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Impact of Inclined Lorentz Force and Schmidt Number on Chemically Reactive Newtonian Fluid Flow on a Stretchable Surface When Stefan Blowing and Thermal Radiation are Significant

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Abstract

The influence of inclined magnetic field and heat and mass transfer of a hydromagnetic fluid on stretching/shrinking sheet with Stefan blowing effects and radiation has been investigated. The elementary viscous equations for momentum, heat and mass transfer, which are highly nonlinear partial differential equations, are mapped into highly nonlinear ordinary differential equations with the help of similarity transformation. The subsequent highly nonlinear differential equation is solved analytically. The exact solution of heat and mass transfer appearances is found in terms of the incomplete gamma function. The species and temperature boundary conditions are assumed to be a linear function of the distance from the origin. Further, the impact of various parameters, such as Chandrasekhar number, thermal radiation, inclined Lorentz force and mass transpiration on velocity and temperature summaries, are conferred in detail.

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Abbreviations

a :

Constant

\({B_{0}}\) :

Magnetic field (Wm−2)

C :

Species concentration (mol m−3)

C w :

Species concentration at the wall (mol m−3)

\(C_{\infty} \) :

Ambient species concentration (mol m−3)

f :

Similarity variable for velocity

k*:

Mean absorption coefficient (m−2)

N R :

\( \left( { = \frac{16\sigma ^{*} T_{\infty }^{3} }{3k^{*} K}} \right) \) Radiation parameter

p :

Pressure of the fluid

Pr:

\( \left( { = \frac{\nu }{\alpha }} \right) \) Prandtl number

Q :

\( \left( { = \frac{{\sigma B_{0}^{2} }}{{a\rho }}} \right) \) Constant magnetic parameter

q r :

Radiative heat flux

q w :

Surface heat flux from the plate (Wm−2)

Sc:

\( \left( { = \frac{\nu }{D}} \right) \) Schmidt number

T :

Fluid temperature (K)

\( T_{\infty } \) :

Surrounding fluid temperature (K)

T w :

Temperature of the surface (K)

u and v :

Velocity components in the x- and y-direction (ms−1)

U w :

Velocity of stretching sheet

v w :

Wall blowing velocity (ms−1)

x and y :

Coordinate systems (m)

′:

Differentiation with respect to \(\eta \)

α :

Thermal diffusivity of fluid (m2s−1)

β :

Constant

\(\Lambda \) :

Stefan blowing parameter

\(\xi \) :

Variable

\(\zeta \) :

Variable

\(\eta \) :

Blasius similarity variable

\(\kappa \) :

Thermal conductivity of fluid (Wm−1K−1)

\(\theta \) :

Similarity variable for temperature

\(\lambda \) :

Stretching/shrinking parameter

λ > 0:

Stretching sheet

λ < 0:

Shrinking sheet

\(\nu \) :

Kinematic viscosity of fluid (m2s−1)

\(\rho \) :

Density of fluid (Kgm−3)

\(C_{P} \) :

Constant pressure specific thermal capacity of the fluid (JK−1)

\( \sigma \) :

Electrical conductivity of fluid (Sm−1)

\(\sigma ^{*} \) :

Stefan-Boltzmann constant

\(\tau \) :

Inclined parameter of magnetic field

\(\phi \) :

Similarity variable for concentration

\( \Gamma \) :

Incomplete gamma function

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Acknowledgements

Anusha T. is thankful to Council of Scientific and Industrial Research (CSIR), New Delhi, for financial support in the form of Junior Research Fellowship: File No. 09/1207(0003)/2020-EMR-I.

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Authors and Affiliations

  1. Department of Mathematics, Davangere University, Shivagangothri, Davangere, 577 007, India

    U. S. Mahabaleshwar & T. Anusha

  2. Institute of Physics “Gleb Wataghin”, State University of Campinas, Campinas, SP, Brazil

    P. H. Sakanaka

  3. Department of Mechanical Engineering, Birla Institute of Technology and Science Pilani, Pilani Campus, Vidya Vihar, Pilani, Rajasthan, 333 031, India

    Suvanjan Bhattacharyya

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  1. U. S. Mahabaleshwar
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Correspondence to Suvanjan Bhattacharyya.

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Mahabaleshwar, U.S., Anusha, T., Sakanaka, P.H. et al. Impact of Inclined Lorentz Force and Schmidt Number on Chemically Reactive Newtonian Fluid Flow on a Stretchable Surface When Stefan Blowing and Thermal Radiation are Significant. Arab J Sci Eng 46, 12427–12443 (2021). https://doi.org/10.1007/s13369-021-05976-y

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