Consider a parallel plate flow problem where the mass fluxes are acting on an infinitesimal control...

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Consider a parallel plate flow problem where the mass fluxes are acting on an infinitesimal control volume along the Cartesian coordinate system. (a) Inlet pu Ayaz y+Ay z+Az, a(pw) [ON + 2(60) A =] AT AVAy +260) AN JAVA= cy 1 pw AxAy x+Ax Outlet + 8(A) AX JAVA= (b) Z, W V. V >X, U ди du dv dw -p+2μ- + λ + + Ox ex dy dz AVA: y+Ay or :+A: TATA: - ΔΙ Surface Forces [30 marks in total] + Ar TATAY Figure 2. Incoming and outgoing (a) mass fluxes and (b) x-directional normal and sheer surface stresses over an infinitely small control volume in a flow over two parallel plate channels. [ +0 AN JAYA= · (a) Using the control volume approach as described in Fig. 2a, derive the mass conservation equation. [10 marks] (b) Given that the flow is incompressible with constant fluid properties, what can be concluded based on the mass conservation equation in (a). du ди dw ἂν + and T₁ = μ + dy dx əz əx (c) Using the control volume approach as described in Fig. 2b, derive the x-momentum equation and deduce the y, z-momentum equations by similarity, given that the fluid is Newtonian in the absence of body forces and with the same conditions applied in (b). The following expressions for the normal and tangential viscous stresses are provided: [5 marks] [15 marks] Consider a parallel plate flow problem where the mass fluxes are acting on an infinitesimal control volume along the Cartesian coordinate system. (a) Inlet pu Ayaz y+Ay z+Az, a(pw) [ON + 2(60) A =] AT AVAy +260) AN JAVA= cy 1 pw AxAy x+Ax Outlet + 8(A) AX JAVA= (b) Z, W V. V >X, U ди du dv dw -p+2μ- + λ + + Ox ex dy dz AVA: y+Ay or :+A: TATA: - ΔΙ Surface Forces [30 marks in total] + Ar TATAY Figure 2. Incoming and outgoing (a) mass fluxes and (b) x-directional normal and sheer surface stresses over an infinitely small control volume in a flow over two parallel plate channels. [ +0 AN JAYA= · (a) Using the control volume approach as described in Fig. 2a, derive the mass conservation equation. [10 marks] (b) Given that the flow is incompressible with constant fluid properties, what can be concluded based on the mass conservation equation in (a). du ди dw ἂν + and T₁ = μ + dy dx əz əx (c) Using the control volume approach as described in Fig. 2b, derive the x-momentum equation and deduce the y, z-momentum equations by similarity, given that the fluid is Newtonian in the absence of body forces and with the same conditions applied in (b). The following expressions for the normal and tangential viscous stresses are provided: [5 marks] [15 marks]