BIZOMAT MAKEOS · Materials
Heat Flow Through a Layered Wall
How much heat flows through this insulated wall, and what are the layer temperatures?
Overall heat transfer coefficient, heat flow and interface temperatures for conduction through up to three plane layers with optional surface film coefficients.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Hot side temperature | °C | Temperature of the hot fluid or inside surface. |
| Cold side temperature | °C | Temperature of the surroundings or cold fluid. |
| Wall area | m² | Wall area. |
| Hot side film coefficient (0 = ignore) | W/(m²·K) | Convection coefficient on the hot side; 0 to treat the hot temperature as the surface temperature. |
| Cold side film coefficient (0 = ignore) | W/(m²·K) | Convection plus radiation coefficient on the cold side (about 8–12 W/m²K for still air). |
| Layer 1 | ||
| Thickness (0 = not used) | mm | Thickness of layer 1 (hot side). |
| Thermal conductivity | W/(m·K) | Conductivity of layer 1 at its mean temperature, from material data. |
| Layer 2 | ||
| Thickness (0 = not used) | mm | Thickness of layer 2. |
| Thermal conductivity | W/(m·K) | Conductivity of layer 2 (insulation conductivity rises with temperature). |
| Layer 3 | ||
| Thickness (0 = not used) | mm | Thickness of layer 3 (cold side). |
| Thermal conductivity | W/(m·K) | Conductivity of layer 3. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Hot side temperature
- What it is
- The temperature on the hot side of the wall: the fluid inside if a hot side film coefficient is entered, otherwise the hot surface itself.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -273 °C to 3000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Heat flow rises in proportion to the temperature difference across the wall.
- Get it right
- With the hot film coefficient at 0 this is treated as the surface temperature, not the fluid temperature.
What this means: Cold side temperature
- What it is
- The temperature on the cold side: the surrounding air or cold fluid if a cold side film coefficient is entered, otherwise the cold surface itself.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -273 °C to 3000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Heat flow rises in proportion to the temperature difference across the wall.
- Get it right
- Use the ambient temperature the wall actually sees, not a design minimum unless that is the case you want.
What this means: Wall area
- What it is
- The face area of the wall through which heat flows, from drawings or by measurement.
- Units and format
- Enter a number in m²: square metres. The form accepts 0.000001 m² to 10000000 m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Heat flow rises in direct proportion; heat flux and temperatures do not change.
- Get it right
- For a thin cylinder or tank use the outside surface area; this tool treats the wall as flat.
What this means: Hot side film coefficient (0 = ignore)
- What it is
- The convection coefficient between the hot fluid and the hot surface, from heat transfer data for the fluid and flow.
- Units and format
- Enter a number in W/(m²·K): watts per square metre per kelvin. The form accepts 0 W/(m²·K) to 100000 W/(m²·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 W/(m²·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher coefficient lowers the surface resistance and raises heat flow slightly.
- Get it right
- 0 means it is ignored and the hot temperature is taken as the surface temperature.
What this means: Cold side film coefficient (0 = ignore)
- What it is
- The combined convection and radiation coefficient between the cold surface and its surroundings, from heat transfer data for the surface and air movement.
- Units and format
- Enter a number in W/(m²·K): watts per square metre per kelvin. The form accepts 0 W/(m²·K) to 100000 W/(m²·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 W/(m²·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher coefficient raises heat flow and brings the outer surface closer to ambient.
- Get it right
- 0 means it is ignored and the cold temperature is taken as the outer surface temperature.
Layer 1
What this means: Thickness (0 = not used)
- What it is
- The thickness of the first layer, the one on the hot side, such as a steel lining or inner skin.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A thicker layer adds resistance and lowers heat flow.
- Get it right
- 0 means the layer is not used, and its conductivity is then ignored.
What this means: Thermal conductivity
- What it is
- How readily the first layer’s material conducts heat, from the material data sheet at its working temperature.
- Units and format
- Enter a number in W/(m·K): W/(m·K). The form accepts 0.000001 W/(m·K) to 10000 W/(m·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 W/(m·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher conductivity lowers this layer’s resistance and raises heat flow.
- Get it right
- Ignored when the layer thickness is 0.
Layer 2
What this means: Thickness (0 = not used)
- What it is
- The thickness of the second, middle layer, often the insulation.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A thicker layer adds resistance and lowers heat flow.
- Get it right
- 0 means the layer is not used. Use the installed, compressed thickness of insulation.
What this means: Thermal conductivity
- What it is
- How readily the second layer’s material conducts heat, from the material data sheet at its mean working temperature.
- Units and format
- Enter a number in W/(m·K): W/(m·K). The form accepts 0.000001 W/(m·K) to 10000 W/(m·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.04 W/(m·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher conductivity lowers this layer’s resistance and raises heat flow.
- Get it right
- Insulation conductivity rises with temperature; use the value at the layer’s mean temperature.
Layer 3
What this means: Thickness (0 = not used)
- What it is
- The thickness of the third layer, the one on the cold side, such as an outer cladding sheet.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A thicker layer adds resistance and lowers heat flow.
- Get it right
- 0 means the layer is not used.
What this means: Thermal conductivity
- What it is
- How readily the third layer’s material conducts heat, from the material data sheet.
- Units and format
- Enter a number in W/(m·K): W/(m·K). The form accepts 0.000001 W/(m·K) to 10000 W/(m·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 W/(m·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher conductivity lowers this layer’s resistance and raises heat flow.
- Get it right
- Ignored when the layer thickness is 0.
Method and formulas
- Resistance per unit area R = 1/h_in + Σ(t ÷ k) + 1/h_out (omitting zero terms).
- U = 1 ÷ R; heat flow Q = U × A × ΔT.
- Each interface temperature drops by q × (layer resistance) from the hot side.
- Example: the default wall loses 673.06 W, and its outer surface runs at 31.731 °C.
Limitations
- Steady, one-dimensional conduction through flat layers; curved walls of small radius and thermal bridges increase the loss.
- Conductivity varies with temperature; use mean-temperature values.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate heat loss from an oven, tank or duct wall
- Choose insulation thickness
- Find the outside surface temperature for touch safety
Who it is for
- Process engineers
- Maintenance engineers
- Design engineers
What you get
- Overall coefficient U
- Heat flow and heat flux
- Cold-side surface temperature
- Interface temperatures
Interpreting the result
- Check the outside surface temperature against your touch-temperature or burn-protection limit.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 371–378. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Conduction through supports
In Cryogenic Design by the Numbers
What it covers: Size a support from its conductivity integral, use a mean conductivity in the layered wall tool, follow the temperature along a strut, compare materials and intercepts, and a cold-end error.
Method explained here · BIZOMAT original book
Heat leak and boil-off
In Cryogenic Liquids by the Numbers
What it covers: Turn a vessel's normal evaporation rate into watts, calculate a foam bath's heat leak with a mean conductivity, bound the open-lid loss by radiation, and find a bath left open between jobs.
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