Write a formula of cooling under natural convection?

The formula for cooling under natural convection can be expressed as:

Q = h * A * ΔT

Where:
Q = Heat transfer rate (W)
h = Convective heat transfer coefficient (W/m^2*K)
A = Surface area for heat transfer (m^2)
ΔT = Temperature difference between the surface and the surrounding fluid (K)

Newton's Law of Cooling:

```
Q = hA(T_s - T_∞)
```

where:

- Q is the heat transfer rate (W)
- h is the convective heat transfer coefficient (W/m²·K)
- A is the surface area (m²)
- T_s is the surface temperature (K)
- T_∞ is the ambient fluid temperature (K)

Grashof Number (Gr):

```
Gr = (gβ(T_s - T_∞)L³)/ν²
```

where:

- g is the acceleration due to gravity (m/s²)
- β is the thermal expansion coefficient (K⁻¹)
- L is the characteristic length (m)
- ν is the kinematic viscosity (m²/s)

Nusselt Number (Nu):

For natural convection, the Nusselt number can be estimated using the Churchill-Chu correlation:

```
Nu = 0.683 + (0.670/(1+0.492/Gr^1/4)⁹/¹⁶))Gr^1/4
```

Convective Heat Transfer Coefficient (h):

```
h = Nu(k/L)
```

where:

- k is the thermal conductivity of the fluid (W/m·K)