### Parallel Plates Channel Natural Convection Equation and Calculator

**Heat Transfer Engineering**

**Thermodynamics**

**Engineering Physics **

Vertical Parallel Plates Channel Natural Convection Equation and Calculator

Average heat transfer coefficient and surface temperature for an isoflux (constant and uniform flux) parallel plate vertical channel open to ambient from both ends in a natural convection environment. The convection calculation are based on Rayleigh number.

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Preview: Vertical Parallel Plates Channel Natural Convection Calculator

Fluid Properties at Film Temperature (Default is for Air at 20C)

Calculations is based on Nusselt number correlations.

T_{p} = T_{a} + q / H A

h = Nu · k / S

The Nusselt number is calculated as:

Nu = { 48 / (Ra_{s } · S/L) + 2.51 (Ra_{s}· S/L)^{(2/5)} }^{-0.5}

where:

Ra_{s} = g Bq ρ^{2} C_{p} S^{4} / k^{2} μ

Ra_{s} (S/L) <= 10 corresponds to the fully developed case and

Ra_{s} (S/L) >= 100 correspond to the isolated plate limit, i.e. for short channel or large spacing independent boundary layers develop on each plate, and the conditions are those of an isolated plate in a quiescent medium.

Prandt Number:

Pr = Cp · μ / k

Rayleigh Number:

Ra =
g · B · q ' · S^{4} · ρ^{2} * Cp / (μ· k^{2} )

Film temperature
at the reference temperature of 20 °C.

T_{f} = (T_{p} + T_{a} ) / 2

Fluid density at at film temperature using perfect gas law:

ρ = ρ_{ref} ( T_{ref} + 273) / ( T_{f} + 273) + 273

T_{ref} = 20 °C

Where:

T_{f} = Film temperature °C

T_{p} = Plate temperature °C

T_{a} = Ambient Temperature °C

C_{p} = Specific Heat
J/kg- °C

B = Coefficient of thermal expansion (1/K)

k = Thermal Conductivity (W/m - °C)

v = Dynamic Viscosity (
kg/m-s )

ρ = Density (kg/m^{3})

Nu = Nusselt Number

W = Width of Channel (m)

H = Height of Channel (m)

S = Channel Gap (m)

q = Total uniform heat load on plates (W)

q' = Flux Heat (W/m^{2})

Pr = Prandtl number

Ra = Raleigh number - for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or natural convection.

h = Average heat transfer coefficient (W/m^{2} - °C)

g = 9.81 (m/s^{2})

**References **

Bar-Cohen, A., and W.M. Rohsenow, *AThermally Optimum Spacing of Vertical Natural Convection Cooled, Parallel Plates, *J. Heat Transfer, 106, 116 1984.

Incropera, De Witt., *Fundamentals of Heat and Mass Transfer *, 3rd ed., John Wiley & Sons, p557, eq.9.46, 1990.

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