19. The equations describing a convection-diffusion problem in heat trans- port are Ju Ju Ju +v...

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19. The equations describing a convection-diffusion problem in heat trans- port are Ju Ju J²u +v Ət ????х მ2 ს u(0, t) = uo, u(x, 0) = 0, u(l, t) = u₁, where u(x, t) is the temperature, v is the (constant) velocity and a is the thermal diffusivity. Consider the following scaling, = a au ƏT + €1 X = 7₁ T = X = - at 12¹ U = " U U1 Show that the above equations may be expressed in the dimensionless form 2 au 8² U Əx 0x² giving formulae for the dimensionless constants €₁ and €2. V = lv α U(0, T) = €2 U(X,0) = 0, U(1,T) = 1, 19. The equations describing a convection-diffusion problem in heat trans- port are Ju Ju J²u +v Ət ????х მ2 ს u(0, t) = uo, u(x, 0) = 0, u(l, t) = u₁, where u(x, t) is the temperature, v is the (constant) velocity and a is the thermal diffusivity. Consider the following scaling, = a au ƏT + €1 X = 7₁ T = X = - at 12¹ U = " U U1 Show that the above equations may be expressed in the dimensionless form 2 au 8² U Əx 0x² giving formulae for the dimensionless constants €₁ and €2. V = lv α U(0, T) = €2 U(X,0) = 0, U(1,T) = 1,