---
title: "A flat metal wall of a storage tank has a thickness \\(d\\) and thermal conductivity \\(k_{\\text{metal}}\\). Thermal energy transfers through the wall at a rate \\(H_0\\) when a constant temperature difference \\(\\Delta T\\) is maintained across its inner and outer surfaces. To reduce heat transfer, a layer of fiberglass insulation of the same thickness \\(d\\) and thermal conductivity \\(k_{\\text{fiber}} = \\dfrac{1}{4}k_{\\text{metal}}\\) is added directly to the outer surface of the wall, while maintaining the same overall temperature difference \\(\\Delta T\\) across the combined two-layer boundary. What is the ratio \\(H_{\\text{new}} / H_0\\) of the new rate of thermal energy transfer to the original rate?"
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url: "https://nerd-notes.com/ubq/116191/"
date_modified: "2026-08-03T11:46:16+00:00"
---

# A flat metal wall of a storage tank has a thickness \(d\) and thermal conductivity \(k_{\text{metal}}\). Thermal energy transfers through the wall at a rate \(H_0\) when a constant temperature difference \(\Delta T\) is maintained across its inner and outer surfaces. To reduce heat transfer, a layer of fiberglass insulation of the same thickness \(d\) and thermal conductivity \(k_{\text{fiber}} = \dfrac{1}{4}k_{\text{metal}}\) is added directly to the outer surface of the wall, while maintaining the same overall temperature difference \(\Delta T\) across the combined two-layer boundary. What is the ratio \(H_{\text{new}} / H_0\) of the new rate of thermal energy transfer to the original rate?

A flat metal wall of a storage tank has a thickness \(d\) and thermal conductivity \(k_{\text{metal}}\). Thermal energy transfers through the wall at a rate \(H_0\) when a constant temperature difference \(\Delta T\) is maintained across its inner and outer surfaces. To reduce heat transfer, a layer of fiberglass insulation of the same thickness \(d\) and thermal conductivity \(k_{\text{fiber}} = \dfrac{1}{4}k_{\text{metal}}\) is added directly to the outer surface of the wall, while maintaining the same overall temperature difference \(\Delta T\) across the combined two-layer boundary. What is the ratio \(H_{\text{new}} / H_0\) of the new rate of thermal energy transfer to the original rate?

![Two side-by-side cross-sectional diagrams labeled Configuration 1 and Configuration 2. On the left, Configuration 1 shows a single vertical wall layer of thickness d with temperature T_H on the left face and T_C on the right face. A horizontal arrow pointing right through the wall is labeled H_0. On the right, Configuration 2 shows two adjacent vertical wall layers each of thickness d. The left layer is labeled k_metal and the right layer is labeled k_fiber = k_metal / 4. Temperature T_H is on the far-left face and T_C is on the far-right face. A horizontal arrow pointing right through both layers is labeled H_new. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785757575-I38qKb.jpg)

- **A.** \(\dfrac{1}{5}\)
- **B.** \(\dfrac{1}{4}\)
- **C.** \(\dfrac{4}{5}\)
- **D.** \(\dfrac{1}{2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116191/*