Natural Convection Thermal Resistance

Rsa = 1 / (h × A)

Quick answer

This calculator solves R_sa = 1 / (h × A) for Surface-to-Ambient Rth. With Convection Coefficient 0.5, Surface Area 10 cm², the result is 2000 °C/W.

Calculator

Result
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Formula

R_sa = 1 / (h × A)

Description

The surface-to-ambient thermal resistance for natural (free) convection depends on the heat transfer coefficient h and the effective surface area. For natural convection in still air, h is typically 5-25 W/(m²·K) depending on surface orientation, geometry, and temperature difference. Vertical surfaces with large temperature differences have higher h. This formula is fundamental for estimating cooling performance of heatsinks, PCBs, and enclosures without forced airflow. In many embedded systems, natural convection is the only cooling mechanism available.

Variables

  • R_sa — Surface-to-ambient thermal resistance (°C/W)
  • h — Convection heat transfer coefficient (W/(m²·K), typically 5-25 for natural convection)
  • A — Effective cooling surface area (m²)

Practical Notes

Typical h values in W/(m²·K): natural convection vertical plate 5-10, horizontal plate (hot side up) 6-12, horizontal plate (hot side down) 3-6, forced convection 25-250 depending on air velocity. Radiation also contributes significantly at moderate temperatures (adds 5-10 W/(m²·K) effective). For rough estimates in natural convection, h ≈ 10 W/(m²·K) is a common starting point.

Symbols and units

Symbol Meaning Default unit Accepted units
Rsa Surface-to-Ambient Rth °C/W °C/W
h Convection Coefficient — —
A Surface Area cm² mm², cm², m²

Step by step

  1. 1. What you know: Convection Coefficient 0.5, Surface Area 10 cm²
  2. 2. The relation: R_sa = 1 / (h × A)
  3. 3. Substitute: h = 0.5, A = 10 cm²
  4. 4. Result: Surface-to-Ambient Rth = 2000 °C/W

Worked examples

Minimum range

Given: Convection Coefficient 0.025, Surface Area 10 mm²

Result: Surface-to-Ambient Rth = 4 × 10⁶ °C/W

Low range

Given: Convection Coefficient 0.25, Surface Area 1 cm²

Result: Surface-to-Ambient Rth = 40000 °C/W

Typical

Given: Convection Coefficient 0.5, Surface Area 10 cm²

Result: Surface-to-Ambient Rth = 2000 °C/W

High range

Given: Convection Coefficient 0.8, Surface Area 100 cm²

Result: Surface-to-Ambient Rth = 125 °C/W

Maximum range

Given: Convection Coefficient 8, Surface Area 0.1 m²

Result: Surface-to-Ambient Rth = 1.25 °C/W

How Surface-to-Ambient Rth changes with Convection Coefficient

Convection Coefficient (input) Surface-to-Ambient Rth (result)
0.05 20000 °C/W
0.125 8000 °C/W
0.25 4000 °C/W
0.375 2667 °C/W
0.5 2000 °C/W
0.75 1333 °C/W
1 1000 °C/W
2 500 °C/W
3.5 285.7 °C/W
5 200 °C/W

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Frequently asked questions

How do you calculate Natural Convection Thermal Resistance?

Use R_sa = 1 / (h × A). With Convection Coefficient 0.5, Surface Area 10 cm², Surface-to-Ambient Rth works out to 2000 °C/W.

What is the formula for Natural Convection Thermal Resistance?

The formula is R_sa = 1 / (h × A). The surface-to-ambient thermal resistance for natural (free) convection depends on the heat transfer coefficient h and the effective surface area.

Related Concepts

All Thermal formulas →
Junction Temperature Full Thermal Chain Required Heatsink Maximum Power (Junction to Case) Thermal Time Constant Forced Convection Heat Transfer Power Derating (Temperature) Natural Convection Thermal Resistance

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