Stability analysis of heat transfer in nanomaterial flow of boundary layer towards a shrinking surface: Hybrid nanofluid versus nanofluid

  1. Aqeel ur Rehman and
  2. Zaheer AbbasORCID Logo

Submitting author affiliation: The Islamia University of Bahawalpur, Bahawalpur, Pakistan

Beilstein Arch. 2021, 202188. https://doi.org/10.3762/bxiv.2021.88.v1

Published 15 Dec 2021

  • Preprint

Abstract

Many boundary value problems (BVPs) have dual solutions in some cases containing one stable solution (upper branch) while other unstable (lower branch). In this paper, MHD flow and heat transfer past a shrinking sheet is studied for three distinct fluids: kerosene hybrid nanofluid, kerosene nanofluid, and kerosene nanofluid. The partial differential equations (PDEs) are turned into ordinary differential equations (ODEs) using an appropriate transformation and then dual solutions are obtained analytically by employing the Least Square method (LSM). Moreover, stability analysis is implemented on the time-dependent case by calculating the least eigenvalues using Matlab routine bvp4c. It is noticed that negative eigenvalue is related to unstable solution i.e., it provides initial progress of disturbance and positive eigenvalue is related to stable solution i.e., the disturbance in solution decline initially. The impacts of various parameters, skin friction coefficient, and local Nusselt number for dual solutions are presented graphically. It is also noted that the results obtained for hybrid nanofluids are better than ordinary nanofluids.

Keywords: Stability analysis; hybrid nanofluid; shrinking sheet; dual solutions; analytical procedure

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Rehman, A. U.; Abbas, Z. Beilstein Arch. 2021, 202188. doi:10.3762/bxiv.2021.88.v1

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© 2021 Rehman and Abbas; licensee Beilstein-Institut.
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