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The Biot number

The Biot number compares the resistance to conduction inside a body with the resistance to convection at its surface. When the Biot number is small, conduction inside the body evens out the temperature fast enough that the whole body can be treated as having one common temperature, called lumped capacitance.

Bi = \dfrac{hL_c}{k}

Biot number,

L_c

= characteristic length

Bi < 0.1

lumped capacitance can be used

Symbols

$Bi$	Biot number
$L_c$	characteristic length (V/A)	m

Example

A plate has $L_c = 8$ mm, $k = 60$ W/(m·K) and is cooled with $h = 40$ W/(m²·K). $Bi = 40\cdot 0.008/60 \approx 0.0053$ , well below $0.1$ .

Always check the Biot number before using lumped capacitance – otherwise the temperature can vary noticeably inside the body.

Practise convection for free →

← Convection in a composite wall · Forced and natural convection →

Part of Heat Transfer: Convection.