Entropy Generation and Consequences of MHD in Darcy–Forchheimer Nanofluid Flow Bounded by Non-Linearly Stretching Surface
Abstract
:1. Introduction
2. Mathematical Modeling
Entropy Generation Modeling
3. Solution Methodology
4. Analysis
5. Conclusions
- Entropy optimization, heat and mass transport in Darcy–Forchheimer and MHD type nanofluid flow surrounded by a non-linear stretching surface is analyzed.
- Rate of Bejan number shows mixed behavior for elevated values of temperature difference parameter. An enhancement is noted for larger values.
- Skin friction enhances for all the parameters involved in momentum equation.
- Heat transfer rate declines while mass transfer intensifies for elevated numbers of thermal radiation parameters.
- Resistive force due to inertia and enhanced friction are the source of enhancement in heat convection.
- The concentration of nanoparticles reduces near the surface, whereas an enhancement is noted in the case of thermophoresis due to stronger thermophoretic force.
- An enhanced variation in stream lines is noted at distance far away from the origin. Near to the origin, this variation is very narrow.
- We observed that a more porous medium offers more retardational force (friction), which continuously diminishes the velocity of the fluid.
- Contour graphs given at and show an enhanced variation at distance sufficiently away from origin. Near to the origin, the variation is very narrow.
- Stream function graphs at and show a very narrow variation in the stream lines. At curves are not spread much as compared to case . Stronger magnetic effect boosts the opposing Lorentz forces which occur in the way of fluid motion and stream lines get affected.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Runge-Kutta 45 Method | |
MHD | Magnetohydrodynamics |
PDE | Partial Differential Equation |
ODE | Ordinary Differential Equation |
Cartesian velocity coordinates/m·s | |
Cartesian distance coordinates/m | |
Velocity (stretching)/m·s | |
m | Stretching rate/s |
Dynamic viscosity/Pa·s | |
Magnetic impact/intensity/A·m | |
Kinematic viscosity/ms | |
Density/kg·m | |
Brownian diffusion | |
thermophoresis | |
T | Temperature distributions /K |
C | Concentration distributions/kg·m |
Electric conductivity of the base fluid/( m) | |
Nanoparticles’ heat capacity/J·mk | |
Fluid’s heat capacity/J·mk | |
Drag force coefficient | |
K | Permeability |
Ratio of heat capacity of fluid and nanoparticles | |
Radiative heat flux | |
Stephen boltzmann constant | |
Mean absorption constant | |
Thermal diffusivity/m | |
k | Thermal conductivity/ |
Dimensionless Parameters | |
M | Magnetic parameter |
Prandtl number | |
Schmidt number | |
Brownian diffusion | |
thermophoresis | |
Sherwood factor | |
Nusselt factor | |
Entropy generation rate in two dimensions | |
Difference ratio | |
Entropy generation rate | |
Temperature difference | |
Brinkman number | |
Diffusive parameter | |
Forchheimer number | |
Porosity | |
Radiation parameter | |
Eckert number | |
Viscosity at initial position | |
Variable | |
Concentration distribution (dimensionless) | |
Temperature distribution (dimensionless) | |
Velocity (dimensionless) |
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M | |||
---|---|---|---|
M | Pr | Nusselt | Sherwood | |||||||
---|---|---|---|---|---|---|---|---|---|---|
0.330523 | 0.5403 | |||||||||
0.294335 | 0.539539 | |||||||||
0.146822 | 0.196834 | |||||||||
0.298447 | 0.550958 | |||||||||
0.294335 | 0.539539 | |||||||||
0.29052 | 0.529184 | |||||||||
0.386878 | 0.542202 | |||||||||
0.294335 | 0.539539 | |||||||||
0.157756 | 0.222705 | |||||||||
0.397385 | 0.501379 | |||||||||
0.294335 | 0.539539 | |||||||||
0.24219 | 0.561276 | |||||||||
0.294335 | 0.539539 | |||||||||
0.374306 | 0.509569 | |||||||||
0.43873 | 0.487011 | |||||||||
0.294335 | 0.539539 | |||||||||
0.271793 | 0.309337 | |||||||||
0.244013 | 0.081471 | |||||||||
0.294335 | 0.539539 | |||||||||
0.26720 | 0.589734 | |||||||||
0.241696 | 0.606221 | |||||||||
0.39101 | 0.495559 | |||||||||
0.321959 | 0.526972 | |||||||||
0.252895 | 0.55839 | |||||||||
0.294335 | 0.539539 | |||||||||
0.290366 | 0.76239 | |||||||||
0.288085 | 0.952778 |
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Rasool, G.; Shafiq, A.; Khan, I.; Baleanu, D.; Sooppy Nisar, K.; Shahzadi, G. Entropy Generation and Consequences of MHD in Darcy–Forchheimer Nanofluid Flow Bounded by Non-Linearly Stretching Surface. Symmetry 2020, 12, 652. https://doi.org/10.3390/sym12040652
Rasool G, Shafiq A, Khan I, Baleanu D, Sooppy Nisar K, Shahzadi G. Entropy Generation and Consequences of MHD in Darcy–Forchheimer Nanofluid Flow Bounded by Non-Linearly Stretching Surface. Symmetry. 2020; 12(4):652. https://doi.org/10.3390/sym12040652
Chicago/Turabian StyleRasool, Ghulam, Anum Shafiq, Ilyas Khan, Dumitru Baleanu, Kottakkaran Sooppy Nisar, and Gullnaz Shahzadi. 2020. "Entropy Generation and Consequences of MHD in Darcy–Forchheimer Nanofluid Flow Bounded by Non-Linearly Stretching Surface" Symmetry 12, no. 4: 652. https://doi.org/10.3390/sym12040652