A spherical pellet of pure silicon initial diameter 1 cm is

A spherical pellet of pure silicon (initial diameter = 1 cm) is suspended in a stream of pure molten aluminum at 800°C. The bulk aluminum velocity is 10 cm/s. As silicon dissolves in the flowing aluminum, the diameter of the pellet decreases with time. Given the large volume of liquid aluminum, it may be considered that the concentration of silicon in the bulk fluid is essentially unchanged with time. The relevant properties are given below.

A. Estimate the initial mass transfer rate from the pellet when its diameter is 1 cm.

B. What is the initial rate at which the pellet diameter changes with time when the pellet diameter is 1 cm?

C. Repeat the calculations in parts (a) and (b) when the pellet diameter is 0.5 cm.

Data: Properties of Al: density = 2350 kg/m3; dynamic viscosity =1.5×10-3 Pa.s; diffusion coefficient of Si in liquid Al = 1×10-8 m2/s. Density of silicon = 2.3 g/cm3.

Please show all steps and explain assumptions.

Al-Si Phase Diagram Weight Percent Silicon 0 10 20 40 80 90 1500 1414 1300 1100 900 700 8804520C 122 (Si) s00-(AI) 10 40 50 60 80 90 100 Atomic Percent Silicon Si

Solution

This Question is related to Pressure Die Casting Process in which the Molten metal is Aluminium is consider:-

Temperature of a Molten Aluminum - 800 degree

Diameter of a Pallet = 1cm

Density of a Material = 2350 kg/m3

Area of a Casting ar which material flow = 3.14*(0.5)² = 0.785 cm²

We consider area in the feeding channels control flow rate into mold cavity & control pouring time

Velocity of the fluid = 10m/s

Velocity = Distance /Time

Distance = 10m = 1000 cm

Volume = Area * Distance of material flow

= 0.785 * 1000 = 785 cm³

Volume of Casting = Weight of Component / Density

785 = Weight of Component / 2.35

Weight of Component = 1844 gms

Volume of Metal throught gate P = Volume of Casting + 10% volume of overflow

P = 785 + 78.5

P = 863.5 cm³

Fill Rate = (P * 1000) t

= (863.5 * 1000 ) / 1

= 8.63 * 10³ cm³/sec

When the Pallet diameter is 0.5 cm

Area of a Casting ar which material flow = 3.14*(0.25)² = 0.196 cm²

Volume = 196.25 cm³

P = 215 cm³

Fill Rate = (215 * 1000 ) / 1

= 2.15 * 10³ cm³/sec

All Calculations is based on Pressure Die Casting