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Furnace Wall Design (Layers, Convection and Radiation from the Surface)

What outside surface temperature and heat loss will this layered furnace wall have, are the layer interfaces within their service temperatures, and what does the loss cost?

Heat loss through a layered furnace or oven wall with the outside surface losing heat by both convection and radiation: the surface temperature found by iteration so that conduction through the layers equals convection plus radiation (radiation as the radiant heat tool), the heat flux and loss for the wall area, the temperature at each interface (as the wall heat loss tool with the combined surface coefficient), the annual energy cost, and checks against the surface touch limit and the service limit of the insulating layer.

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How this tool works

Inputs, units and where to find them

InputUnitTypical source
Hot face temperature°CTemperature of the hot face of the lining.
Ambient temperature°CAir temperature outside the furnace.
Layers (hot face first)
Layer 1 thicknessmmThickness of the hot-face layer (refractory brick or castable).
Layer 1 conductivityW/m·KConductivity of layer 1 at its mean temperature.
Layer 2 thicknessmmThickness of the insulating layer.
Layer 2 conductivityW/m·KConductivity of layer 2 at its mean temperature.
Layer 3 thickness (shell)mmThickness of the steel shell (0 if none).
Layer 3 conductivityW/m·KConductivity of the shell.
Outside surface
Convection coefficientW/m²·KNatural convection coefficient at the outer surface (about 5–10 indoors).
Surface emissivityEmissivity of the outer surface (about 0.8 painted or oxidised steel).
Wall aream²Area of wall.
Largest surface temperature°CHighest outside surface temperature you allow.
Service limit at the layer 1–2 interface°CHighest temperature the insulating layer may see (its service limit).
Hours per yearhHours per year at temperature.
Energy price$/kWhEnergy price.

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 face temperature
Illustration: Hot face temperatureA thermometer whose level rises with Hot face temperature; the level follows the value you type.TExample: 900 °CHot face temperature
What it is
The temperature at the inside (hot) face of the lining, the face exposed to the furnace atmosphere.
Units and format
Enter a number in °C: degrees Celsius. The form accepts 0.000001 °C to 2000 °C. Required: the tool does not calculate until every input is valid.
Example
The form opens with 900 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Ambient temperature
Illustration: Ambient temperatureA thermometer whose level rises with Ambient temperature; the level follows the value you type.TExample: 25 °CAmbient temperature
What it is
The temperature of the air surrounding the outside of the furnace.
Units and format
Enter a number in °C: degrees Celsius. The form accepts -50 °C to 60 °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.

Layers (hot face first)

What this means: Layer 1 thickness
Illustration: Layer 1 thicknessThe cross-section of a plate or wall with a dimension across its thickness, marking Layer 1 thickness.t₁section through the materialExample: 115 mmLayer 1 thickness
What it is
The thickness of the first layer, the one facing the furnace heat, such as refractory brick or castable.
Units and format
Enter a number in mm: millimetres. The form accepts 0 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
Example
The form opens with 115 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Layer 1 conductivity
Illustration: Layer 1 conductivityHeat flowing from a hot side to a cold side through a wall or into a material; Layer 1 conductivity sets how much heat moves or is stored.hotcoldk₁Example: 1.2 W/m·KLayer 1 conductivity
What it is
The thermal conductivity of the hot-face material at its mean working temperature, from the refractory supplier.
Units and format
Enter a number in W/m·K: W/m·K. The form accepts 0.01 W/m·K to 100 W/m·K. Required: the tool does not calculate until every input is valid.
Example
The form opens with 1.2 W/m·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Layer 2 thickness
Illustration: Layer 2 thicknessThe cross-section of a plate or wall with a dimension across its thickness, marking Layer 2 thickness.t₂section through the materialExample: 230 mmLayer 2 thickness
What it is
The thickness of the second layer, normally the insulation behind the hot face.
Units and format
Enter a number in mm: millimetres. The form accepts 0 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
Example
The form opens with 230 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Layer 2 conductivity
Illustration: Layer 2 conductivityHeat flowing from a hot side to a cold side through a wall or into a material; Layer 2 conductivity sets how much heat moves or is stored.hotcoldk₂Example: 0.15 W/m·KLayer 2 conductivity
What it is
The thermal conductivity of the insulating layer at its mean working temperature, from the supplier data sheet.
Units and format
Enter a number in W/m·K: W/m·K. The form accepts 0.01 W/m·K to 100 W/m·K. Required: the tool does not calculate until every input is valid.
Example
The form opens with 0.15 W/m·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Layer 3 thickness (shell)
Illustration: Layer 3 thickness (shell)The cross-section of a plate or wall with a dimension across its thickness, marking Layer 3 thickness (shell).t₃section through the materialExample: 6 mmLayer 3 thickness (shell)
What it is
The thickness of the outer steel shell or casing; zero if there is no shell.
Units and format
Enter a number in mm: millimetres. The form accepts 0 mm to 200 mm. Required: the tool does not calculate until every input is valid.
Example
The form opens with 6 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Layer 3 conductivity
Illustration: Layer 3 conductivityHeat flowing from a hot side to a cold side through a wall or into a material; Layer 3 conductivity sets how much heat moves or is stored.hotcoldk₃Example: 50 W/m·KLayer 3 conductivity
What it is
The thermal conductivity of the outer shell or casing material, from material data.
Units and format
Enter a number in W/m·K: W/m·K. The form accepts 0.01 W/m·K to 400 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.

Outside surface

What this means: Convection coefficient
Illustration: Convection coefficientHeat flowing from a hot side to a cold side through a wall or into a material; Convection coefficient sets how much heat moves or is stored.hotcoldhcExample: 8 W/m²·KConvection coefficient
What it is
The natural convection heat transfer coefficient between the outer wall surface and the surrounding air.
Units and format
Enter a number in W/m²·K: watts per square metre per kelvin. The form accepts 1 W/m²·K to 100 W/m²·K. Required: the tool does not calculate until every input is valid.
Example
The form opens with 8 W/m²·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Get it right
Convection only; the tool adds radiation separately from the emissivity.
What this means: Surface emissivity
Illustration: Surface emissivityA number line with a marker at the value of Surface emissivity, between its lowest and highest accepted values.0.051εExample: 0.8Surface emissivity
What it is
The emissivity of the outer surface, which sets how much heat it radiates to the surroundings.
Units and format
Enter a plain number with no unit. The form accepts 0.05 to 1. Required: the tool does not calculate until every input is valid.
Example
The form opens with 0.8 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Get it right
A fraction from 0 to 1, set by the surface finish and paint.
What this means: Wall area
Illustration: Wall areaA shaded shape whose enclosed surface is the area Wall area.AenclosedsurfaceExample: 10 m²Wall area
What it is
The outside area of furnace wall built with this lining, used to turn heat flux into total heat loss.
Units and format
Enter a number in m²: square metres. The form accepts 0.000001 m² to 100000 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.
What this means: Largest surface temperature
Illustration: Largest surface temperatureA thermometer whose level rises with Largest surface temperature; the level follows the value you type.TExample: 70 °CLargest surface temperature
What it is
The highest outside surface temperature you allow, for personnel protection or for equipment near the furnace.
Units and format
Enter a number in °C: degrees Celsius. The form accepts 0.000001 °C to 300 °C. Required: the tool does not calculate until every input is valid.
Example
The form opens with 70 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Get it right
Check your workplace safety requirements for touch temperatures.
What this means: Service limit at the layer 1–2 interface
Illustration: Service limit at the layer 1–2 interfaceA thermometer whose level rises with Service limit at the layer 1–2 interface; the level follows the value you type.TExample: 1000 °CService limit at the layer 1–2 interface
What it is
The service temperature limit of the insulating layer, compared with the temperature where it meets the hot-face layer.
Units and format
Enter a number in °C: degrees Celsius. The form accepts 0.000001 °C to 2000 °C. Required: the tool does not calculate until every input is valid.
Example
The form opens with 1000 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Hours per year
Illustration: Hours per yearA timeline from a start mark to an end mark; Hours per year is the time between them.startendtExample: 4000 hHours per year
What it is
The hours per year the furnace runs at this temperature, used for the annual energy and cost.
Units and format
Enter a number in h: hours. The form accepts 0.000001 h to 8784 h. Required: the tool does not calculate until every input is valid.
Example
The form opens with 4000 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Energy price
Illustration: Energy priceA price tag on one unit of measure; Energy price is the cost for each unit (per hour, per kilogram and so on).$cost foreach unitExample: $0.08/kWhEnergy price
What it is
What you pay per kilowatt-hour of the fuel or electricity that heats the furnace.
Units and format
Enter a number in $/kWh: money per kilowatt-hour. The form accepts $0/kWh to $10/kWh. Required: the tool does not calculate until every input is valid.
Example
The form opens with $0.08/kWh as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Get it right
The tool costs the heat lost, not fuel bought; for fired furnaces divide the fuel price by the burner efficiency.

Method and formulas

  1. Conduction resistance R = Σ t ÷ k per square metre; flux q = (T_hot − T_s) ÷ R.
  2. At the surface q = h_c (T_s − T_a) + ε σ (T_s⁴ − T_a⁴) (radiation as the radiant heat tool); solve for T_s by bisection.
  3. Interface temperatures fall by q × t ÷ k across each layer (as the wall heat loss tool with the combined coefficient).
  4. Loss = q × area; energy = loss × hours.
  5. Example: the shell runs at 62.288 °C, losing 514.16 W/m² (5.1416 kW); the insulation sees 850.73 °C.

Limitations

  • Constant conductivities; real refractories vary strongly with temperature.
  • Steady state; heat stored in the lining during start-up is not included.
  • Example values are illustrations. Replace them with values for your actual task.

Typical uses

  • Design a refractory and insulation lining
  • Check a furnace shell surface for burn risk
  • Estimate the running cost of wall losses

Who it is for

  • Furnace engineers
  • Plant engineers
  • Energy managers

What you get

  • Surface temperature, flux and heat loss
  • Interface temperatures
  • Annual energy cost and checks

Interpreting the result

  • Most of the temperature drop should occur in the insulating layer; the brick protects it from the hot face.

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.

BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.

Open the Furnace Wall Design (Layers, Convection and Radiation from the Surface) calculator

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