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Finite difference simulation of free convection of non-Newtonian nanofluids with radiation effects over a truncated wavy cone

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Abstract

This study explores the consequences of free convective laminar two-dimensional flow with the effects of thermal radiation of power-law non-Newtonian water–Cu nanofluids over the frustum of a cone whose sides are wavy shaped. The flow is described by some well-known equations of fluid dynamics, such as the equation of continuity, momentum and energy equation having the Rosseland diffusion model for radiation effect. These governing equations are transformed into non-dimensional boundary-layer equations, which are solved by using the marching order implicit finite difference method. The numerical results are obtained by varying pertinent parameters, such as the radiation–conduction parameter \(R_d\), the surface heating parameter \(\theta _w\), power-law index n and nanoparticle volume fraction \(\epsilon \). The numerically calculated findings are reported with respect to the velocity and temperature distributions, streamlines, isotherms, local skin friction coefficient and average Nusselt number using graphs. According to the obtained results, \(R_d\), \(\epsilon \) and \(\theta _w\) accelerate the convection process. Hence, velocity, skin friction, as well as the rate of heat transfer enhance. On the other hand, an increasing power-law index decreases the convection process. As a result, velocity, skin friction as well as the rate of heat transfer reduce. The present study of non-Newtonian nanofluid with radiation effect over a truncated wavy cone is a novel study. The motto of the existing numerical effort is to observe the situations considering non-Newtonian nanofluid fluids and how the considered parameters reflected their behaviour with non-Newtonian viscosity and radiation–conduction effects. The obtained result of this present study is validated with the work of Pop and Na (Int. J. Nonlinear Mech. 34, 925, 1999). The findings of their investigation of free convective flow in a vertical cone are compared with the current work and the comparison showed an excellent agreement.

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Acknowledgements

Md Mamun Molla gratefully acknowledges the North South University for the financial support as a faculty research grant  (Grant No. CTRG-22-SEPS-09). He also acknowledges the Ministry of Science and Technology (MOST), the government of Bangladesh for providing the financial support for this research  (Grant No. EAS/SRG-222427).

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Authors and Affiliations

  1. Department of Mathematics & Physics, North South University, Dhaka, 1229, Bangladesh

    Amzad Hossain & Meratun Junnut Anee

  2. Center for Applied Scientific Computing (CASC), North South University, Dhaka, 1229, Bangladesh

    Amzad Hossain, Meratun Junnut Anee & Md Mamun Molla

  3. Department of Mathematics, Jagannath University, Dhaka, Bangladesh

    Sharaban Thohura

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  1. Amzad Hossain
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  2. Meratun Junnut Anee
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  3. Sharaban Thohura
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  4. Md Mamun Molla
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Correspondence to Md Mamun Molla.

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Hossain, A., Anee, M.J., Thohura, S. et al. Finite difference simulation of free convection of non-Newtonian nanofluids with radiation effects over a truncated wavy cone. Pramana - J Phys 97, 168 (2023). https://doi.org/10.1007/s12043-023-02642-w

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  • DOI: https://doi.org/10.1007/s12043-023-02642-w

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