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Magnetohydrodynamic nonlinear thermal convection nanofluid flow over a radiated porous rotating disk with internal heating

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Abstract

Nonlinear convective flow and heat transfer characteristics are analyzed between stationary nonporous and porous rotating disks utilizing graphene nanoparticles in a water and ethylene glycol base fluid. Heat transfer characteristics are analyzed via incorporating thermal radiation and heat absorption/generation. The governing fluid equations are computed numerically using Runge–Kutta based shooting technique after employing appropriate transformations. Characteristics of sundry variables are elaborated graphically as well as through the construction of Table for water base and ethylene glycol based graphene nanoparticles. It is observed that improvements in nonlinear convection variable owing to temperature and heat generation variable improve wall friction in radial direction. Improvement in Hartman number decreased wall friction in radial and tangential directions along with Nusselt number in graphene/ethylene glycol and graphene/water nanofluid. Ethylene glycol based graphene nanofluid takes less time for execution as compared to water based nanofluid.

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Abbreviations

\(u,v,w\) :

Velocity components of fluid phase in \(\,\,r,\phi ,z\) directions \(\left( {{\text{ms}}^{ - 1} } \right)\)

\(T\) :

Temperature of the nanofluid \(\left(K \right)\)

\(T_{1}\) :

Temperature at fixed impermeable disk \(\left(K \right)\)

\(T_{2}\) :

Temperature at rotating porous disk \(\left(K \right)\)

\(\upsilon\) :

Kinematic viscosity \(\left( {{\text{m}}^{2} \,{\text{s}}^{ - 1} } \right)\)

\(g\) :

Acceleration due to gravity \(\left( {{\text{m}}\,{\text{s}}^{ - 2} } \right)\)

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

Density of the nanofluid \(\left( {{\text{kg}}\,{\text{m}}^{ -3} } \right)\)

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

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

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

Density of the nanoparticles \(\left( {{\text{kg}}\,{\text{m}}^{ -3} } \right)\)

\(\mu_{f}\) :

Dynamic viscosity of the base fluid \(\left( {{\text{kg}}\;{\text{ms}}^{ - 1} } \right)\)

\(\mu_{{{\text{nf}}}}\) :

Dynamic viscosity of the nanofluid \(\left( {{\text{kg}}\;{\text{ms}}^{ - 1} } \right)\)

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

Specific heat capacity at constant pressure of the fluid (\({\text{J}}\,{\text{kg}}^{ - 1} {\text{K}}^{ - 1}\))

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

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

\(\left( {\rho c_{\rm{p}} } \right)_{\rm{nf}}\) :

Effective heat capacity \(\left( {{\text{kg}}\,{\text{m}}^{ - 3} {\text{K}}^{ - 1} } \right)\)

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

Effective heat capacity of the particle medium (\({\text{kg}}\,{\text{m}}^{ - 3} {\text{K}}^{ - 1}\))

\(\alpha_{{{\text{nf}}}}\) :

Diffusion coefficient \(({\text{m}}^{2} {\text{s}}^{ - 1} )\)

\(\nu_{{{\text{nf}}}}\) :

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

\(\sigma^{*}\) :

Stefan–Boltzmann constant \(({\text{W}}\;{\text{m}}\,{\text{K}}^{ - 4} )\)

\(\sigma\) :

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

\(k^{*}\) :

Mean absorption coefficient

\(M\) :

Hartman Number

\(\phi\) :

Nano particle volume fraction

\(\Pr\) :

Prandtl number

\(R\) :

Radiation parameter

\(Q\) :

Heat generation/absorption coefficient

\(\zeta\) :

Similarity variable

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

Skin friction coefficient

\(Nu_{{\text{x}}}\) :

Local Nusselt number

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

Local Reynolds number

\(l\) :

Distance between two disks

\(\Omega \,\) :

Angular speed of the rotating disk

\(\varepsilon\) :

Measure of the angular speed or momentum of the of the rotating porous disk

\(W\) :

Suction velocity at which fluid is withdrawn from the rotating porous disk (Injection if \(W\) is negative.)

\(\alpha_{1}\) :

Thermal buoyancy variable

\(\beta_{{\text{t}}}\) :

Nonlinear convection variable

\(\delta\) :

Heat generation variable

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Authors and Affiliations

  1. Department of Mathematics, Kristu Jayanti College, Autonomous, Bangalore, Karnataka, 560077, India

    S. Mamatha Upadhya

  2. Department of Mathematics, Sri Venkateswara University, Tirupati, 517502, India

    R. L. V. Renuka Devi

  3. Department of Mathematics, GITAM School of Science, GITAM University, Bangalore, Karnataka, India

    C. S. K. Raju

  4. Mechancal Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Hafiz Muhammad Ali

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  1. S. Mamatha Upadhya
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Upadhya, S.M., Devi, R.L.V.R., Raju, C.S.K. et al. Magnetohydrodynamic nonlinear thermal convection nanofluid flow over a radiated porous rotating disk with internal heating. J Therm Anal Calorim 143, 1973–1984 (2021). https://doi.org/10.1007/s10973-020-09669-w

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