Vol.:(0123456789) 1 3 Engineering with Computers https://doi.org/10.1007/s00366-020-01139-z ORIGINAL ARTICLE Wavelet strategy for fow and heat transfer in CNT‑water based fuid with asymmetric variable rectangular porous channel Sapna Pandit 1  · Seema Sharma 1 Received: 18 April 2020 / Accepted: 31 July 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020 Abstract In the present work, the characteristics of physical model unsteady nanofuid fow and heat transfer in an asymmetric porous channel are analyzed numerically using wavelet collocation method. Using similarity transformation, unsteady two- dimensional fow model of nanofuid in a porous channel through expanding or contracting walls has been transformed into a system of nonlinear ordinary diferential equations (ODEs). Then, the obtained nonlinear system of ODEs is solved via wavelet collocation method. The efect of various emerging parameters, such as nanoparticle volume fraction, Reynolds number (Re), and expansion ratio have been analyzed on velocity and temperature profles. Numerical results have been presented in form of fgures and tables. For some special cases, the obtained numerical results are compared with exact one and found that the results are good in agreement with exact solutions. Keywords Nanofuid · Porous channel · Heat transfer · Expansion ratio · Reynolds number · Single-walled carbon nanotubes (SWCNTs) · Multi-walled carbon nanotubes (MWCNTs) · Scale-3 Haar wavelets Abbreviations  u Velocity component in  x direction  v Velocity component in  y direction  Nanoparticle volume fraction T Temperature R Re Pr Prandtl number p Pressure ρ Density µ Viscosity C p Specifc heat in constant pressure k Thermal conductivity a Distance between parallel plates  Expansion and Contraction ratio Nu Nusselt Number t Time  Kinematic viscosity Subscripts f Base Fluid nf Nanofuid w Wall l Lower wall u Upper wall 1 Introduction Transfer of the heat efciently at an economical cost is one of the most vital issues of the current century. That is why, heat transfer is an active area of research among scientists and researchers with the aim of achieving a highly efcient transport system at a low expense carrier for diferent cat- egories of fuids. The present communication addresses the fow of heat and mass transfer mechanisms of nanofuid fow inside a rectangular channel along with dilating and squeez- ing porous walls. Such types of channels with expanding and contracting walls are involved in many physical and bio- logical circumstances such as regularly dispersed irrigation, coolant circulation, flling machines, bio-fuid transporta- tion in living organisms, manufacturing process of sheets and papers, propellant combustion, and industrial cleansing systems. From the energy-saving point of view, improvement in heat transfer in electronic cooling and heat exchangers, etc. has been a tremendously important topic of research. Therefore, scientists are trying to develop new mechanisms that are highly efcient thermally. For example, researchers are trying to improve the stability of nanoparticles in a base fuid to enhance their conductivity. * Sapna Pandit sappu15maths@gmail.com 1 Department of Mathematics, Gurukula Kangri Vishwavidyalaya, Haridwar, UK 249404, India