Heat Conduction Through a Two-Layer Wall Calculator

The steady heat flow, thermal resistance and interface temperature of a wall made of two layers.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Heat flows from the hot side to the cold side through each layer in series. Each layer has a thermal resistance R = t / (k A), where t is its thickness, k its thermal conductivity and A the area. The total resistance is the sum, and the heat flow is the temperature difference divided by that sum.

Typical conductivities: concrete about 1, brick about 0.7, mineral wool about 0.04, steel about 50 W/m·K. A thin layer of good insulation usually dominates the total resistance.

Formulas used

  • R = \frac{t}{k A}
  • Q = \frac{T_h - T_c}{R_1 + R_2}

Worked example

With the default numbers in the calculator above:

  1. Thermal resistance of each layer: 0.01 and 0.125 K/W
  2. Total resistance (in series): 0.135 K/W
  3. Heat flow: 1333 W
  4. Heat flux: 133 W/m²
  5. Temperature at the interface: 187 °C

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Is convection at the surfaces included?

No. Only conduction through the layers. Surface films add a little resistance in still air.

How do I find the interface temperature?

The calculator gives it. It is the hot temperature minus the heat flow times the resistance of the first layer.

Is this steady state?

Yes. It does not include heating up or cooling down over time.

Related calculators

Further reading: Incropera and DeWitt, Fundamentals of Heat and Mass Transfer; Cengel, Heat and Mass Transfer.

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