19. The equations describing a convection-diffusion problem in heat trans- port are Ju Ju Ju +v t ???? 2 u(0, t) = uo, u(x, 0) = 0, u(l, t) = u, where u(x, t) is the temperature, v is the (constant) velocity and a is the thermal diffusivity. Consider the following scaling, = a au T + 1 X = 7 T = X = - at 12 U = " U U1 Show that the above equations may be expressed in the dimensionless form 2 au 8 U x 0x giving formulae for the dimensionless constants and 2. V = lv U(0, T) = 2 U(X,0) = 0, U(1,T) = 1,