I need to find how much insulation is needed for a tank to maintain a certain temperature. Using these formulas I need to achieve a R total value of atleast $15$ or more. The tank is stainless steel, dimensions $0\mathrm{.}25$in thick, $0\mathrm{.}6$m radius, and $1\mathrm{.}13$m tall.

Constants I found $($not sure if they are right$)$

kmetal$=15$w$/$mk

kinsulation$=0\mathrm{.}01$w$/$mk

convective heat transfer $($h$)=7\mathrm{.}5$w$/$m$^2$k

I am getting very low R total values unless adding on a unrealstic amount of insulation thickness to these formulas. Please help me $R_{\text{b}\text{o}\text{t}}=\frac{x_{\text{m}\text{e}\text{t}\text{a}\text{l}}}{k_{\text{m}\text{e}\text{t}\text{a}\text{l}}{A}_{\text{b}\text{o}\text{t}}}+\frac{x_{\text{i}\text{n}\text{s}}}{k_{\text{i}\text{n}\text{s}}{A}_{\text{b}\text{o}\text{t}}}+\frac{1}{h_{\text{b}\text{o}\text{t}}{A}_{\text{b}\text{o}\text{t}}}$

$R_{\text{s}\text{i}\text{d}\text{e}}^{}=\frac{ln(\frac{r_2}{r_1})}{2k_{\text{m}\text{e}\text{t}\text{a}\text{l}}H}+\frac{ln(\frac{r_3}{r_2})}{2k_{\text{i}\text{n}\text{s}\text{u}\text{l}}H}+\frac{1}{h_{\text{s}\text{i}\text{d}\text{e}}{A}_{\text{o}\text{u}\text{t}}}$

$R_{\text{t}\text{o}\text{p}}=\frac{x_{\text{m}\text{e}\text{t}\text{a}\text{l}}}{k_{\text{m}\text{e}\text{t}\text{a}\text{l}}{A}_{\text{t}\text{o}\text{p}}}+\frac{x_{\text{i}\text{n}\text{s}}}{k_{\text{i}\text{n}\text{s}}{A}_{\text{t}\text{o}\text{p}}}+\frac{1}{h_{\text{t}\text{o}\text{p}}{A}_{\text{t}\text{o}\text{p}}}$

$\frac{1}{R_{\text{t}\text{o}\text{t}\text{a}\text{l}}}=\frac{1}{R_{\text{t}\text{o}\text{p}}}+\frac{1}{R_{\text{b}\text{o}\text{t}}}+\frac{1}{R_{\text{s}\text{i}\text{d}\text{e}}}$

Figure $4-$ Modeling heat loss from an insulated tank $($left$)$ can be achieved by estimating the total series and parallel resistances to heat transfer with the equations shown above on the right. Additional variables include surface area $(A),$ thermal conductivity $(k),$ layer thicknesses $(x),$ inner tank radius $(r_1),$ outer tank radius $(r_2),$ and outer insulation radius $(r_3).$