Study on MHD Flow over a Stretching Surface with Convective Boundary Condition by Numerical Method

The thermal and mass diffusive MHD flow through a stretching sheet has been inspected in the presence of a chemically reactive solute under convective boundary conditions in the present paper. The non-linear PDEs of the system concerning the flow, temperature, and species are recasted into a set of non-linear ODEs using ST. The consequential system of the differential equations is numerically resolved by using an implicit FDS in combination with the QL technique. The velocity ratio factor plays an important role in reducing the thickness of the velocity boundary layer, whereas the presence of magnetic parameters decreases the thickness of the velocity boundary layer profile. The study reveals that the fluid moves away from the surface during injection, resulting in a fall of the velocity gradient, whereas the opposite effect is observed in suction. The thermal and concentration boundary layer thicknesses are influenced by non-dimensional numbers, namely Prandtl and Schmidt numbers. The reaction rate parameter acts as a decelerating agent, and it thins the solute boundary layer formed in the neighborhood of the sheet. An increase in the convective parameter leads to an increase in the plate surface temperature. The present results of the paper are compared with the existing one, and good agreement is found between them.

Effects of the Flow Speed on Dendritic Growth in Phase-Field Simulation of Binary Alloy with Convection

A phase-field approach which incorporates mass and momentum and solute conservation equations for simulation of Al-Si binary alloy solidification is studied. The effect of force flow on the dendrite growth and solute profile during the solidification of binary alloy were investigated. The results indicate that dendritic grows unsymmetrically under a forced flow, the growth velocity of the upstream tip is faster than the downstream tip. With the force flow, the upstream tip grows faster due the thinner solute boundary layer. The solute gradient in the solid/liquid interface regions of the upstream tip is higher than that of the downstream tip. The faster the flow velocity, the greater the solute gradients in the solid/liquid interface regions of the upstream tip, the thinner the diffusion layer before the upstream tip. The downstream tip is opposed to the upstream tip. The simulations agree qualitatively with the solidification theoretical results.

Phase-Field Simulation of Directional Solidification Microstructure Evolution in a Binary Alloy

In order to obtain the directional microstructure of different supersaturation and growing velocity, three simulations is calculated with different initial temperature. When the initial temperature is 1576K, and the supersaturation and growing velocity are smaller. The average space length of columnar crystals is bigger, and the directional microstructure grows by the wide columnar crystals. Microsegregation is smaller; when the initial temperature is 1574K, the supersaturation and growing velocity increase. when the initial temperature falls to 1566K, the planar interface comes back, and microsegregation decreases rapidly. The directional microstructure grows by the thinnest columnar crystals. At the same time, the transverse solute profiles and solute boundary layer are also talked in this paper.

The Coarsening of Dendrite Arm Spacing during Solidification of Al-Cu-Mn Alloy

A secondary dendrite arm spacing coarsening model for multi-component alloy is proposed, where the back diffusion flux in solid is simplified by introducing the parameter of solute boundary layer,δi. The simplified model was applied to the predication of the secondary arm spacing of directional solidified Al-Cu-Mn alloy. The good agreement between the experimental results and the calculated lines shows that this simplified model is satisfactory for the prediction of dendrite arm coarsening during solidification in multi-component alloys.

SOLUTE FIELD ACROSS DIFFUSE INTERFACE DURING TRANSIENT PROCESS OF BINARY ALLOYS SOLIDIFICATION IN PHASE FIELD MODE

The establishment of solute boundary layer is studied by using a quantitative phase field model during the initial transient stage of binary alloys solidification. Results reveal that the time-dependent solute distribution shows good agreements with the previous analytical results. The planar instability is discussed according to the time-dependent constitutional supercooling with different pulling velocities. Moreover, the critical pulling velocity of planar instability can be obtained by investigating the interface velocity of the critical instability with different pulling velocities.