1 Introduction
2 Modelling of the physical problem
2.1 Problem statement and governing equations
2.2 Physical boundary conditions
2.3 Non-dimensional problem
2.4 Engineering coefficients
3 Implementation of numerical method
3.1 Validation of numerical computations
A | Mukhopadhyay and Gorla [19] | Sharidan et al. [20] | Chamkha et al. [21] | Present study |
---|---|---|---|---|
0.0 | – | – | – | 1.00000 |
0.2 | – | – | – | 1.068013 |
0.4 | – | – | – | 1.134691 |
0.6 | – | – | – | 1.199125 |
0.8 | 1.261479 | 1.261042 | 1.261512 | 1.261043 |
1.2 | 1.377850 | 1.377722 | 1.378052 | 1.377723 |
1.4 | – | – | – | 1.432846 |
2.0 | – | – | 1.587370 |
4 Discussion of graphical results
4.1 Impacts of unsteadiness parameter
4.2 Impacts of Weissenberg number
4.3 Impacts of Brownian motion parameter
4.4 Impacts of thermophoresis parameter
4.5 Impacts of Prandtl number
4.6 Impacts of Lewis number
A | \(\beta^{ * }\) | \(We\) | \(Re_{x}^{1/2} C_{fx}\) |
---|---|---|---|
0.0 | 0.3 | 2.0 | 0.46805 |
0.7 | – | – | 0.497807 |
1.4 | – | – | 0.513561 |
2.0 | – | – | 0.523043 |
0.2 | 0.0 | – | 0.474937 |
– | 0.2 | – | 0.714153 |
– | 0.4 | – | 0.83401 |
– | 0.6 | – | 0.92544 |
– | 0.8 | – | 1.00168 |
– | 0.3 | 1.0 | 0.715694 |
– | – | 2.0 | 0.479109 |
– | – | 3.0 | 0.345023 |
– | – | 4.0 | 0.270663 |
\(A\) | \(\beta^{ * }\) | \(Pr\) | \(Nt\) | \(Nb\;\) | \(Le\) | \(Re_{x}^{ - 1/2} Nu_{x}\) | \(Re_{x}^{ - 1/2} Sh_{x}\) |
---|---|---|---|---|---|---|---|
0.0 | 0.3 | 0.72 | 0.1 | 0.2 | 1.0 | 0.915093 | 0.671930 |
0.7 | – | – | – | – | – | 1.18310 | 0.926204 |
1.4 | – | – | – | – | – | 1.39156 | 1.10673 |
2.0 | – | – | – | – | – | 1.54809 | 1.23959 |
0.2 | 0.2 | – | – | – | – | 1.04339 | 0.794434 |
– | 0.4 | – | – | – | – | 1.06648 | 0.815047 |
– | 0.6 | – | – | – | – | 1.08310 | 0.830594 |
– | 0.8 | – | – | – | – | 1.96080 | 0.843116 |
– | 0.3 | 1.0 | – | – | – | 1.19642 | 0.949338 |
– | – | 3.0 | – | – | – | 1.90716 | 1.99536 |
– | – | 5.0 | – | – | – | 2.13629 | 2.83588 |
– | – | 7.0 | – | – | – | 2.17731 | 3.57517 |
– | – | 0.5 | 0.2 | – | – | 0.808876 | 0.351777 |
– | – | – | 0.4 | – | – | 0.795233 | − 0.123751 |
– | – | – | 0.6 | – | – | 0.782066 | − 0.579199 |
– | – | – | 0.8 | – | – | 0.769339 | − 1.01574 |
– | – | – | 0.5 | 0.1 | – | 0.800539 | − 1.606290 |
– | – | – | – | 0.3 | – | 0.776840 | 0.0632418 |
– | – | – | – | 0.5 | – | 0.753927 | 0.396419 |
– | – | – | – | 0.7 | – | 0.731779 | 0.538701 |
– | – | – | – | 0.2 | 1.0 | 0.788590 | − 0.35391 |
– | – | – | – | – | 5.0 | 0.758201 | 1.50967 |
– | – | – | – | – | 10.0 | 0.747420 | 2.75713 |
– | – | – | – | – | 15.0 | 0.742076 | 3.67417 |
5 Conclusions
- The most practical outcome of this study was that the fluid velocity was significantly enhanced by higher viscosity ratio parameter.
- Temperature of the nanofluids was considerably promoted by the thermophoresis phenomenon.
- Heat transfer rate was elevated by higher values of Lewis number.
- Velocity, temperature, and concentration profiles were depressed by increasing the unsteadiness parameter.
- Larger values of Brownian motion parameter created an enhancement in temperature profile due to higher thermal conductivity of the liquid.