A two-dimensional square enclosure (all solid walls) filled with air is subjected to a linearly varying temperature on one of its vertical walls (say \(T=\left(x_{2} / L\right) T_{\max }\), where \(L\) is the characteristic dimension) and a constant temperature on the other vertical wall, which is less than that of \(T_{\max }\). If the horizontal walls are assumed to be adiabatic, obtain solutions for the flow and heat transfer inside the enclosure for different Rayleigh numbers. Refer to Chapter 7 for nondimensional scales.