Unsteady Magnetohydrodynamic Radiative Casson Nanofluid within Chemically Reactive Flow over a Stretchable Surface with Variable Thickness through a Porous Medium
Abstract
:1. Introduction
2. Analysis and Formulation of the Problem
3. Numerical Results
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Cf | local skin-friction coefficient (N·m−2) |
Cp | specific heat at constant pressure (J/kg·K) |
Gr | Grashof number (-) |
g | acceleration due to gravity (m s−2) |
B | strength of the magnetic field (Tesla) |
kf | thermal conductivity of the fluid (W/m K) |
ks | thermal conductivity of the solid (W/m K) |
Ec | Eckert number (-) |
K | porosity parameter (-) |
Nt | thermophoretic parameter |
Nb | Brownian motion parameter |
Sc | Schmidt number (-) |
fw | surface flow flux parameter (-) |
Rc | Chemical reaction parameter |
M | magnetic parameter (-) |
NT | temperature ratio parameter (-) |
Nu | local Nusselt number (-) |
Pr | Prandtl number (-) |
qr | radiative heat flux (W/m2) |
Rd | radiative parameter (-) |
Re | Reynolds number (-) |
Shx | Sherwood number (-) |
Q | heat generation coefficient (J/m2·K·s) |
Tf | temperature of the fluid (K) |
qw | surface heat flux (w/m2) |
qc | mass flux (kg/m2·s) |
T∞ | temperature of the ambient fluid (K) |
Tw | temperature at the surface (K) |
(u, v) | fluid velocities in the x, y-directions (ms−1) |
(x, y) | axis direction (m) |
Greek symbols | |
ψ | stream function (kg/m·s) |
Θ | nanofluid dimensionless temperature (-) |
Φ | nanofluid dimensionless concentration (-) |
τw | shearing stress (N/m2) |
ρ | density of the fluid (kg m−3) |
µ | dynamic viscosity of the fluid (N s/m2) |
υ | kinematic viscosity (N s/m2) |
γ | thermal variation parameter (W/m3·K) |
α | conjugate conduction heat parameter |
θ | dimensionless temperature (-) |
heat generation factor (-) | |
volume fraction (-) | |
β | coefficient of thermal expansion (1/K) |
η | space variable (-) |
Subscripts | |
w | wall conditions |
∞ | ambient temperature |
Superscript | |
\ | differentiation with respect to y |
References
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Pr | Elbashbeshy [3] | Ishak [4] | Ibrahim [5] | Present Study | |
---|---|---|---|---|---|
−θ\(0) | −θ\(0) | −θ\(0) | −f\\(0) | −θ\(0) | |
0.72 | 0.808 | 0.8086 | 0.8095 | 1.0000 | 0.80864 |
1.0 | 1.0 | 1.0 | 1.0001 | 1.0000 | 1.0000 |
10 | 3.7207 | 3.7202 | 3.7208 | 1.0000 | 3.7207 |
Pr = 10, β = 5, At = 0.1, Nb = 0.5, ϕ = 0.05, fw = 1, M = 1.0, Rd = 0.5, λ = 0.2, δ = 0.2, γ = 0.5, α = 0.5, Rc = 0.2, K = 0.2, Ec = 0.5, Nt = 0.5, m = 1, Sc = 10.0, n = 1. | ||||||
---|---|---|---|---|---|---|
γ | β | Sc | M | −f\\(0) | −θ\(0) | −C\(0) |
0 | 5 | 10 | 1.0 | 1.896675 | 2.256345 | 4.787477 |
0.5 | 1.878542 | 2.228124 | 4.715303 | |||
1 | 1.860481 | 2.200052 | 4.643463 | |||
1.5 | 1.842493 | 2.172133 | 4.571964 | |||
2 | 1.824579 | 2.144371 | 4.500815 | |||
0.5 | 0.5 | 10 | 1.0 | 1.824765 | 0.02412134 | 6.678931 |
1 | 1.85813 | 1.453518 | 5.398466 | |||
2 | 1.871352 | 1.961246 | 4.950035 | |||
5 | 1.878542 | 2.228124 | 4.715303 | |||
0.5 | 0.5 | 5 | 1.0 | 1.878542 | 2.228124 | 4.715303 |
10 | 1.920071 | 2.655981 | 9.524478 | |||
15 | 1.935082 | 2.916045 | 14.31092 | |||
20 | 1.942566 | 3.09288 | 19.10896 | |||
0.1 | 0.5 | 10 | 0.2 | 1.403348 | 1.917512 | 0.3306047 |
1 | 1.704235 | 1.632986 | 0.5422387 | |||
2 | 2.019402 | 1.273092 | 0.8306606 | |||
3 | 2.290982 | 0.9057231 | 1.140812 |
Pr = 6.2, β = 2, A = 0.8, fw = 2, Sc = 10.0, λ = 0.5, α = 0.5, ẟ = 0.2, Rc = 0.3, K = 0.2, Ec = 0.5, Nt = 0.2, Nb = 0.1, γ = 0.5, m = 1, n = 2, M = 3 | |||||
---|---|---|---|---|---|
Rd | ϕ | Rc | −f\\(0) | −θ\(0) | −C\(0) |
0 | 0.05 | 0.3 | 2.97296 | 4.770681 | 12.2837 |
0.2 | 2.969926 | 4.239647 | 13.26994 | ||
0.8 | 2.961826 | 3.223742 | 15.12073 | ||
1.6 | 2.952785 | 2.49741 | 16.40074 | ||
0.8 | 0 | 2.699535 | 3.260639 | 15.0950 | |
0.05 | 2.864129 | 3.338922 | 14.9355 | ||
0.1 | 2.964379 | 3.494682 | 14.63177 | ||
0.15 | 3.004126 | 3.698014 | 14.24473 | ||
0.2 | 2.989678 | 3.922428 | 13.82292 | ||
0.8 | 0.05 | 0 | 2.86105 | 3.082186 | 15.0847 |
1 | 2.864047 | 3.100647 | 18.95979 | ||
2 | 2.86548 | 3.110097 | 21.52028 | ||
3 | 2.866947 | 3.120559 | 25.26479 | ||
4 | 2.86861 | 3.134327 | 32.89318 |
Pr = 7, β = 0.5, A = 0.1, Nt = 0.5, Nb = 0.5, Sc = 10.0, Rd = 0.5, λ = 0.2, α = 0.2, Rc = 0.2, ϕ = 0.05, γ = 0.5, M = 1, fw = 0.2, K = 0.3, Ec = 0.5 | |||||||
---|---|---|---|---|---|---|---|
fw | K | Ec | m | n | −f\\(0) | −θ\(0) | −C\(0) |
−0.7 | 0.3 | 0.5 | 1 | 2 | 1.166979 | 0.6896947 | 2.128103 |
−0.5 | 1.244454 | 0.725028 | 2.530241 | ||||
0 | 1.466949 | 0.8371657 | 4.175094 | ||||
0.5 | 1.729128 | 0.9243421 | 7.03585 | ||||
0.7 | 1.844753 | 0.9296373 | 8.493711 | ||||
0.2 | −0.7 | 1.221034 | 1.467047 | 4.862795 | |||
−0.3 | 1.369453 | 1.234478 | 4.976422 | ||||
0 | 1.471461 | 1.05878 | 5.069695 | ||||
0.3 | 1.567185 | 0.8816247 | 5.169064 | ||||
0.7 | 1.686805 | 0.6427757 | 5.310168 | ||||
0.3 | 0 | 1.586038 | 2.333166 | 4.397425 | |||
0.5 | 1.567185 | 1.357548 | 5.169064 | ||||
0.7 | 1.558611 | 0.8816247 | 5.612531 | ||||
1 | 1.544367 | 0.1232255 | 6.556958 | ||||
0.5 | 1 | 1.567185 | 0.8816247 | 5.169064 | |||
2 | 1.576039 | 1.405037 | 5.738256 | ||||
3 | 1.582981 | 1.834487 | 6.289898 | ||||
2 | 1 | 1.566207 | 1.088665 | 5.366438 | |||
2 | 1.576039 | 1.405037 | 5.738256 | ||||
3 | 1.582743 | 1.671965 | 6.084604 |
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Sedki, A.M.; Qahiti, R. Unsteady Magnetohydrodynamic Radiative Casson Nanofluid within Chemically Reactive Flow over a Stretchable Surface with Variable Thickness through a Porous Medium. Energies 2023, 16, 7776. https://doi.org/10.3390/en16237776
Sedki AM, Qahiti R. Unsteady Magnetohydrodynamic Radiative Casson Nanofluid within Chemically Reactive Flow over a Stretchable Surface with Variable Thickness through a Porous Medium. Energies. 2023; 16(23):7776. https://doi.org/10.3390/en16237776
Chicago/Turabian StyleSedki, Ahmed M., and Raed Qahiti. 2023. "Unsteady Magnetohydrodynamic Radiative Casson Nanofluid within Chemically Reactive Flow over a Stretchable Surface with Variable Thickness through a Porous Medium" Energies 16, no. 23: 7776. https://doi.org/10.3390/en16237776
APA StyleSedki, A. M., & Qahiti, R. (2023). Unsteady Magnetohydrodynamic Radiative Casson Nanofluid within Chemically Reactive Flow over a Stretchable Surface with Variable Thickness through a Porous Medium. Energies, 16(23), 7776. https://doi.org/10.3390/en16237776