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Thermal analysis of Casson micropolar nanofluid flow over a permeable curved stretching surface under the stagnation region

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Abstract

We consider a curved surface upon which the Casson micropolar nanofluid flow is discharged to understand the behavior of such flow and heat progression. The non-Newtonian fluid flow is controlled with the introduction of a magnetic force which is directed against the flow to alter the moment of flow. An increase in the numerical value of modified Hartmann number slows down the flow by adding discharge against the flow. Lorentz force produced by increasing the curve of the channel suppresses the flow velocity. The micropolar parameter reduces the drag and helps in increasing the fluid flow. Mathematical modeling of the problem is done by taking into account the conventional assumptions taken in fluid flow theories. The modeled equations are simplified by considering similar transformation variables used in the contemporary literature. Numerical result is obtained by using bvp4c solver used in MATLAB by allowing the acceptable tolerance level at 1e−4. Various tests are carried out to choose the best match of the parametric values which help in achieving the defined boundary conditions. The output of the various solutions is plotted under varying values of different parameters, and henceforth the changes occurred are noted and discussed. The behavior of velocity, microrotational, temperature and concentration profiles is observed by comparing the graphical and tabular values. The role of different physical quantities under different parametric assumptions for stretching/shrinking channel is also taken into account and highlighted.

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Abbreviations

\(K(1)\) :

Micropolar parameter

\(\varepsilon (1)\) :

Non-dimensional parameter

\({\text{Re}}_{{\text{s}}} (1)\) :

Reynolds number

\(n(1)\) :

Micro-gyration

\(N\,\left( {{\text{m}}\;{\text{s}}^{{ - {1}}} } \right)\) :

Angular velocity components

\(u, v\,\left( {\text{m}} \right)\) :

Velocity components

\(K^{*} (1)\) :

Curvature parameter

\(u\,\left( {{\text{m}}\;{\text{s}}^{ - 1} } \right)\) :

Velocity vector r-direction

\(\beta (1)\) :

Casson fluid parameter

\({\text{Sh}}_{{\text{s}}} \left( 1 \right)\) :

Sherwood number

\(N_{{\text{T}}} \left( 1 \right)\) :

Thermophoresis parameter

\(\lambda (1)\) :

Stretching parameter

\(\gamma (1)\) :

Dimensionless parameter

\(\alpha\, \left( {{\text{m}}^{2} \;{\text{s}}^{ - 1} } \right)\) :

Thermal diffusivity

T (K):

Temperature

\(T_{{\text{w}}} \,\left( {\text{K}} \right)\) :

Wall temperature

\(T_{\infty }\, \left( {\text{K}} \right)\) :

Ambient temperature

\(S\left( 1 \right)\) :

Suction/injection parameter

\(M(1)\) :

Modified Hartmann number

\(k\,\left( {{\text{Ns}}\;{\text{m}}^{ - 2} } \right)\) :

Vertex viscosity

\(\left( {c_{{\text{p}}} } \right)_{{\text{f}}} \left( {{\text{J}}\;{\text{kg}}^{ - 1} \;{\text{K}}^{ - 1} } \right)\) :

Heat capacity of fluid

\(s\,\left( {\text{m}} \right)\) :

Arc length

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

Brownian motion parameter

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

Wall shear stress

\({\text{Ec}}(1)\) :

Eckert number

\({\text{Re}}_{{\text{s}}} (1)\) :

Reynolds number

\({\text{Le}}\) :

Lewis number

\({\Pr}(1)\) :

Prandtl number

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

Radius of curvature

\(\rho \left( {{\text{kg}}\;{\text{m}}^{ - 3} } \right)\) :

Fluid density

\(\nu \left( {{\text{m}}^{2} \;{\text{s}}^{ - 1} } \right)\) :

Viscosity of kinematic

\(\tau (1)\) :

Ratio between heat capacity and base fluid

\(\mu \left( {{\text{Ns}}\;{\text{m}}^{ - 2} } \right)\) :

Dynamic viscosity

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Authors and Affiliations

  1. Department of Mathematics, AIR University, Islamabad, 44000, Pakistan

    Mohammad Amjad & Iffat Zehra

  2. Mathematics and Its Applications in Life Sciences Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    S. Nadeem

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    S. Nadeem

  4. Department of Mathematics, Quaid-I-Azam University, Islamabad, 45320, Pakistan

    Nadeem Abbas

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Amjad, M., Zehra, I., Nadeem, S. et al. Thermal analysis of Casson micropolar nanofluid flow over a permeable curved stretching surface under the stagnation region. J Therm Anal Calorim 143, 2485–2497 (2021). https://doi.org/10.1007/s10973-020-10127-w

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