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Chemically reactive solute transfer in a moving fluid over a moving surface

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Abstract

The distribution of a solute, undergoing a chemical reaction, between a moving surface and a moving stream is analyzed in this paper: uniform concentration at the boundary is assumed. The governing nonlinear partial differential equations are first transformed into nonlinear ordinary differential equations (ODEs) by a similarity transform, and then the ODEs are solved numerically by a shooting method. The obtained numerical results are compared with the known results in the literature in order to demonstrate the validity of the solutions. Furthermore, analytical results are provided for some parameter regimes. The effects of the governing parameters on the flow and chemical fields are examined. The numerical results indicate that dual solutions exist when the sheet and the free stream move in the opposite directions. These results are in agreement with Ishak et al. (Chem Eng J 148:63–67, 2009), where the results were obtained without chemical reaction. The concentration boundary layer thickness decreases with an increase in the Schmidt number and reaction rate parameter. Moreover, mass absorption at the plate is noted in the case of a constructive chemical reaction.

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Abbreviations

C :

Concentration of the species

C w :

Concentration at the surface

C ∞ :

Concentration far away from the surface

D :

Molecular diffusivity

f :

Non-dimensional stream function

f′:

Streamwise velocity

k :

Rate of chemical conversion

r :

velocity ratio parameter

Sc :

Schmidt number

U w :

Velocity of the surface

U ∞ :

Free stream velocity

β :

Reaction rate parameter

η :

Similarity variable

μ :

Dynamic viscosity

ν :

Kinematic viscosity

ψ :

Stream function

ρ :

Density of the fluid

φ :

Non-dimensional concentration

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Authors and Affiliations

  1. Department of Mathematics, The University of Burdwan, Burdwan, 713104, WB, India

    Swati Mukhopadhyay

  2. Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL, 32816-1364, USA

    Kuppalapalle Vajravelu

  3. Department of Mathematics, University of Central Florida, Orlando, FL, 32816-1364, USA

    Kuppalapalle Vajravelu & Robert A. Van Gorder

Authors
  1. Swati Mukhopadhyay
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  2. Kuppalapalle Vajravelu
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  3. Robert A. Van Gorder
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Correspondence to Kuppalapalle Vajravelu.

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Mukhopadhyay, S., Vajravelu, K. & Van Gorder, R.A. Chemically reactive solute transfer in a moving fluid over a moving surface. Acta Mech 224, 513–523 (2013). https://doi.org/10.1007/s00707-012-0764-3

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  • DOI: https://doi.org/10.1007/s00707-012-0764-3

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