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Exponential space-dependent heat generation impact on MHD convective flow of Casson fluid over a curved stretching sheet with chemical reaction

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Abstract

The present article focuses on the effect of exponential space-dependent heat source on magneto-hydrodynamic Casson fluid flow over a curved stretching sheet along with chemical reaction and convective heat and mass flux boundary conditions. The equations that govern the flow are reduced from system of partial differential equations to system of ordinary differential equations with the assistance of similarity transformations, and after that, they are solved using the numerical technique Runge–Kutta–Fehlberg fourth–fifth-order method. The obtained numerical values are plotted through graphs for velocity, temperature and concentration profiles with various parameters, and the variations based on these plots are discussed. Here, it is incurred that the velocity and concentration fields increase with increasing curvature parameter, whereas temperature profile shows inverse relation. Also, increment of Casson parameter shows the significant change in all flow profiles. Both thermal Biot number and concentration Biot number have increasing impact on temperature and concentration profiles, respectively.

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Abbreviations

\(a\) :

Stretching constant (m)

\(B_{0}\) :

Applied magnetic field (Tesla)

\({\text{Bi}}_{1}\) :

Thermal Biot number

\({\text{Bi}}_{2}\) :

Concentration Biot number

\(C\) :

Dimensional concentration (mol m−3)

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

Concentration at the surface (mol m−3)

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

Skin friction coefficient

\(C_{\infty }\) :

Ambient concentration (mol m−3)

\(D\) :

Diffusion coefficient (m2 s−1)

\(f'\) :

Dimensionless velocity

\(h_{1}\) :

Convective heat transfer coefficient (W m−2 K−1)

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

Convective mass transfer coefficient (m s−1)

\(k^{*}\) :

Thermal conductivity (W m−1 K−1)

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

Local Nusselt number

\(p\) :

Pressure (Pa)

\(P\) :

Dimensionless pressure

\({ \Pr }\) :

Prandtl number

\(Q\) :

Heat source/sink parameter (J)

\(Q_{0}\) :

Space-dependent heat source (J)

\(R\) :

Dimensional radius of curvature

\(R^{*}\) :

Chemical reaction parameter

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

Local Reynolds number

\(r,s\) :

Local coordinates

\({\text{Sc}}\) :

Schmidt number

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

Local Sherwood number

\(T\) :

Fluid temperature (K)

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

Fluid temperature at the surface (K)

\(T_{\infty }\) :

Ambient fluid temperature (K)

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

Wall heat flux (J)

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

Wall mass flux (kg s−1 m−2)

\(u\) :

Velocity component along s-direction (m s−1)

\(v\) :

Velocity component along r-direction (m s−1)

\(\phi\) :

Dimensionless concentration

\(\theta\) :

Dimensionless temperature

\(\eta\) :

Independent coordinate

\(\nu\) :

Kinematic viscosity of the fluid (m2 s−1)

\(\mu\) :

Dynamic viscosity of the fluid (kg m−1 s−1)

\(\rho\) :

Density of the fluid (kg m−3)

\(\sigma\) :

Electrical conductivity of the fluid (S m−1)

\(\beta\) :

Casson parameter

\(\alpha\) :

Thermal diffusivity of the fluid (m2 s−1)

\(\kappa\) :

Dimensionless curvature parameter

\(\rho C_{\text{p}}\) :

Specific heat capacitance of the fluid (J kg−1 K−1)

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

Wall shear stress (N m−2)

\(\delta\) :

Dimensionless chemical reaction parameter

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  1. Department of PG Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, India

    B. Nagaraja & B. J. Gireesha

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Nagaraja, B., Gireesha, B.J. Exponential space-dependent heat generation impact on MHD convective flow of Casson fluid over a curved stretching sheet with chemical reaction. J Therm Anal Calorim 143, 4071–4079 (2021). https://doi.org/10.1007/s10973-020-09360-0

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