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Illustration of homogeneous–heterogeneous reactions on the MHD boundary layer flow through stretching curved surface with convective boundary condition and heat source

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Abstract

The objective of the current study is to develop an investigation on the magnetohydrodynamic flow of viscous liquid through a nonlinear curved enlarging sheet due to the occurrence of heat source. The observation of heterogeneous and homogeneous reactions with the properties of heat source and transverse magnetic field is reflected in this discussion. Further, in a novel approach, the convective heating mechanism enriches the flow phenomena significantly. The governing partial differential equations are successfully transformed into the dimensionless form by using appropriate similarity transformations. The resultant non-dimensional form of equations is computed via the numerical scheme. The properties of the proposed physical constraints are observed and explored their significant behavior graphically. Additionally, the physical properties like surface drag force and local Nusselt numbers are calculated and presented in tabular form. Further, the major outcomes of the study reveal that the fluid velocity retards significantly for higher values of curvature constraint and stretching index and temperature of fluid enhances for the increasing power law stretching index along with the additional Biot number and heat source.

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Abbreviations

\(A,\,B\) :

Chemical species/–

\(a,\,b\) :

Concentrations/moles m−3

\(a_1\) :

Positive constant/–

\(B_0\) :

Applied magnetic field/\({\text{N}}\,{\text{m}}^{1} \,{\text{A}}^{ - 1}\)

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

Coefficient of skin friction/–

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

Fluid density/\({\text{kg}}\,{\text{m}}^{3}\)

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

Coefficients of diffusion for species \({\text{A}}\)/\({\text{m}}^2 {\text{s}}^{1}\)

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

Coefficients of diffusion for species B/\({\text{m}}^2 {\text{s}}^{1}\)

\(f^{\prime}\) :

Non-dimensional velocity/–

\(h\) :

Non-dimensional concentration/–

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

Convective coefficient/\({\text{W}}\,{\text{m}}^{2} \,{\text{K}}^{ - 1}\)

\(k\) :

Thermal conductivity/\({\text{W}}\,{\text{m}}^{1} \,{\text{K}}^{ - 1}\)

\(K\) :

Curvature parameter/–

\(k_1\) :

Homogeneous reaction parameter/–

\(k_2\) :

Heterogeneous reaction parameter/–

\(k_{\text{c}} ,\,\;k_{\text{s}}\) :

Rate constants/–

\(M\) :

Magnetic number/–

\(n\) :

Power law stretching index/–

\(p\) :

Pressure/\({\text{N}}\,{\text{m}}^{2}\)

Pr :

Prandtl number

\(Q_0\) :

Volumetric heat coefficient/\({\text{J}}\,{\text{K}}^{1} \,{\text{m}}^{ - 3}\)

\(Q\) :

Heat source/sink parameter/–

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

Wall heat flux/\({\text{W}}\,{\text{m}}^{2}\)

\(R\) :

Radius/m

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

Local Reynolds number/–

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

Species \(A\) mass flux/ moles m−2

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

Species \(B\) mass flux/ moles m−2

\(Sc\) :

Schmidt number/–

\(s,\,r\) :

Coordinate axes/–

\(Sh_{\text{x(A)}}\) :

Sherwood number for species \(A\)/–

\(Sh_{\text{x(B)}}\) :

Sherwood number for species \(B\)/–

\(T\) :

Temperature/K

\(T_\infty\) :

Ambient fluid temperature/K

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

Convective surface temperature/K

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

Surface velocity/ms−1

\(u,\,v\) :

Velocity components/ms−1

\(\gamma\) :

Biot number/–

\(\mu\) :

Dynamic viscosity/\({\text{kg}}\,{\text{m}}^{1} {\text{s}}^{ - 1}\)

\(\rho\) :

Fluid density/\({\text{kg}}\,{\text{m}}^{3}\)

\(\nu\) :

Kinematic viscosity/\({\text{m}}^2 {\text{s}}^{1}\)

\(\theta\) :

Dimensionless temperature/–

\(\phi\) :

Dimensionless concentration/–

\(\delta\) :

The ratio of the diffusion coefficient

\(\sigma\) :

Electrical conductivity/\({\text{simens }}{\text{m}}^{1}\)

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

Shear stress at wall/\({\text{N}}\,{\text{m}}^{2}\)

\(\zeta\) :

Similarity variable

\(f\) :

Fluid particle

\(w\) :

At wall

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Arunachal Pradesh, Jote, Papum Pare District, Arunachal Pradesh, 791113, India

    Ram Prakash Sharma

  2. Department of Basic & Applied Science, National Institute of Technology, Jote, Papum Pare District, Arunachal Pradesh, 791113, India

    Abhishek Sharma

  3. Department of Mathematics, Siksha ‘O’ Anusandhan Deemed to be University, Bhubaneswar, Odisha, 751030, India

    S. R. Mishra

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  1. Ram Prakash Sharma
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Sharma, R.P., Sharma, A. & Mishra, S.R. Illustration of homogeneous–heterogeneous reactions on the MHD boundary layer flow through stretching curved surface with convective boundary condition and heat source. J Therm Anal Calorim 148, 12119–12132 (2023). https://doi.org/10.1007/s10973-023-12466-w

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