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.