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Cross-diffusion and chemical reaction effects of a MHD nanofluid flow inside a divergent/convergent channel with heat source/sink

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Abstract

This paper examined the problem associated with incompressible viscous nanofluid flow inside shrinking and stretching walls. Flow is contemplated from a sink or source through channel. MHD, radiation, heat source/sink, chemical reaction and cross-diffusion consequences are considered to find out about the nature of various profiles like: velocity, mass as well as temperature. Later on by using non-dimensional parameters, we obtain PDE from governing equations after which these are figure out by using OHAM. A valuable agreement is obtained on comparing the results with previous research studies. Ranges for various non-dimensional parameters are considered during present work, which are likewise: opening angle \(\left( {{ - 9}^{ \circ } \le \alpha \le {9}^{ \circ } } \right)\), Reynolds number \(\left( {40 \le {\text{Re}} \le 60} \right)\), nanoparticles volume fraction \(\left( {0 \le {\varphi } \le 0.15} \right)\), magnetic parameter \(\left( {{0 \le { M} \le 110}} \right)\), radiation parameter \(\left( {0 \le Rd \le 0.1} \right)\), Prandtl number \(\left( {1 \le \Pr \le 6.2} \right)\), heat source/sink parameter \(\left( {0 \le Hs \le 0.8} \right)\), Eckert number \(\left( {0 \le Ec \le 0.01} \right)\), Dufour number \(\left( {0 \le D_{\text{f}} \le 2.4} \right)\), Schmidt number \(\left( {0 \le Sc \le 1.39} \right)\), chemical reaction parameter \(\left( {0 \le K \le 1.6} \right)\), Soret number \(\left( {0 \le Sr \le 0.57} \right)\) and stretching/shrinking parameter \(\left( { - 2.8 \le C^{*} \le 2.8} \right)\). It is predicted that for divergent channel the velocity function reduces, whereas it shows contrast nature for convergent channel with an enhancement in the volume fraction of nanoparticles. With rise in Soret as well as Dufour number, there is rise in temperature and fall down in concentration function.

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Abbreviations

\(A,B\) :

Constant parameters (–)

\(B_{0}\) :

Magnetic field (N m−1 A−1)

\(B_{1}\) :

Constant parameter (–)

\(c_{\text{p}}\) :

Specific heat (J kg−1 K−1)

\(c_{\text{s}}\) :

Concentration susceptibility (mol m−3)

\(C\) :

Concentration (mol m−3)

\(C_{\text{f}}\) :

Skin friction coefficient (–)

\(C_{\text{w}}\) :

Concentration at the plate (mol m−3)

\(C^{*}\) :

Stretching/shrinking parameter (–)

\(D\) :

Mass diffusion coefficient (m2 s−1)

\(D_{\text{f}}\) :

Dufour number (–)

\(Ec\) :

Eckert number (–)

\(f\) :

Dimensionless velocity (–)

\(Hs\) :

Heat source/sink parameter (–)

\(k\) :

Thermal conductivity (W m2 K−1)

\(k_{1}\) :

Chemical reaction rate (mol m−3 s−1)

\(k^{*}\) :

Mean absorption coefficient (–)

\(K\) :

Chemical reaction parameter (–)

\(K_{\text{T}}\) :

Thermal diffusion ratio (m−2 s−1)

\(M\) :

Magnetic parameter (–)

\(Nu\) :

Nusselt number (–)

\(p\) :

Pressure (N m−2)

\(\Pr\) :

Prandtl number (–)

\(q_{\text{m}}\) :

Surface mass flux (kg s −1 m−2)

\(q_{\text{rad}}\) :

Radiative heat flux (kg s −3)

\(q_{\text{w}}\) :

Surface heat flux (W m−2)

\(Q_{0}\) :

Heat source/sink (J)

\(r\) :

Cylindrical coordinate (–)

\(Rd\) :

Radiation parameter (–)

\({\text{Re}}\) :

Reynolds number (–)

\(s\) :

Stretching/shrinking rate (m2 s−1)

\(Sc\) :

Schmidt number (–)

\(Sh\) :

Sherwood number (–)

\(Sr\) :

Soret number (–)

\(T\) :

Temperature (K)

\(T_{\text{w}}\) :

Surface temperature of channel (K)

\(T_{0}\) :

Free stream temperature (K)

\(u\) :

Velocity component in the radial direction (m s−1)

\(u_{\text{c}}\) :

Rate of movement in the radial direction (m2 s−1)

\(u_{\text{w}}\) :

Wall velocity component in the radial direction (m s−1)

\(\alpha\) :

Angle of the channel (–)

\(\phi\) :

Dimensionless concentration (–)

\(\varphi\) :

Nanoparticles volume fraction (–)

\(\eta\) :

Dimensionless angle (–)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\theta\) :

Cylindrical coordinate (–)

\(\Theta\) :

Dimensionless temperature (–)

\(\rho\) :

Density (kg m−3)

\(\sigma\) :

Electrical conductivity (s m−1)

\(\sigma^{*}\) :

Stefan–Boltzmann constant (–)

\(\tau_{\text{w}}\) :

Shear stress on the wall (N m−2)

\(f\) :

Base fluid

\(nf\) :

Nanofluid

\(s\) :

Nanoparticle

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Authors and Affiliations

  1. Department of Mathematics, S. S. Jain Subodh P.G. (Autonomous) College, Jaipur, Rajasthan, India

    Khushbu Bhaskar

  2. Department of Mathematics & Statistics, Manipal University Jaipur, Jaipur, 303007, Rajasthan, India

    Kalpna Sharma & Kajal Bhaskar

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Bhaskar, K., Sharma, K. & Bhaskar, K. Cross-diffusion and chemical reaction effects of a MHD nanofluid flow inside a divergent/convergent channel with heat source/sink. J Therm Anal Calorim 148, 573–588 (2023). https://doi.org/10.1007/s10973-022-11525-y

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