Please read 4D.2 with Part (a) in BSL and 1. Derive 4D.2.-1 by writing down all assumptions, postulates, and boundary/initial conditions following the standard approach as discussed in the class...

Please read 4D.2 with Part (a) in BSL and 1. Derive 4D.2.-1 by writing down all assumptions, postulates, and boundary/initial conditions following the standard approach as discussed in the class (assumptions and postulates must be indicated). Convert the equation into dimensionless form as indicated in the problem statement. 2. Develop the NUMOL equations for each node including the boundaries. 3. Write down a Matlab code (main+subroutine). 4. Generate the curves in Fig. 4D.2 using NUMOL and the code by choosing N = 21, record results from τ = 0 to 2 with intervals of 0.05 and ξ [0–1]. 5. Is the above solution grid-independent? Find grid-independent solution to at least 4 digit accuracy after decimal point. Problem 2 Viscous Heating in Laminar Tube Flow Please read 11B.2. with Part (a) in BSL and 1. Derive 11B.2.-1 using the step-by-step assumptions, postulates and write down boundary/initial conditions following the standard approach as discussed in the class (assumptions and postulates must be indicated). Assume that the fluid has a constant, uniform inlet temperature of T0 and the tube wall has a constant, uniform temperature of Tw. Convert the equation into dimensionless form via: ( ) ( ) Pe z R k C V R z R z R r r T T T T w p z = = = − −  = 0 ,max 0 , * , *  The final equation must have Brinkman (Br) number and r*, z*, and  only. 2. Develop the NUMOL equations for each node. 3. Write down a Matlab code (main+subroutine). 4. Generate dimensionless temperature profiles for z* values of 0 to 2 with 0.1 intervals and r*[0,1] using NUMOL and the code by choosing N = 21. Perform this for Brinkman # of 1 and find gridindependent solution to at least 4 digit accuracy after decimal point. 5. Repeat step 4 for Brinkman # of 0, 0.1, and 10 and comment on the impact of Br #. Here use the same N that has yielded grid-independent solution in step 4 for all other Br #.