$1.$ There is a steam pipe with a $10[$mm$]$ thick thermal insulation coating on a steel pipe with an outer diameter of $45[$mm$].$ The temperature of the pipe wall and the surface temperature of the film are measured and are $170$ and $20,$ respectively. The thermal conductivity of the insulation film is $0\mathrm{.}25[$BTU$/$m$-$min $"$F$].$ Find the heat loss per $1$m of pipe length. $($However$,$ The thermal resistance of steel is ignored.$)$

$2.$ High$-$pressure steam is flowing through a steel pipe with an outer diameter of $0\mathrm{.}1[$in$].$ To insulate, it is wrapped with $0\mathrm{.}1[$in$]$ thick magnesia carbonate $($k $=0\mathrm{.}067)$ and then $0\mathrm{.}05[$in$]$ thick asbestos $($k $=0\mathrm{.}094)$ is wrapped over this to insulate. The temperature of the inner wall of the pipe and the outer surface of the asbestos are $220$ degrees Celsius, respectively. It was $$ and $30.$ Find the heat loss per $1$ m of pipe length and the temperature of the contact surface. $($However$,$ the heat resistance of steel is ignored.$)$

$3.$ We intend to make a $15[$cm$]$ thick cork layer made of powder and use it as a flat$-$walled thermoelectric material. When the temperature on the cold side of a cork wall is $60\backslash$deg F$,$ the temperature on the hot side is $250\text{'}$F$.$ The thermal conductivity of cork is $0\mathrm{.}055[$BTU$/$m$-$min$-$F$]$ at $32\backslash$deg F and $0\mathrm{.}078[$BTU$/$m$-$min$-$F$]$ at $200\backslash$deg F$.$ If the heat transfer area of $$the wall is $20$ m$^2,$ how much heat is lost through this wall in hours and calories?

$4.$ There is a furnace wall made up of three layers of carborantham, firebricks, and insulating bricks. When the thickness is $10[$cm$],10[$in$],$ and $0\mathrm{.}1[$ft$],$ respectively, the thermal conductivity is $15.11.0\mathrm{.}8[$kcal$/$mmin$-].$ When the temperature of the inner wall is $2200[]$ and the temperature of the outer wall is $110[],$ how much heat is lost per hour from $1[$m$^2]$ of wall?

$5.$ When the thermal conductivity of the wall of a cylinder with an inner diameter of $5[$cm$]$ and an outer diameter of $15[$cm$]$ is $1100[$cal$/$mhr$*$F$]$ and the outer surface temperature is $250[$F$],$ and the inner temperature is $50[$F$],$ the cylinder wall $1[$m$]]$ How much $[$kcal$/$hr$]$ is the heat loss?

$6.$ Water flows through a steel pipe with a thickness of $2[$mm$]$ and an outer diameter of $17[$mm$],$ and the outside is heated with saturated water vapor. The thermal conductivity of the steel pipe is $40[$kcal$/$mh$],$ and the film coefficient of water is $6000[$kcal$/$m$^2$hr$].$ At this time

What is the overall heat transfer coefficient $[$kcal$/$m$^2$hr$]?($Saturated water vapor: $9000[$kcal$/$m$^2$hr$])$

$7.$ On one side of a $0\mathrm{.}5[$cm$]$ thick metal wall with an annual conductivity of $40[$kcal$/$mhr$],$ water at $220[]$ flows, and on the other side, water at $100[]$ flows. When the heat transfer coefficients of the dura mater on both sides of the wall are $9000$ and $4800[$kcal$/$m$^2$hr$],$ respectively, what is the overall heat transfer coefficient?

$8.$ Find the equivalent diameter $($D$)$ of a shell$-$and$-$tube heat exchanger with two heat pipes with an outer diameter of $3[$m$]$ among a jacket with an inner diameter of $25[$m$].$