ONE FORMULA, ONE ANSWER
Internally heated slab center temperature calculator
Calculate the steady maximum center temperature of a uniformly heated slab whose two surfaces have the same prescribed temperature. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Maximum temperature at the slab center
Enter values and select Calculate.
Tmax = Tₛ + q‴L²/(2k); t = 2L
Assumptions
Required: steady one-dimensional conduction across a wide slab, constant conductivity and uniform nonnegative volumetric heat generation. L is the half-thickness; the full thickness is 2L. The input temperature is the equal temperature of both solid surfaces, rather than a fluid temperature. Excluded: edge loss, contact resistance and transient temperature changes.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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