# Numerical study of natural convection in fully open tilted cavities

## Abstract

A numerical simulation of two-dimensional laminar natural convection in a fully open tilted square cavity with an isothermally heated back wall is conducted. The remaining two walls of the cavity are adiabatic. Steady-state solutions are presented for Grashof numbers between 10{sup 2} and 10{sup 5} and for tilt angles ranging from {minus}60{degree} to 90{degree} (where 90{degree} represents a cavity with the opening facing down). The fluid properties are assumed to be constant except for the density variation with temperature that gives rise to the buoyancy forces, which is treated by the Boussinesq approximation. The fluid concerned is air with Prandtl number fixed at 0.71. The governing equations are expressed in a normalized primitive variables formulation. Numerical predictions of the velocity and temperature fields are obtained using the finite-volume-based power law (SIMPLER: Semi-Implicit Method for Pressure-Linked Equations Revised) algorithm. For a vertical open cavity ({alpha} = 0{degree}), the algorithm generated results that were in good agreement with those previously published. Flow patterns and isotherms are shown in order to give a better understanding of the heat transfer and flow mechanisms inside the cavity. Effects of the controlling parameters-Grashof number and tilt angle-on the heat transfer (average Nusselt number) are presented andmore »

- Authors:

- Publication Date:

- Research Org.:
- Kuwait Univ. (KW)

- OSTI Identifier:
- 20001223

- Alternate Identifier(s):
- OSTI ID: 20001223

- Resource Type:
- Journal Article

- Journal Name:
- Heat Transfer Engineering

- Additional Journal Information:
- Journal Volume: 20; Journal Issue: 3; Other Information: PBD: Jul-Sep 1999; Journal ID: ISSN 0145-7632

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 14 SOLAR ENERGY; CAVITY RECEIVERS; SOLAR ARCHITECTURE; NATURAL CONVECTION; CALCULATION METHODS; MATHEMATICAL MODELS

### Citation Formats

```
Elsayed, M.M., Al-Najem, N.M., El-Refaee, M.M., and Noor, A.A.
```*Numerical study of natural convection in fully open tilted cavities*. United States: N. p., 1999.
Web. doi:10.1080/014576399271448.

```
Elsayed, M.M., Al-Najem, N.M., El-Refaee, M.M., & Noor, A.A.
```*Numerical study of natural convection in fully open tilted cavities*. United States. doi:10.1080/014576399271448.

```
Elsayed, M.M., Al-Najem, N.M., El-Refaee, M.M., and Noor, A.A. Wed .
"Numerical study of natural convection in fully open tilted cavities". United States. doi:10.1080/014576399271448.
```

```
@article{osti_20001223,
```

title = {Numerical study of natural convection in fully open tilted cavities},

author = {Elsayed, M.M. and Al-Najem, N.M. and El-Refaee, M.M. and Noor, A.A.},

abstractNote = {A numerical simulation of two-dimensional laminar natural convection in a fully open tilted square cavity with an isothermally heated back wall is conducted. The remaining two walls of the cavity are adiabatic. Steady-state solutions are presented for Grashof numbers between 10{sup 2} and 10{sup 5} and for tilt angles ranging from {minus}60{degree} to 90{degree} (where 90{degree} represents a cavity with the opening facing down). The fluid properties are assumed to be constant except for the density variation with temperature that gives rise to the buoyancy forces, which is treated by the Boussinesq approximation. The fluid concerned is air with Prandtl number fixed at 0.71. The governing equations are expressed in a normalized primitive variables formulation. Numerical predictions of the velocity and temperature fields are obtained using the finite-volume-based power law (SIMPLER: Semi-Implicit Method for Pressure-Linked Equations Revised) algorithm. For a vertical open cavity ({alpha} = 0{degree}), the algorithm generated results that were in good agreement with those previously published. Flow patterns and isotherms are shown in order to give a better understanding of the heat transfer and flow mechanisms inside the cavity. Effects of the controlling parameters-Grashof number and tilt angle-on the heat transfer (average Nusselt number) are presented and analyzed. The results also revealed that the open-cavity Nusselt number approaches the flat-plate solution when either Grashof number or tilt angle increases. In addition, a correlation of the Nusselt number in terms of the Grashof number and tilt angle is developed and presented; a comparison is made with available data from other literature.},

doi = {10.1080/014576399271448},

journal = {Heat Transfer Engineering},

issn = {0145-7632},

number = 3,

volume = 20,

place = {United States},

year = {1999},

month = {9}

}