An exchanger wall has fluid on both sides, so heat crosses three resistances in series: the inside film, the metal, the outside film. Resistances in series ADD, which is why the overall coefficient is written upside down: $\dfrac{1}{U} = \dfrac{1}{h_i} + \dfrac{L}{k} + \dfrac{1}{h_o}$.

The subscripts name sides, not order: i is the inside film, in $\mathrm{W/(m^2 \cdot K)}$, and o is the outside film in the same unit. $L$ is the separating wall's thickness in metres and $k$ its conductivity in $\mathrm{W/(m \cdot K)}$, so $L/k$ is the wall's own area-specific resistance in $\mathrm{m^2 \cdot K/W}$. $U$, the overall coefficient, comes out in $\mathrm{W/(m^2 \cdot K)}$ like the films it is built from — and it is always smaller than the smallest of them, because a chain cannot beat its weakest link.

That last sentence is the whole sanity check. If your U comes out larger than either film coefficient, you added coefficients instead of resistances. It is the commonest single error in this material.

Then service happens. Scale, silt and biofilm lay down one more resistance, quoted by TEMA as a fouling factor $R_f$ in $\mathrm{m^2 \cdot K/W}$ — the very same unit an insulation R-value wears. It joins the sum directly: $\dfrac{1}{U_f} = \dfrac{1}{U_c} + R_f$, where subscript c is clean (new surfaces) and subscript f is fouled (service condition). Typical values: 0.0002 for treated cooling water, 0.0005 for river water. Tiny numbers, and on a good exchanger they take a fifth of its performance — because the better the clean U, the more a fixed resistance costs. Fouling only ever lowers U; if yours went up, the sign is wrong.