Classical thermodynamics, heat transfer Definition

Thermal boundary layer

Builds on Boundary layer Temperature Prandtl number Reynolds number

Definition

Consider a steady flow of a fluid along a wall $y = 0$ . Here $x \ge 0$ is the distance along the wall from its leading edge and $y \ge 0$ is the distance from the wall. Let $T(x, y)$ be the temperature of the fluid and $T_w$ the wall temperature. Let $T_\infty \ne T_w$ be the temperature of the fluid far from the wall. Let $\theta(x, y) = (T(x, y) - T_w)/(T_\infty - T_w)$ be the dimensionless temperature, so that $\theta = 0$ at the wall and $\theta \to 1$ as $y \to \infty$ . The thermal boundary layer thickness $\delta_T(x)$ is the smallest $y \ge 0$ with $\theta(x, y) = 0.99$ . The thermal boundary layer is the region $0 \le y < \delta_T(x)$ next to the wall.

Remarks

Example: laminar flow at speed $U$ over a flat plate at uniform temperature, with Prandtl number $\Pr = 1$ and negligible viscous heating. Then $u/U$ and $\theta$ solve the same boundary layer equation with the same boundary values, so $\theta = u/U$ . Hence $\delta_T$ equals the velocity boundary layer thickness, about $5x / \sqrt{\mathrm{Re}_x}$ , where $\mathrm{Re}_x = Ux/\nu$ is the local Reynolds number and $\nu$ the kinematic viscosity. For other laminar flat-plate flows with $\Pr \gtrsim 0.6$ , the ratio $\delta_T / \delta$ is close to $\Pr^{-1/3}$ .

Non-example: if $T_\infty = T_w$ , then $\theta$ is not defined and there is no thermal boundary layer, although a velocity boundary layer still forms.

Other measures of the thickness, such as the thermal displacement thickness $\int_0^\infty (1 - \theta) \, dy$ , are also used.

Reading path

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Boundary layer concept
Prandtl number concept
Reynolds number concept
Temperature concept
Thermal boundary layer definition

Tag	`CRNK6NQ60W`
URI	`m2://CRNK6NQ60W`
Kind	definition
Writing	W0 stub
MSC	80A19, 76D10, 76R05
Defines	Thermal boundary layer
Uses	Boundary layer, Temperature, Prandtl number, Reynolds number
Changed	3 November 2026

Thermal boundary layer

Definition

Remarks

Reading path

Further reading

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