Convection heat transfer coefficient

Convection heat transfer coefficient is introduced in the relation between wall temperature, temperature of the fluid (at a point sufficiently remote from the wall) and the power flowing from the wall to the fluid: Thus if a known coefficient α, we can simply calculate the heat transfer between the fluid (whether gas) and the surface of the solid body. The problem is to determine the coefficient α for a particular arrangement of a liquid. Experimental data were organized by various authors in certain practices often using a theory dimensionless quantities.

## 1. Procedure according to: M.A.Michejev: Základy sdílení tepla, Praha 1952

The first step is to determine whether is natural or forced convection

### 1.1. Natural convection

The movement of the fluid is caused by thermal changes of its density. The procedure is following:

• We calculate Grashoff number (Gr)
• We calculate Prandtl number (Pr)
• We calculate Nusselt number (Nu) from calculated Gr a Pr
• We calculate α from Nu.

Grashoff number Gr ,

where

β - thermal volume expansion of the liquid at an average temperature between the wall and the liquid Tstř = (TWall + TFluid) / 2
For ideal gas (air) is formula β = 1/Tstř. Tstř Must be put in Kelvin. For water 20°C: β = 207*10-6 K-1

ΔT - the absolute value of the temperature difference between the wall and the liquid: ΔT = |TWall - TFluid|.

g - gravity acceleration (9.81 m/s2)

l - so called. characteristic dimension. For vertical, diagonal and curved surfaces, and body is it height (dimension in the direction of gravitational force), with horizontal plates and freely runarounded surfaces is it smallest horizontal dimension.

ν - kinematic viscosity of the fluid at an average temperature between the wall and the liquid Tavg.

- Prandtlovo číslo Pr ,

where

ν - kinematic viscosity of the fluid at an average temperature between the wall and the liquid a – thermal diffusivity (a = λ / (ρ∙c)) at an average temperature between the wall and the liquid

For air is approximately Pr = 0.7.

- Calculation Nusselt number (Nu) from Gr a Pr

Nusselt is calculated of the product ofPr∙Gr by using following formula ,

where c a n are constants which are dependet from following table :

Pr∙Grcn
1∙10-3 - 5∙1021.181/8
5∙102 - 2∙1070.541/4
2∙107 - 1∙10130.1351/3

- Calculation α from Nu

For calculation α is used following formula: ,

kde

λ – is thermal conductivity at an average temperature between the wall and the liquid Tstř = (TWall + TFluid) / 2

l – is characteristic dimension.(same how in calculating for Gr)