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For a double-pipe heat exchanger, the inside and outside heat transfer coefficients are $100$ and $200 \; \text{W m}^{-2} \text{K}^{-1},$ respectively. The thickness and thermal conductivity of the thin-walled inner pipe are $1 \; \text{cm}$ and $10 \; \text{W m}^{-1} \text{K}^{-1},$ respectively. The value of the overall heat transfer coefficient is __________ $\text{W m}^{-2} \text{K}^{-1}.$

- $0.016$
- $42.5$
- $62.5$
- $310$