Manage passive air convection between rooms?

[RichardL]

Layout
Downstairs Dining room - 6m x 4m room, with staircase

Upstairs landing - 4m x 4m directly above the dining room and connecting to 3x bedrooms,

100% electrically heated - Dining room:A2A, Bed1: A2A + Bed2/3: Infrared panels

Challenge

The challenge - the bedrooms have their own heating and fine, the landing however has a cold spot by the window (where its traditional wet radiator was & your traditional cold spot)

 

The original plan was the A2A in the dining room downstairs, + B1 might flow into all upstairs areas - but in actuality I suspect the air is just reaching equilibrium and not moving.

Proposal/thought
A vent between the dining room and the landing immdiately above it - its the other side from the stairs so - posit - might setup a convection loop.

I'm assuming the vent will be different air flow capacity to the staircase, being orders of magnitude smaller, so one will prefer to let the warm air downstairs up and/or the colder air upstairs down & only then reach equilibrium when the heat is more evenly distributed between the two?

Sound transfer between floors is not an issue.


Sure - naive simple thinking with no maths and no experience in modelling air flow 
Its also potentially a simple project with 15cm of duct and vents top/bottom and wondered if its worth a play?

Q
How do I learn more about convection between rooms or ducting rules of thumb?