# Core stratification effects on natural convection in inclined cavities

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## Abstract

A numerical and experimental study has been made on the flow and heat transfer in inclined air-filled cavities with aspect ratios 1–18 at Ra numbers from 2·10^{4}–5·10^{5} and angles of inclination from 40 to 90°. Core stratification influences the flow. Due to this there arises a torque with two components depending on angle of inclination. On basis of the two torques the computed effects on flow and temperature fields can be explained. For the heat transfer a scaling law could be derived. Experimental data validate the numerical studies.

### Keywords

Experimental Data Heat Transfer Convection Torque Experimental Study### Nomenclature

*A*Aspect ratio:

*H/D**D*Distance between hot and cold plate

*g*Gravitational acceleration

- Gr
Grashof number:

*g;*(*T*_{ H }-*T*_{ c })*D*^{3}/*v*^{2}*H*Distance between lower and upper side wall of cavity

*k*Thermal conductivity air

*l*Dimensionless length

- Nu
Nusselt number α

*D/k**p*Dimensionless pressure

*P*/ρ*g*β(*T*_{ H }−*T*_{ c })*D**P*Pressure

- Ra
Raleigh number:

*g*(*T*_{ H }−*T*_{ c })*D*^{3}/ν*a**T*Temperature

*u*Dimensionless velocity:

*U*ν/*g*β(*T*_{ H }−*T*_{ c })*D*^{2}*U*Velocity component

*x*-direction- \(\tilde u\)
Scaled dimensionless velocity (sin ϕ)

^{−1/2}*u**v*Dimensionless velocity:

*V*ν/*g*β(*T*_{ H }−*T*_{ c })*D*^{2}*V*Velocity component

*y*-direction*x*Dimensionless coordinate

*X/D**X*Coordinate along hot plate and along

*H**y*Dimensionless coordinate

*Y/D**Y*Coordinate perpendicular to hot plate

- \(\tilde y\)
Scaled dimensionless coordinate: (sin ϕ)

^{1/4}*y*

### Greek symbols

- α
Heat transfer coefficient at hot plate

- β
Thermal expansion coefficient

- θ
Dimensionless temperature:

*T−T*_{ c }/*T*_{ H }*−T*_{ c }- ϕ
Angle of inclination relative horizontal

- ρ
Air density

- σ
Torque

- τ
Dimensionless temperature gradient along

*X*-coordinate at central point- ν
Air kinematic viscosity

- ω
Torque proportionality factor: sin ϕ+τ cos ϕ

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### References

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