Thermal convection in the presence of heating can be modelled by dT/dt + u dT/dx

Question

Thermal convection in the presence of heating can be modelled by
dT/dt + u dT/dx + v dT/dy = Q/cp + k (d^2t/dx^2 + d^2T/dy^2)

( all are partial derivatives, Q is volumetric flow rate)
Assume that the maximum temperature Tmax and the average temperature Tavg are
known, and assume that for temperature T, we can nondimensionalize T-Tavg using
(Tmax-Tavg) as a scale. Let u and v be scaled by U0, and let x and y be scaled by L.
The parameter , which is the Greek letter kappa has units of m2/s and is called the
thermal conductivity.
Assuming the time scale to be given by L/U, nondimensionalize this equation and
indicate what the non-dimensional parameters are.
5

Explanation / Answer

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