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Darcy–Forchheimer flow under rotating disk and entropy generation with thermal radiation and heat source/sink

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Abstract

This article investigates the second law of thermodynamics for chemically reactive Sisko nanofluid by a rotating disk saturated with non-Darcy porous medium. Thermophoresis and Brownian motion on irreversibility has been examined through Buongiorno model. The novel features of nonlinear thermal radiation, Joule heating, MHD and non-uniform heat source/sink are accounted. Modified Arrhenius model is executed to characterize the impact of activation energy. The governing flow equations are solved and validated numerically by adopting Runge–Kutta–Fehlberg method. It is noticed from the present analysis that irreversibility rate and Bejan number have reverse behavior for Brinkman number. Growing behavior of concentration is witnessed for greater estimations of activation energy variable. Total entropy generation has significant impact on reaction rate constant.

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Abbreviations

\(B_{1}\) :

Magnetic field strength

\({\hat{\text{B}}\text{e}}\) :

Bejan number

\({\text{Br}}\) :

Brinkman number

\(\left( {\hat{C},\hat{C}_{\infty } } \right)\) :

Nanoparticle and ambient volume fraction

\(C_{{{\text{F}}_{1} }}\) :

Skin friction coefficient

\(\left( {D_{\text{B}} ,D_{\text{T}} } \right)\) :

Brownian and thermophoretic diffusion coefficients

\(\hat{E}_{\text{a}}\) :

Activation energy parameter

\(\hat{F}_{\text{r}}\) :

Forchheimer number

\(F_{1} \left( {\xi_{1} } \right)\) :

Similarity function

\(F_{2}\) :

Non-uniform inertia coefficient

\(K^{*}\) :

Permeability of porous space

\(K_{\text{r}}^{2}\) :

Reaction rate constant

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

Boltzmann constant

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

Mean absorption coefficient

Le:

Lewis number

\(M_{2}\) :

Magnetic parameter

\(\hat{N}_{1 }\) :

Buoyancy ratio forces

\(\left( {\hat{N}_{\text{b}} ,\hat{N}_{\text{t}} } \right)\) :

Brownian and thermophoresis parameters

\(\hat{N}_{\text{G}}\) :

Entropy generation rate

\(\hat{N}_{\text{r}}\) :

Radiation parameter

\({\text{Nu}}_{{{\text{z}}_{1} }}\) :

Local Nusselt number

\(p\) :

Fitted rate constant

\(\Pr\) :

Prandtl number

\(\left( {S_{1} ,S_{2} } \right)\) :

Space- and temperature-dependent heat source/sink coefficients

\(S_{3}\) :

Stretching parameter

Sc:

Schmidt number

\(S_{\text{a}}\) :

Material parameter

\({\text{Sh}}_{{{\text{z}}_{1} }}\) :

Sherwood number

\(\left( {\hat{T}_{\text{w}} ,\hat{T}_{\infty } } \right)\) :

Surface and ambient temperature

\(\left( {\hat{\beta }_{\text{T}} ,\hat{\beta }_{\text{C}} } \right)\) :

Nonlinear thermal and solutal convection parameters

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

Thermal diffusivity

\(\delta_{1}\) :

Temperature difference

\(\delta_{2}\) :

Concentration difference variable

\(\sigma_{2}\) :

Electrical conductivity of base fluid

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

Mixed convection parameter

\(\xi_{2}\) :

Chemical reaction parameter

\(\eta_{1}\) :

Reaction rate constant

\(\left( {\varGamma_{1} ,\varGamma_{3} } \right)\) :

Linear thermal expansion coefficients

\(\left( {\varGamma_{2} ,\varGamma_{4} } \right)\) :

Nonlinear solutal expansion coefficients

\(\varTheta_{1}\) :

Dimensionless temperature

\(\phi_{1}\) :

Dimensionless concentration

\(\hat{\varOmega }_{1}\) :

Angular velocity

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Authors and Affiliations

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

    Sohail Nadeem

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

    Sohail Nadeem

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

    Misbah Ijaz

  4. Department of Mathematics, HITEC University, Cantt. Taxila, Rawalpindi, Punjab, 47080, Pakistan

    Muhammad Ayub

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  1. Sohail Nadeem
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Correspondence to Misbah Ijaz.

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Nadeem, S., Ijaz, M. & Ayub, M. Darcy–Forchheimer flow under rotating disk and entropy generation with thermal radiation and heat source/sink. J Therm Anal Calorim 143, 2313–2328 (2021). https://doi.org/10.1007/s10973-020-09737-1

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