Sakiadis flow
Figure 18 Effect of different values of \(Sr\) on concentration profiles
The numerical computations have been done for different parameters and we selected the following values: Prandtl number \((Pr)\) is taken to be\(0.72\) which corresponds to air and positive value of the buoyancy parameters \(Gr_{x}>0\), which corresponds to the cooling problem, the local magnetic field parameter \((M_{x}=1,\ 2,\ 3,\ 4,\ 5)\), local Grashof number \((Gr_{x}=0.1,\ 0.2,\ 0.3,\ 0.4,\ 0.5)\), Eckert number\((Ec=1,\ 2,\ 3,\ 4,\ 5)\), Prandtl number\((Pr=0.72,\ 1,\ 3,\ 4,\ 5)\), Dufour number\((D_{f}=0.1,\ 1.1,\ 1.2,\ 1.3,\ 1.4)\), Soret number \((Sr=1.00)\), Schmidt number \((Sc=1.00)\), local Solutal Grashof number\((Gc_{x}=0.1)\), variable thermal conductivity parameter\((\varepsilon=0.1)\) and thermal radiation parameter\((k_{0}=0.5)\) respectively. The effects of \(Gr_{x}\), \(M_{x}\),Ec, \(\Pr\) and \(D_{f}\) on local skin-friction coefficient, local Nusselt number and local Sherwood number are shown in Tables (1) – (3).
Table 1 shows the influence of the flow parameter on skin-friction coefficient for Blasius and Sakiadis flow. Increase \(Gr_{x}\),Ec and \(\Pr\) brings an increase in skin-friction coefficient as increase in \(M_{x}\) and \(D_{f}\) results in the decrease of skin-friction coefficient for Blasius and Sakiadis flow respectively. Table (2) and (3) shows the flow parameters influence on the Nusselt and Sherwood numbers. Increase in local Grashof number\((Gr_{x})\) results in the increase of both Nusselt and Sherwood numbers for Blasius flow but decreases for Sakiadis flow. Increase in Eckert number \((Ec)\) brings an increase in Nusselt and Sherwood numbers for both Blasius and Sakiadis flow. But decreases in Nusselt and Sherwood number for Blasius-Sakiadis flow with increasing values of Dufour number \((D_{f})\).
From Tables (2) and (3), increasing values of \(M_{x}\) and \(\Pr\), results in increasing values of Nusselt and Sherwood numbers both for Blasius and Sakiadis flow. Increase in \(M_{x}\) brings a decrease in both Nusselt and Sherwood numbers for Blasius-Sakiadis flow which are in agreement with the observations of Gangadhar (see Table (3)).
Table 1 Computation of skin-friction coefficient\(f^{{}^{\prime\prime}}\left(0\right)\) for several values of the varying governing parameters