Fundamental principles and constitutive relations
Problem 1.) Shortly after you light a candle, the flame reaches the melting temperature (To). It has an initial length of Lo that will decrease while melting. There is a net heat flux qo to the top surface of the candle and convective heat transfer to the atmosphere (T∞ with heat coefficient h) from the side.
Derive the governing equations and state the boundary conditions to determine Temperature profile and the length of the candle L(t).
Problem 2.Figure 2 shows a membrane reactor where an enzyme-catalyzed reaction A →B occurs. The enzyme is immobilized in the membrane. The concentrations of the feed stream and product stream of A (CA) and B (CA) maintains as shown in the figure. A thin coating layer is applied in order to accelerate the diffusion of A to the membrane and restricts the flux of B across the layer and the flux is followed by
NBz(h)=KcCB(h) where Kc is the permeability coefficient. The reaction is the Figure 2. Membrane reactor first-order and homogenous.
Derive the governing equations and boundary conditions to determine the concentrations of the reactant and product in the membrane.
Make the governing equations dimensionless and find the corresponding boundary conditions.
Problem 3. Two immiscible incompressible Newtonian fluids ( 1, 1for fluid1 and 2, 2for fluid2) flow between two infinite plates separated by a height H1 as shown below. The bottom plate is stationary, while the top moves at a constant velocity Vo. The Flow is steady and laminar.
Problem4. (10 points) Put the following vector-calculus forms into Tensor Notation form using the Kronecker delta and permutation symbol:
