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CritPt / Challenge_31_main / Consider flow between two parallel plates heated from below and cooled from…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

code template

Code

def answer():
    r"""
    Return the value of critical Rayleigh number and associated critical horizontal wavenumber.

    Inputs
    ----------
    None

    Outputs
    ----------
    Ra_c: float, critical Rayleigh number
    kx: float, associated critical horizontal wavenumber
    """

    # ------------------ FILL IN YOUR RESULTS BELOW ------------------
    Ra_c = ...
    kx = ...
    # ---------------------------------------------------------------

    return Ra_c, kx

problem description

# Problem setup: Consider flow between two parallel plates heated from below and cooled from above (i.e., Rayleigh-Benard convection) with Prandtl number

Pr=1

and horizontally periodic boundary conditions. The boundary condition on the top wall is free-slip with fixed temperature, and the boundary condition on the bottom wall is no-slip with constant heat flux. # Main problem: What are the critical Rayleigh number (allowing

\pm 0.5

error) and associated critical horizontal wavenumber (allowing

\pm 0.02

error), where above this critical Rayleigh number, the conduction base state is linearly unstable?

Plain-text mathematical notation (without MathML)


# Problem setup:
Consider flow between two parallel plates heated from below and cooled from above (i.e., Rayleigh-Benard convection) with Prandtl number Pr=1 and horizontally periodic boundary conditions. The boundary condition on the top wall is free-slip with fixed temperature, and the boundary condition on the bottom wall is no-slip with constant heat flux.


# Main problem:
 What are the critical Rayleigh number (allowing ±0.5 error) and associated critical horizontal wavenumber (allowing ±0.02 error), where above this critical Rayleigh number, the conduction base state is linearly unstable?

Original LaTeX notation


# Problem setup:
Consider flow between two parallel plates heated from below and cooled from above (i.e., Rayleigh-Benard convection) with Prandtl number $Pr=1$ and horizontally periodic boundary conditions. The boundary condition on the top wall is free-slip with fixed temperature, and the boundary condition on the bottom wall is no-slip with constant heat flux.


# Main problem:
 What are the critical Rayleigh number (allowing $\pm 0.5$ error) and associated critical horizontal wavenumber (allowing $\pm 0.02$ error), where above this critical Rayleigh number, the conduction base state is linearly unstable?

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Source and history

upstream_id / Original problem ID: Challenge_31_main
task_id: 53634481-bef5-5a83-9be9-c3cffe4819f4
task_key: train--Challenge~5f31~5fmain
task_revision_id: 1
config / split: / train

Official source

initial import