A web search will reveal many numerical (CFD) investigations of this type of system, as there are various heated enclosures used throughout industry, business, and home. Most often, these enclosures aren't just empty boxes, which makes each of the investigations (often graduate studies) unique. Before you spend too much time looking for an appropriate empirical relationship for natural convection, you should prepare or describe what makes your particular problem interesting and worth pursuing. What's in the box and why is it heated?

You can find the following articles useful

International Journal of Heat and Mass Transfer

Volume 139, August 2019, Pages 121-129📷

Experimental investigation on very-high-Rayleigh-number thermal convection in tilted rectangular enclosures

You can change the tilting angle to get vertical or horizontal enclosure

https://www.sciencedirect.com/science/article/abs/pii/S0017931019308415

Dear Feyza,

The Rayleigh number is the characteristic non-dimensional measure of the temperature difference prescribed across the fluid layer, and is defined by Ra ≡ α△T gH3/νκ, where α is the isobaric thermal expansion coefficient of the fluid in the container, T the temperature difference between the bottom and top walls, g the acceleration due to gravity and H the vertical dimension of the convection cell; ν and κ are, respectively, the kinematic viscosity and the thermal diffusivity of the fluid.

Nusselt number is a dimensionless parameter used in calculations of heat transfer between a moving fluid and a solid body. It is the ratio of convection heat transfer to conduction heat transfer. In fluid dynamics, the Nusselt number (Nu) is the ratio of convective to conductive heat transfer. It is a key parameter in determining mode of heat transfer also makes heat transfer co efficient ,h non dimensionalize. Nusselt number is required to find 'h' which is convective heat transfer coefficient.

Nusselt number can never be less than 1because the convective flux can be zero but the molecular flux term will be similar in the numerator and the denominator. Therefore, the minimum value of Nusselt numberis 1 when the convective flux is zero.

Correlation between th Nusselt and Reynolds

The larger the Nusselt number, the more effective the convection. A larger Nusselt number corresponds to more effective convection, with turbulent flow typically in the 100–1000 range. For turbulent flow, the Nusselt number is usually a function of the Reynolds number and the Prandtl number.

Paper for the reference (http://users.ictp.it/~krs/pdf/2006_007.pdf)

Nusselt number, Nu, where Nu is the ratio of the measured total heat flux to that due to molecular conduction for the same T and H. A Nusselt number, Nu, in turbulent thermal convection in a cylindrical container of aspect ratio 4. The highest Rayleigh number achieved was Ra = 2 × 1013. Heat transfer and temperature fluctuation data for aspect ratio 4 with Ra up to 2 × 1013. For 108 < Ra < 1010, the logNu–logRa slope is nearly give the correlation between Nusselt number and Reynolds number.

One of the paper shows the result correlation, observed value for a slope logNu–logRa slope 0.31 with Ra= = 3.1 × 109. It is clear that there is a strong long-time correlation between opposite sidewall sensors, indicative of a well ordered and robust mean wind, while no clear correlation exists between the sidewall fluctuations and those of the centre.

Hope this content is helpful for you.

Ashish

Dear Gamal B. Abdelaziz ,

Thank you for your shares. They are useful to me.

Best regards.

Feyza Bilgin

greeting

more details about the natural convection in the horizontal rectangular enclosure you can be find in the

- "Engineering Heat Transfer" By N.V. Suryanarayana.

- " Heat and Mass Transfer A practical Approach) by Yunus A.Cengel.

I hope it be useful to you

Dear Ali Dawood Salman,

Thank you for your answer.

I looked at several books and articles. However, I can not find the Nusselt correlation for rectangular enclosures (horizontal and vertical) because the lower aspect ratio (AR

I'm so sorry Dr. Feyza Bilgin , I just have the hard copy for the references that I mentioned before. if your work about the photo-voltaic, also you can fined the reference: " Solar Energy Fundamentals and Application" by H. P. Garg, J. Parkash.

With my respect.

Gamal suggest good articles

Incropera textbook