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Thermal radiation and chemical reaction influence on MHD boundary layer flow of a Maxwell fluid over a stretching sheet containing nanoparticles

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Abstract

The heat and mass transfer properties of a two-dimensional electrically conducting incompressible Maxwell fluid have been explored in the existence of, chemical reaction, heat generation/absorption, and thermal radiation. This was done by moving the fluid through a stretched sheet. Polymer extrusion and metal thinning are two instances of the vast importance of this topic from a practical standpoint. Using the appropriate similarity variables, it is feasible to non-dimensionalize the PDEs regulating the stream and their related boundary conditions. Fourth- and fifth-order Runge–Kutta–Fehlberg schemes are utilized to solve the resulting modified ODEs. The impact of the many thermo-physical parameters embedded in the system on the velocity, temperature, and concentration has been identified and quantitatively analyzed. When comparing our observations to those found in the literature, we find a lot of concordances when looking at case studies. The concentration distribution becomes more intense as the estimations of the chemical reaction parameter are improved, and the effect of thermal radiation is greater as the temperature rises. Thermophoresis is a transport force that arises when a temperature gradient exists. An increase in thermophoresis leads to a hotter surface since a thicker boundary layer means a higher temperature there.

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Abbreviations

\(\alpha\) :

Thermal diffusivity \(\left( {{\text{m}}^{2} \;{\text{s}}^{ - 1} } \right)\)

\(\mu\) :

Dynamic viscosity \(\left( {{\text{kg m}}^{2} \;{\text{s}}^{ - 1} } \right)\)

\({\text{Nr}}\) :

Radiation parameter

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

Maxwell fluid relaxation time

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

Mean fluid temperature \(\left( {\text{K}} \right)\)

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

Fluid temperature close to the wall \(\left( {\text{K}} \right)\)

\(T_{\infty }\) :

Fluid temperature at infinity (K)

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

Specific heat at constant pressure \(\left( {{\text{J}}\;{\text{kg}}^{{ - {1}}} \;{\text{K}}} \right)\)

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

Density of the particles

\(T\) :

Fluid temperature (K)

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

Density of the base fluid \(\left( {{\text{kg}}\;{\text{m}}^{ - 3} } \right)\)

\(B_{0}\) :

Magnetic field coefficient

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

Thermal diffusion ratio parameter

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

Thermophoretic diffusion

\(\theta\) :

Dimensionless temperature of the fluid \(\left( {\text{K}} \right)\)

\(k\) :

Thermal conductivity \(\left( {{\upomega }\;{\text{m}}^{ - 1} \;{\text{K}}^{ - 1} } \right)\)

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

Mass diffusivity \(\left( {{\text{m}}^{2} \;{\text{s}}^{ - 1} } \right)\)

\(\upsilon\) :

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

\(\rho\) :

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

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

Concentration susceptibility

\(\sigma\) :

Electrical conductivity \(\left( {{\Omega }^{ - 1} {\text{m}}^{ - 1} } \right)\)

\(k_{1}\) :

Chemical reaction parameter

\(\varphi\) :

Dimensionless fluid concentration \(\left( {{\text{mol}}\;{\text{m}}^{ - 3} } \right)\)

\(u,v\) :

Dimensionless velocities along x-and y-axis \(\left( {{\text{m}}\;{\text{s}}^{ - 1} } \right)\)

\({\text{Pr}}\) :

Prandtl number

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

Concentration of the fluid at wall \(\left( {{\text{mol}}\;{\text{m}}^{ - 3} } \right)\)

\(C_{\infty }\) :

Fluid concentration at infinity \(\left( {{\text{mol}}\;{\text{m}}^{ - 3} } \right)\)

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

Brownian diffusion

\(M\) :

Magnetic parameter

\(C\) :

Fluid concentration \(\left( {{\text{mol}}\;{\text{m}}^{ - 3} } \right)\)

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  1. Department of Mathematics, Anurag University, Venkatapur, Hyderabad, 500 088, Telangana, India

    M. Anil Kumar & Y. Dharmendar Reddy

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Kumar, M.A., Reddy, Y.D. Thermal radiation and chemical reaction influence on MHD boundary layer flow of a Maxwell fluid over a stretching sheet containing nanoparticles. J Therm Anal Calorim 148, 6301–6309 (2023). https://doi.org/10.1007/s10973-023-12097-1

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