This page calculates the natural convection heat transfer between two concentric cylinders maintained at constant temperatures. The calculation is based on Rayleigh number and is valid for Rayleigh numbers below 107. 

Define the dimensions of the cylinders and their temperatures. You also need to define the fluid properties. This page will calculate the heat convected between the cylinders based on the flow conditions.

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Cylinders and Flow Conditions

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

Description Symbol Value Units
Film Temperature = (Ti+To)/2 Tf oC
Specific Heat Cp J/kg-oC
Coefficient of Thermal Expansion B 1/K
Thermal Conductivity k W/m-oC
Dynamic Viscosity µ kg/m-s
Density at reference temperature of 20 C rhoref kg/m3
Density calculated at film temperature Tf rho kg/m3

Cylinders Dimensions

Description Symbol Value Units
Length L Meters
Inner Cylinder Diameter Di Meters
Outer Cylinder Diameter Do Meters
Inner Cylinder Temperature Ti oC
Outer Cylinder Temperature To oC

Results for Concentric Cylinders

Description Symbol Value Units
Gap between cylinders d m
Effective conductivity keff W/m-oC
Prandlt Number = Cp*µ / k Pr None
Rayleighd = gB rho2Cp(Ti-To)d3 / kµ Rad None
Rayleighc* = Rad (ln(Do/Di))4) / d3(Di-3/5+Do-3/5)5 Rac* None
Heat transfer = 2Pi keff L (Ti-To) / ln(Do/Di) q W

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