Impacts of Casson Model on Hybrid Nanofluid Flow over a Moving Thin Needle with Dufour and Soret and Thermal Radiation Effects
Abstract
:1. Introduction
2. Mathematical Formulation of the Problem
3. Method of Solution
4. Results and Discussions
5. Conclusions
- The boundary layer that forms around the needle is equally tiny in size.
- The series solution is obtained with the proposed HAM method. HAM gives better approximations than other numerical methods.
- In total, 2% nanoparticles are included and the rate of heat transfer increases up to 45%.
- The Casson parameter tends to makes the flow field smaller. Physically, increasing the Casson parameter causes an enhancement in the fluids dynamic viscosity, which reduces the fluid motion and results in a decrease in the profile of velocity.
- As the magnetic field strength increases, the velocity profiles become narrower, because magnetic fields produce Lorentz forces that oppose motion.
- As a result of the thermal radiation being included, heat is transferred more quickly.
- As the radiation parameter is increased, the temperature within the boundary layer naturally increases, because thermal radiation is dominant over a thermal conduction heat transfer.
- The rates of mass and heat transfer as well as the Dufour and Soret effects are accelerated, because with the Dufour effect, the concentration gradient affects the flow of thermal energy flux, and higher Soret numbers correspond to a greater temperature gradient, resulting in a greater convective flow.
- The present results are useful in the cooling technology and thermal science community.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
MHD | Magnetohydrodynamics | |
HAM | Homotopy Analysis Method | |
c | needle radius (m) | |
velocity at the surface (m.s−1) | ||
wall concentration | ||
temperature at the surface (K) | ||
ambient concentration | ||
temperature of mass fluid (K) | ||
coefficient of mean absorption (c.m−1) | ||
concentration susceptibility | ||
free stream velocity (m.s−1) | ||
specific heat (kg−1.J) | ||
mass diffusion coefficient (m2.s−1) | ||
ambient temperature (K) | ||
velocity components along x and r directions (m.s−1) | ||
radiative heat flux (kg.m2.s−3) | ||
ratio of thermal diffusion | ||
Skin friction | ||
Sherwood number | ||
C | fluid concentration | |
Nusselt number | ||
Greek symbols | ||
kinematic viscosity (m2.s−1) | ||
Casson parameter | ||
fluid density (kg.m−3) | ||
velocity ratio parameter | ||
dynamic viscosity of a fluid (m2.s−1) | ||
Stefan-Boltzmann constant (W.m−2.K−4) | ||
Subscripts | ||
hnf | hybrid nanofluid | |
‘ | differentiation w.r.t. | |
nf | nanofluid | |
f | fluid | |
ambient |
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Properties | Al2O3 | Cu | Ethylene Glycol |
---|---|---|---|
(kg.m−3) | 3970 | 8933 | 1190 |
(W.m−1.K−1) | 40 | 400 | 0.258 |
(J.kg−1.K−1) | 765 | 385 | 2400 |
(.m−1) |
Properties | Nanofluid | Hybrid Nanofluid |
---|---|---|
Density | ||
Heat capacity | ||
Dynamic viscosity | ||
Thermal conductivity | ||
Electrical Conductivity |
Order | |||
---|---|---|---|
1 | 0.50000 | 1.00001 | 1.00001 |
5 | 0.50002 | 1.00005 | 1.00004 |
10 | 0.50004 | 1.00011 | 1.00008 |
15 | 0.50006 | 1.00015 | 1.00012 |
20 | 0.50009 | 1.0002 | 1.00016 |
25 | 0.50011 | 1.00025 | 1.0002 |
30 | 0.50013 | 1.0003 | 1.00024 |
35 | 0.50016 | 1.00035 | 1.00029 |
40 | 0.50018 | 1.0004 | 1.00033 |
M | Du | Rd | ||||
---|---|---|---|---|---|---|
1 | 0.1 | 0.2 | 0.2 | −2.30857 | −1.92005 | −1.75259 |
1.4 | −1.63701 | 1.46098 | 1.46092 | |||
1.7 | 1.46086 | 1.04996 | 1.04996 | |||
2 | 1.04991 | 1.04987 | 1.04983 | |||
1 | 0.1 | 0.2 | 0.2 | −2.30857 | −2.37217 | −2.43422 |
0.2 | −2.4948 | 1.46113 | 1.46059 | |||
0.3 | 1.46006 | 1.45955 | 1.05001 | |||
0.4 | 1.0496 | 1.0492 | 1.04881 | |||
1 | 0.1 | 0.2 | 0.1 | −2.30857 | −2.30857 | −2.30857 |
0.2 | −2.30857 | 1.17214 | 1.46113 | |||
0.3 | 1.71912 | 1.9514 | 1.0528 | |||
0.4 | 1.05001 | 1.04792 | 1.04628 | |||
1 | 0.1 | 0.1 | 0.2 | −2.30857 | −2.30857 | −2.30857 |
0.2 | −2.30857 | 1.44608 | 1.46113 | |||
0.3 | 1.4762 | 1.49127 | 1.05029 | |||
0.4 | 1.05001 | 1.04974 | 1.04946 |
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Reddy, V.S.; Kandasamy, J.; Sivanandam, S. Impacts of Casson Model on Hybrid Nanofluid Flow over a Moving Thin Needle with Dufour and Soret and Thermal Radiation Effects. Math. Comput. Appl. 2023, 28, 2. https://doi.org/10.3390/mca28010002
Reddy VS, Kandasamy J, Sivanandam S. Impacts of Casson Model on Hybrid Nanofluid Flow over a Moving Thin Needle with Dufour and Soret and Thermal Radiation Effects. Mathematical and Computational Applications. 2023; 28(1):2. https://doi.org/10.3390/mca28010002
Chicago/Turabian StyleReddy, Vinodh Srinivasa, Jagan Kandasamy, and Sivasankaran Sivanandam. 2023. "Impacts of Casson Model on Hybrid Nanofluid Flow over a Moving Thin Needle with Dufour and Soret and Thermal Radiation Effects" Mathematical and Computational Applications 28, no. 1: 2. https://doi.org/10.3390/mca28010002