids are constructed by expanding the Tiwari and Das model, which are then solved numerically via Keller box approaches. The accuracy of the results is emphasized by comparing them with the previous published outcomes. Nanosolid volume fraction 0≤χ≤0.1, combined convection −1≤λ≤5, radiation factor 0.1≤R≤6, Weissenberg number 0.2≤We≤ 0.9, and magnetic factor 0.1≤M≤1 are the factors that have been taken into consideration to examine the energy transfer performance of Williamson hybrid nanofluid. Numerical and graphical outcomes are obtained using MATLAB, analyzed, and discussed in depth. According to the outcomes, the Weissenberg number reduces energy transfer and friction forces. Both the combined convective coefficient and the radiation factor improved the rate of energy transfer and increased the velocity of the host fluid. The fluid velocity and rate of energy transfer can be reduced by increasing the magnetic factor. The nanoparticle combination of silver and aluminum oxide (Ag-Al2O3) has demonstrated superiority in enhancing the energy transfer rate and velocity of the host fluid.
We have elaborated the numerical schemes of collocation methods and mechanical quadrature methods for approximate solution of singular integro-differential equations with kernels of Cauchy type. The equations are defined on the arbitrary smooth closed contours of complex plane. The researched methods are based on Fejér points. Theoretical background of collocation methods and mechanical quadrature methods has been obtained in Generalized Hölder spaces.
Space time integration plays an important role in analyzing scientific and engineering models. In this paper, we consider an integrodifferential equation that comes from modelingθ˙neuron networks. Here, we investigate various schemes for time discretization of a theta-neuron model. We use collocation and midpoint quadrature formula for space integration and then apply various time integration schemes to get a full discrete system. We present some computational results to demonstrate the schemes.
The present paper deals with the justification of solvability conditions and properties of solutions for weakly singular integro-differential equations by collocation and mechanical quadrature methods. The equations are defined on an arbitrary smooth closed contour of the complex plane. Error estimates and convergence for the investigated methods are established in Lebesgue spaces.
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