# Non linear time dependent problem - Natural Convection

**URL:** <https://community.freefem.org/t/non-linear-time-dependent-problem-natural-convection/1546>\
**Category:** General Discussion\
**Created:** [February 22, 2022, 11:14am UTC](https://community.freefem.org/t/non-linear-time-dependent-problem-natural-convection/1546 "2022-02-22T11:14:43Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![D\_N\_Sarkar](https://avatars.discourse-cdn.com/v4/letter/d/0ea827/32.png) [@D\_N\_Sarkar](https://community.freefem.org/u/D_N_Sarkar)\
**Post date:** [February 22, 2022, 11:14am UTC](https://community.freefem.org/t/non-linear-time-dependent-problem-natural-convection/1546/1 "2022-02-22T11:14:43Z")

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This is with respect to the code: [Non linear time dependent problem - #2 by frederichecht](https://community.freefem.org/t/non-linear-time-dependent-problem/856/2)

In this code, natural convection within sqaure cavity (bottom wall hot, top wall cold) is being simulated. For such flows, convection starts at Rayleigh number, Ra ~ 2585 (value obtained from literature).

As I understand the code, the first Rayleigh number to be used in this code is such that it gives a trivial solution (Ra = 1e3), i.e., there is no convection. The next Rayleigh numbers should be such that it gives non-trivial solutions. If I use Ra = 3000, it is giving wrong Nusselt number.

How much about the critical Rayleigh number should a Ra value be used to get correct Nusselt number results?