
Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Semester satu, dua, tiga, empat, dan lima
Typology: Exercises
1 / 1
This page cannot be seen from the preview
Don't miss anything!
Homework # 1 Magister Program in Chemical Engineering Universitas Gadjah Mada Due date: November 7, 2018
3
2 A huge volcanic material in the form of a 2 m diameter sphere is slowly cooled and solidified due to the contact with the surrounding air which is at 20 oC. The molten rock is comprised mostly of molten silica with a melting point (Tm) of 650 oC. As part of a disaster mitigation team, you are asked to study the cooling process of the molten rock. Due to the slow heat transfer between the surface of the sphere and the air, you may assume that the Nusselt number is 2. Heat transfer within the solidified rock can be modeled with a quasi steady state approach. You can start your work by applying equation of change on the solidified part between Rm and Ro by neglecting the transient part. Solved the resulted differential equation using the applicable boundary condition. We may assume the molten part has a uniform temperature of Tm. The freezing zone is moving closer to the center of the sphere as the time passes a. By writing a heat balance that equate the amount of heat released by the freezing along the freezing front equal to heat released to the air from the sphere surface, obtain a differential equation that describe the change of Rm with time. b. Estimate the surface temperature after 30 days of cooling (literally it means also 30 days after the volcanic eruption). c. Estimate Rm 30 days of cooling. Estimated physical and thermal properties of the rock: Latent heat of freezing () = 400 J/g, thermal conductivity of the solid rock : 3.5 W/(m.K), density of the molten rock (s) = 3 g/cm^3 Thermal conductivity of air: 0.024 W/(m.K)
Melting rock
Solidified rock
Rm
Ro