# Study on natural convection in a rectangular enclosure with a heating source

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## Abstract

The natural convective heat transfer in a rectangular enclosure with a heating source has been studied by experiment and numerical analysis. The governing equations were solved by a finite volume method, a SIMPLE algorithm was adopted to solve a pressure term. The parameters for the numerical study are positions and surface temperatures of a heating source i.e., Y/H=0.25, 0.5, 0.75 and 11°C≦ΔT≦59°C. The results of isotherms and velocity vectors have been represented, and the numerical results showed a good agreement with experimental values. Based on the numerical results, the mean Nusselt number of the rectangular enclosure wall could be expressed as a function of Grashof number.

## Key Words

Heating source Low Reynolds Number Turbulence Model Nusselt Number Grashof Number## Nomenclature

- a
Grid space regulation coefficient

- g
Gravity acceleration [m/s

^{2}]- Gr
Grashof number\(\left( {G_r = \frac{{g\beta (T_h - T_c ) H^3 }}{{\nu ^2 }}} \right)\)

- H
Vertical wall length [m]

*K*Turbulent energy [m

^{2}/s^{2}]- L
Horizontal wall length [m]

- Nu
Local Nusselt number\(\left( {Nu = \left. {\frac{{hL}}{k} = \frac{{\partial \theta }}{{\partial X}}} \right|_{X = 0} } \right)\)

- \(\overline {Nu} \)
Mean Nusselt number\(\left( {\overline {Nu} = \frac{1}{L}\int {Nu \cdot dy} } \right)\)

- Pr
Prandtl number

- T
Temperature [°C]

- T
_{h} Heating source temperature [°C]

- T
_{c} Cooled wall temperature [°C]

- ΔT
Temperature difference [°C]

- U
X direction velocity [m/s]

- V
Y direction velocity [m/s]

- β
Thermal expansion coefficient [K

^{−1}]*δ*_{ij}Kronecker delta

- ε
Turbulent energy dissipation rate

*μ*_{t}Turbulent eddy viscosity [kg/ms]

- ρ
Density [kg/m

^{3}]

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