HEAT CONDUCTION IN SPHERES Lecture Slide: Yosua Heru Irawan

HEAT CONDUCTION IN CYLINDERS AND SPHERES Heat transfer through the pipe can be modeled as steady and one-dimensional. The temperature of the pipe depends on one direction only (the radial r-direction) and can be expressed as T = T(r). This situation is approximated in practice in long cylindrical pipes and spherical containers. Heat is lost from a hot-water pipe to the air outside in the radial direction, and thus heat transfer from a long pipe is one-dimensional.

Conduction resistance of the cylinder layer A long cylindrical pipe (or spherical shell) with specified inner and outer surface temperatures T1 and T2. Conduction resistance of the cylinder layer

A spherical shell with specified inner and outer surface temperatures T1 and T2. Conduction resistance of the spherical layer

for a cylindrical layer for a spherical layer The thermal resistance network for a cylindrical (or spherical) shell subjected to convection from both the inner and the outer sides.

Multilayered Cylinders and Spheres The thermal resistance network for heat transfer through a three-layered composite cylinder subjected to convection on both sides.

Once heat transfer rate Q has been calculated, the interface temperature T2 can be determined from any of the following two relations:

Perpindahan Panas pada container berbentuk bola: Diketahui sebuah container berbentuk bola dengan diameter dalam 5 m, dengan ketebalan 1,5 cm dan k = 15 W/m.C. container digunakan untuk menyimpan air es dengan temperatur 0 C. container disimpan pada ruangan dengan temperatur 30 C, temperatur dinding ruangan juga diasumsikan 30 C. permukaan luar container diasumsikan mempuyai emisivitas permukaan 1 (black body) sehingga sehingga perpindahan panas diantara permukaan container dan lingkungan melalui proses konveksi dan radiasi. Koefisien konveksi di dalam container h in = 80 W/m2.C dan koefisien konveksi di luar container h out = 10 W/m2.C. Hitunglah : perpindahan panas dari dalam container ke lingkungan luar!

Menghitung luas permukaan container dalam dan luar: Menghitung koefisien perpindahan kalor radiasi:

Menghitung hambatan thermal: Menghitung laju perpindahan kalor total:

Coba kerjakan soal yang sama dengan sebelumnya: Diameter dalam container = 10 m