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**Natural convection flow from a vertical permeable flat plate with variable surface temperature and species concentration.**
*(English)*
Zbl 0982.76082

The authors study the free convection over a vertical permeable flat plate with variable surface temperature and species concentration. The basic equations of motion are first transformed into a set of three non-similar boundary layer equations using appropriate transformations. These equations are then solved by four different methods: by perturbation method for small transpiration parameter, by asymptotic method for large transpiration parameter, and by Keller-box method and local non-similarity method for any value of transpiration parameter. Consideration is given to the situation where the buoyancy forces have aiding effects, for various possible combinations of buoyancy ratio \(w\), temperature and concentration parameter \(n\), and Schmidt number \(Sc\) for a fixed value of Prandtl number \(\text{Pr}= 0.72\) (air).

Detailed numerical calculations have been done, and the results are presented in terms of local Nusselt and Sherwood numbers as well as in terms of velocity, temperature and concentration profiles. It is found that the asymptotic solutions for small and large values of transpiration parameter are in very good agreement with the results obtained by Keller-box and local non-similarity methods. The authors show that the increase in Schmidt number leads to the increase in momentum boundary layer thickness and to the decrease in thermal and concentration boundary layer thickness. Also, the increase in the buoyancy parameter \(w\) leads to the increase in local Nusselt and Sherwood numbers. An increase in the transpiration parameter \(\zeta\) leads to the decrease in momentum, thermal and concentration boundary layer thickness.

The paper is well written, and prevous work on this topic is referenced in detail.

Detailed numerical calculations have been done, and the results are presented in terms of local Nusselt and Sherwood numbers as well as in terms of velocity, temperature and concentration profiles. It is found that the asymptotic solutions for small and large values of transpiration parameter are in very good agreement with the results obtained by Keller-box and local non-similarity methods. The authors show that the increase in Schmidt number leads to the increase in momentum boundary layer thickness and to the decrease in thermal and concentration boundary layer thickness. Also, the increase in the buoyancy parameter \(w\) leads to the increase in local Nusselt and Sherwood numbers. An increase in the transpiration parameter \(\zeta\) leads to the decrease in momentum, thermal and concentration boundary layer thickness.

The paper is well written, and prevous work on this topic is referenced in detail.

Reviewer: Ioan Pop (Cluj-Napoca)

### MSC:

76R10 | Free convection |

76M45 | Asymptotic methods, singular perturbations applied to problems in fluid mechanics |

76M20 | Finite difference methods applied to problems in fluid mechanics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

### Keywords:

parametric investigation; free convection; vertical permeable flat plate; variable surface temperature; species concentration; boundary layer equations; perturbation method; small transpiration parameter; asymptotic method; large transpiration parameter; Keller-box method; local non-similarity method; buoyancy force
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\textit{S. Hussain} et al., Eng. Comput. (Bradf.) 17, No. 6--7, 789--812 (2000; Zbl 0982.76082)

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DOI

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