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Chin. Phys. B, 2022, Vol. 31(4): 044701    DOI: 10.1088/1674-1056/ac229b

Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H2O nanofluid on a flat surface in a porous medium: A stability analysis

Astick Banerjee1, Krishnendu Bhattacharyya2,†, Sanat Kumar Mahato1, and Ali J. Chamkha3
1 Department of Mathematics, Sidho-Kanho-Birsha University, Purulia 723104, India;
2 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India;
3 Faculty of Engineering, Kuwait College of Science and Technology, Doha District, Kuwait
Abstract  The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems. So, here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H2O nanofluid on a flat surface in a porous medium is examined. Moreover, the thermal radiation and viscous dissipation effects are considered. The problem governing partial differential equations are converted into self-similar coupled ordinary differential equations and those are numerically solved by the shooting method. The computed results can reveal many vital findings of practical importance. Firstly, dual solutions exist for decelerating unsteady flow and for accelerating unsteady and steady flows, the solution is unique. The presence of nanoparticles affects the existence of dual solution in decelerating unsteady flow only when the medium of the flow is a porous medium. But different shapes of nanoparticles are not disturbing the dual solution existence range, though it has a considerable impact on thermal conductivity of the mixture. Different shapes of nanoparticles act differently to enhance the heat transfer characteristics of the base fluid, i.e., the water here. On the other hand, the existence range of dual solutions becomes wider for a larger permeability parameter related to the porous medium. Regarding the cooling rate of the heated surface, it rises with the permeability parameter, shape factor (related to various shapes of Cu-nanoparticles), and radiation parameter. The surface drag force becomes stronger with the permeability parameter. Also, with growing values of nanoparticle volume fraction, the boundary layer thickness (BLT) increases and the thermal BLT becomes thicker with larger values of shape factor. For decelerating unsteady flow, the nanofluid velocity rises with permeability parameter in the case of upper branch solution and an opposite trend for the lower branch is witnessed. The thermal BLT is thicker with radiation parameter. Due to the existence of dual solutions, a linear stability analysis is made and it is concluded that the upper branch and unique solutions are stable solutions.
Keywords:  Cu-H2O nanofluid      various shapes of nanoparticles      unsteady stagnation-point flow      dual solutions      stability analysis  
Received:  13 May 2021      Revised:  15 July 2021      Accepted manuscript online:  01 September 2021
PACS:  47.15.Cb (Laminar boundary layers)  
  47.15.Fe (Stability of laminar flows)  
  44.30.+v (Heat flow in porous media)  
Corresponding Authors:  Krishnendu Bhattacharyya     E-mail:,

Cite this article: 

Astick Banerjee, Krishnendu Bhattacharyya, Sanat Kumar Mahato, and Ali J. Chamkha Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H2O nanofluid on a flat surface in a porous medium: A stability analysis 2022 Chin. Phys. B 31 044701

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