Sentence examples for branch solutions from inspiring English sources
Velocity profiles for upper and lower branch solutions are shown in Fig. 4a, b, respectively.
The temperature increases as φ increases and decreases as γ increases in the case of shrinking sheet (upper and lower branch solutions [Fig. 7b, c]).
Further, Figure 7 shows that Cu-water nanofluid has the highest local Nusselt number compared with Ag-water nanofluid and water for the upper branch solutions.
The temperature profile decreases with the increasing values of |δ| and increases with the increase of φ in both upper and lower branch solutions (Fig. 8b, c).
Dual solutions are obtained in shrinking sheet beyond a suction critical point which are classified as upper and lower branch solutions.
On the other hand, Ag-water nanofluid has the highest local Nusselt number compared with Cu-water nanofluid and water for the lower branch solutions.
The velocity profile for upper branch solution and lower branch solution is presented in Fig. 6a, b, respectively.
For the upper branch solution, the value of β increases with γ, |δ| and φ, and an opposite behaviour is noted for lower branch solution.
Eq. 17IV gives a unique solution for the stretching sheet and upper branch solution for the shrinking sheet.
Equation 17IV gives a unique solution for the stretching sheet and upper branch solution for the shrinking sheet.
The increasing values of nanoparticle volume fraction decrease the velocity components in stretching sheet and shrinking sheet lower branch solution and increase the velocity profile in shrinking sheet lower branch solution.
