Wavelet Operational Matrices and Lagrange Interpolation Differential Quadrature-Based Numerical Algorithms for Simulation of Nanofluid in Porous Channel

Abstract

This work analyses the features of nanofluid flow and thermal transmission (NFTT) in a rectangular channel which is asymmetric by developing two numerical algorithms based on scale-2 Haar wavelets (S2HWs), Lagrange’s interpolation differential quadrature technique (LIDQT), and quasilinearization process (QP). In the simulation procedure, first of all, using similarity transformation (ST), the governing unsteady 2D flow model is changed into two highly non-linear ODEs. After that, QP is applied to linearize the non-linear ODEs, and finally S2HWs and LIDQT are used to simulate the non-linear system of ODEs. In results and discussion section, the parameters Reynolds number (R), expansion ratio and Nusselt (Nu), and nanoparticle volume fraction $\left(\phi \right)$ are analysed with respect to velocity and temperature profiles. The proposed techniques are easy to implement for fluid and heat transfer (FHT) problems.