Radial Conduction Through a Cylindrical Wall
Calculate steady radial heat flow through a concentric cylindrical wall.
Try this formula
Calculate heat rate; positive radially outward or choose another supported quantity.
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Try this formula
Calculate heat rate; positive radially outward or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Heat rate; positive radially outward
Enter the known values to see the result.
Conduction is steady, one-dimensional, and radial, with constant positive conductivity. There is no internal heat generation and end effects are negligible. Use 0 < r_i < r_o and prescribed inner and outer wall temperatures.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, mechanics, and consistent SI units
Source
Teng-Jui Lin — CHEM E 330 — Transport Processes IReference equation: Radial transport in cylindrical systems. FormuLab wrote new explanations, assumptions, applications, and numerical examples. Integrated source flux over the cylindrical area 2πrL; distinguished flux from total heat rate.
Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering Expansion, under CC BY 4.0.
Adapted standard equations and added original lesson text, variables, SI examples, and assumptions. Integrated source flux over the cylindrical area 2πrL; distinguished flux from total heat rate.
Definition
Heat crosses larger cylindrical surfaces as it moves outward. Integrating this changing area produces a logarithmic radius ratio, rather than the simple thickness-over-area relation for a plane wall.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Heat rate; positive radially outward | ||
| Thermal conductivity | ||
| Cylinder length | ||
| Inner-wall absolute temperature | ||
| Outer-wall absolute temperature | ||
| Outer radius | ||
| Inner radius |
Real-World Applications
Pipe walls
Estimate heat conduction through a cylindrical material layer.
Insulation studies
Compare cylindrical layers with specified boundary temperatures.
Worked Example
Problem
A 2 m cylindrical wall has k = 0.2 W/(m·K), radii 0.02 m and 0.04 m, and inner/outer temperatures 400 K and 300 K. Find the heat rate.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Radial transport in cylindrical systems. FormuLab wrote new explanations, assumptions, applications, and numerical examples. Integrated source flux over the cylindrical area 2πrL; distinguished flux from total heat rate.
Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering Expansion, under CC BY 4.0.
Adapted standard equations and added original lesson text, variables, SI examples, and assumptions. Integrated source flux over the cylindrical area 2πrL; distinguished flux from total heat rate.
Assumptions
- • Conduction is steady, one-dimensional, and radial, with constant positive conductivity.
- • There is no internal heat generation and end effects are negligible.
- • Use 0 < r_i < r_o and prescribed inner and outer wall temperatures.
Languages
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