Quality Management Systems –You have to complete the attached Book1 – Case Study and upload it before the due date posted in Course Syllabus in BB (November 12, 2020).
ECH6285Fall Semester, 2020Homework 4Assigned – November 10, 2020; Due – November 18, 2020, 11:59 PMFollow the homework format given in the syllabus and discussed in class. Make sure you previewyour pdf file prior to submitting it.• Add a signed cover sheet – a template is provided with this HW assignment• Add a header on each page that gives your name, assignment date, and page number.• Ensure all work is in portrait orientation including plots and any schematics• Ensure that there a sufficient margin (0.5 to 1 inch) and nothing is written in the margins.• Check for legibility and single file submission with correct page orderEnsure that you submit your assignment in Canvas by the deadline. It is a good practice to havea draft submitted 12-24 hours prior to deadline so that you are not scrambling at the last minuteor unable to submit due to unanticipated issues. Only the last submission that is uploaded will begraded.1Problem 1 (150 points): In class we have discussed the modeling of hydrodynamic and thermal boundary layers near a flat plate under the simplifying assumptions of steady laminar flow,Newtonian fluid, and constant physical properties (ρ, µ, k, Cp).As part of that discussion, an approach employing dimensionless variables with combination ofvariables yielded two non-linear ODEs for the boundary layers.yyxUo ToTw(xStarting with the following three simplified equations:∂ux∂x +∂uy∂y = 0 ρux∂ux∂x + uy∂ux
∂y
∂∂y µ∂ux∂y ρCpux∂T∂x + uy∂T∂y = k∂2T∂y2determine the ODEs and boundary conditions for the hydrodynamic and thermal boundary layers with the following changes.• temperature of the flat plate is not constant but a function of distance from the leading edge:Tw(x) − To = AxN where A and N are constants• viscosity is temperature dependent and follows the relation1
µ
γµo(T − Tr) where Tr = To −1γand γ, µo are constantsUse the following transformations:η =ypνox/UoΨ = pνoUox f(η)where νo = µo/ρ is a kinematic viscosity at To and Ψ is the streamfunction.For the dimensionless temperature, use the following transformations:θ(η) = T − ToTw − Toθr =Tr − ToTw − ToClearly show your steps.
Problem 2 (150 points):Using the ODEs and BCs from problem 1, numerically solve for the profiles for the dimensionlessvelocity component in the x-direction and the dimensionless temperature.For your numerical solution, pick one value from the following ranges of the parameters:NP r =µoCpk∈ (5, 10) N ∈ (0.3, 0.6) θr ∈ (−2, −0.5)(i). Plot the dimensionless velocity component in the x-direction as a function of η. Determinethe value of η that indicates the hydrodynamic boundary layer thickness as per the criterionthat uxUo= 0.99(ii). Plot the dimensionless temperature as a function of η. Determine the value of η that indicatesthe thermal boundary layer thickness as per the criterion that θ = 0.01.(iii). After you have created the plots, briefly compare and comment on the results you obtain withthe case discussed in class where the viscosity and wall temperature were constant.Make sure that the plots have titles and axes are labeled. Use a software like Matlab (or Excelor Mathematica or Maple). Attach your code/spreadsheet with clear comments for calculations orexplain the steps/formulae.3ECH 6285 Cover Sheet Fall 2020Homework #:Declaration• I attest that the work being submitted for grading my own.• I have not used any unauthorized resource.• I have not copied the work of another person.NameSignature4
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