1. Natural convection is a good example of coupled heat and momentum. Shown below are two infinite parallel plates filled with a fluid that are maintained at uniform temperatures T1 (cold) and T2 (hot). Assume the following linear variation in the temperature in the x-dir T=Tm+dy(2T2T1), where Tm=(2T2+T1) The density varies with temperature as: =m(1(TTm)) Use the equations of motion to derive an expression for vx(y) in terms of any or all of y,d,T1,T2,M, ,,g. You can take the variation of the pressure in x direction to be of the normal hydrostatic variation so that you can substitute the following terms of the x-balance as: (xP+gx)mg(TTm)