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 φ are analysed with respect to velocity and temperature profiles. The proposed techniques are easy to implement for fluid and heat transfer (FHT) problems.

Modelling and Simulation of Fluid Flow through a Circular Cylinder with High Reynolds Number: A COMSOL Multiphysics Study

“…For this purpose, we draw two lines before and after the circle which is equidistant from the circle and to determine the velocity magnitude as well as pressure by the numerical procedure through COMSOL Multiphysics 5.4. In Figure 10, we found the velocity magnitude in line 1 before the circle and line 2 Numerical results [28] Numerical results [29] Numerical results [30] Present code after the circle, and it is deducted that the ow rate in the middle of the channel is minimum. It is showing that after striking o the uid with the circular obstacle, the uid losses it is power and slows down and therefore vortex can be seen there.…”

“…e velocity and the temperature profiles were discussed in the terms of volume fraction, expansion ratio, and the Reynolds number. e characteristics of thermal transmission of the nanofluid flow through an asymmetric channel were discussed [30]. ree main algorithms were applied to the governing partial differential equations to develop the simulation in the rectangular channel.…”

Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method

“…RK4 is used to overcome time dependent problems. Differential quadrature method is realized as the unknown function at any grid spacing f and its derivatives are approximated as a weighted sum of full the functional values at certain grids in all calculation domain as follows [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]:…”

“…where A x ir and B x ir are the 1st and 2nd weighting coefficients [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. The computed 1st and 2nd derivatives weighting coefficients are various based on choice of shape function.…”

“…Rosa et al [38] applied Differential quadrature technique to estimate the identification of the stiffness of structural elements. Alqahtani and Jiwari [39] studied 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 quasi linearization process (QP). Mohammad et al [40] employed DQM for numerical simulation of unsteady open channel flow.…”