Q$9$ : A compressed air pipe with conductivity k and with inner radius $r_1$ and outer radius

$r_2$ is subjected to uniform heat flux on the inner surface q$"$ and convection on the outer

surface $T_{},h_{}.$ Calculate a$)$ The mathematical formulation b$)$ the variation of temperature

in the pipe $.$

Q$10$ : A pipe with conductivity k and with inner radius $r_1$ and outer radius $r_2$ is

subjected to convection on the inner surface $T_1,h_1,$ and convection on the outer surface

$T_2,h_2$ where $T_1>T_2.$ Calculate a$)$ The mathematical formulation b$)$ the variation of

temperature in the pipe $.$

Q$11$A pipe with conductivity k and the inner surface with radius $r_1$ and the outer

surface with radius $r_2,$ the inner surface at constant temperature $T_1$ while the outer surface

at a uniform heat flux q$".$ Calculate a$)$ The mathematical formulation b$)$ the variation of

temperature in the pipe $.$

Q$12$ : A pipe with conductivity k $,$ the inner surface with radius $r_1$ and the outer surface

with radius r $2,$ the inner surface is heated with constant temperature $T_1$ while the outer

surface is subjected to the ambient $T_{},h_{}.$ Calculate a$)$ The mathematical formulation b$)$

the variation of temperature in the pipe