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title: "A composite wall consists of two solid rectangular layers in direct thermal contact, placed between a hot reservoir at constant temperature \\(T_H\\) and a cold reservoir at constant temperature \\(T_C\\). Layer 1 has thickness \\(L_1\\) and thermal conductivity \\(k_1\\), while Layer 2 has thickness \\(L_2\\) and thermal conductivity \\(k_2\\). Both layers have the same cross-sectional area \\(A\\) perpendicular to the heat flow, and heat transfer occurs only along the direction of thickness under steady-state conditions. Which of the following expressions correctly represents the rate of thermal energy transfer \\(\\dfrac{Q}{\\Delta t}\\) through the composite wall?"
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url: "https://nerd-notes.com/ubq/116185/"
date_modified: "2026-08-03T11:46:11+00:00"
---

# A composite wall consists of two solid rectangular layers in direct thermal contact, placed between a hot reservoir at constant temperature \(T_H\) and a cold reservoir at constant temperature \(T_C\). Layer 1 has thickness \(L_1\) and thermal conductivity \(k_1\), while Layer 2 has thickness \(L_2\) and thermal conductivity \(k_2\). Both layers have the same cross-sectional area \(A\) perpendicular to the heat flow, and heat transfer occurs only along the direction of thickness under steady-state conditions. Which of the following expressions correctly represents the rate of thermal energy transfer \(\dfrac{Q}{\Delta t}\) through the composite wall?

A composite wall consists of two solid rectangular layers in direct thermal contact, placed between a hot reservoir at constant temperature \(T_H\) and a cold reservoir at constant temperature \(T_C\). Layer 1 has thickness \(L_1\) and thermal conductivity \(k_1\), while Layer 2 has thickness \(L_2\) and thermal conductivity \(k_2\). Both layers have the same cross-sectional area \(A\) perpendicular to the heat flow, and heat transfer occurs only along the direction of thickness under steady-state conditions. Which of the following expressions correctly represents the rate of thermal energy transfer \(\dfrac{Q}{\Delta t}\) through the composite wall?

![A horizontal composite wall composed of two adjacent rectangular layers sandwiched between two thermal reservoirs. On the left is a region labeled T_H. In the middle, layer 1 of width L_1 and thermal conductivity k_1 is in direct contact with layer 2 of width L_2 and thermal conductivity k_2 to its right. Both layers have the same vertical height and cross-sectional area A. To the right of layer 2 is a region labeled T_C. An arrow points to the right showing the direction of heat flow from T_H to T_C. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785757571-1xYDhf.jpg)

- **A.** \(\dfrac{k_1 k_2 A (T_H - T_C)}{k_1 L_2 + k_2 L_1}\)
- **B.** \(\dfrac{(k_1 + k_2) A (T_H - T_C)}{L_1 + L_2}\)
- **C.** \(\dfrac{k_1 k_2 A (T_H - T_C)}{k_1 L_1 + k_2 L_2}\)
- **D.** \(\dfrac{2 k_1 k_2 A (T_H - T_C)}{(k_1 + k_2)(L_1 + L_2)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116185/*