Consider convection and diffusion in one dimension as in the figure with = temperature, position...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider convection and diffusion in one dimension as in the figure → with = temperature, position x, convection u and the boundary conditions as indicated. A source distribution S applies as in the figure → at t>0 with a = -200; b= 100, x₁=0.6 m, x2 = 0.2 m. The transient convection diffusion is described by (ρφ) θρυφ) _ ὃ ap = Ət əx əx ????х a. with Node aw 1 2 0 Length L = 1.5 m is divided into 45 grid points (8x = 0.0333 m), while F = pu=2.0, D=1/8x = 0.9. Show that the discretisation for a general node (except x=0 and x=L) gives Ax (p=62AX+F. Op + (30E-20p-w)] - Fu [ow + (30p-20w-ww)] = Dee - #r) - D₂(p = 0w) Fc[Op where op is the previous value for op; initially op=0 for all points. For point A: mirroring for node W (where =0) gives 4-op and For point B the zero gradient boundary gives B = OP. b. Show that this gives the discretisation as apop = awow+aEE + app + Su pax dp Ar ap = aw+ag + ap+ (Fe-Fw)-Sp and discretisation parameters are as given in the table below (next page). Source S is linearised to S+Spor. ag Dw+Fw De A 3-44 Dw+Fw De x-0 6-0 45 Dw+Fw 0 0 0 0 Sp De+4-D₁+F₁) (D₁+F₁) 0₁ + / Felp - 3 2-0 u-2.0 m/s Su a+b 1 ; ap ax X-L and show that the B F. (30p-w)+F(0w +20p-30g) Fw(30p-20w-ww) +Fe(Ow+20p-30E) F (30p-20w-ww) X-L do/dx-0 PA (90p-80A-DE) (9 Consider convection and diffusion in one dimension as in the figure → with = temperature, position x, convection u and the boundary conditions as indicated. A source distribution S applies as in the figure → at t>0 with a = -200; b= 100, x₁=0.6 m, x2 = 0.2 m. The transient convection diffusion is described by (ρφ) θρυφ) _ ὃ ap = Ət əx əx ????х a. with Node aw 1 2 0 Length L = 1.5 m is divided into 45 grid points (8x = 0.0333 m), while F = pu=2.0, D=1/8x = 0.9. Show that the discretisation for a general node (except x=0 and x=L) gives Ax (p=62AX+F. Op + (30E-20p-w)] - Fu [ow + (30p-20w-ww)] = Dee - #r) - D₂(p = 0w) Fc[Op where op is the previous value for op; initially op=0 for all points. For point A: mirroring for node W (where =0) gives 4-op and For point B the zero gradient boundary gives B = OP. b. Show that this gives the discretisation as apop = awow+aEE + app + Su pax dp Ar ap = aw+ag + ap+ (Fe-Fw)-Sp and discretisation parameters are as given in the table below (next page). Source S is linearised to S+Spor. ag Dw+Fw De A 3-44 Dw+Fw De x-0 6-0 45 Dw+Fw 0 0 0 0 Sp De+4-D₁+F₁) (D₁+F₁) 0₁ + / Felp - 3 2-0 u-2.0 m/s Su a+b 1 ; ap ax X-L and show that the B F. (30p-w)+F(0w +20p-30g) Fw(30p-20w-ww) +Fe(Ow+20p-30E) F (30p-20w-ww) X-L do/dx-0 PA (90p-80A-DE) (9
Expert Answer:
Answer rating: 100% (QA)
To show the discretization for a general node except x0 and xL we can start with the given equation ddx S Applying the finite difference method we can discretize the equation using the central differe... View the full answer
Related Book For
Posted Date:
Students also viewed these finance questions
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
The table below represents stocks and their expected returns under each state of the economy. The portfolio's weights are as follows 50% is invested in grapefruit, 25% in orange, and 25% in lemon....
-
KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
-
On 1 June 2019, Manchester United Ltd bought 48 million ordinary shares in Chelsea FC Ltd paying GHS 280 million cash. The summarised statement of financial position for the two entities as at 31...
-
A drum of 200-mm radius is attached to a disk of radius rA = 150 mm. The disk and drum have a combined mass of 5 kg and a combined radius of gyration of 120 mm and are suspended by two cords. Knowing...
-
The adjustment made when approximating a discrete random distribution with a continuous one is called the __________________ correction. In Exercises 5 and 6, fill in each blank with the appropriate...
-
The trial balance of URNO 1 Child Care, Inc., does not balance. The following errors are detected: a. Cash is understated by $5,000. b. A \($3,000\) debit to Accounts receivable was posted as a...
-
Part 1 Modify your program from Learning Journal Unit 7 to read dictionary items from a file and write the inverted dictionary to a file. You will need to decide on the following: How to format each...
-
Walmart is considering purchasing a new automated forklift. the sales quote consists of quarterly payments of $37,200 for five years at 7.6% interest. what is the purchase price?
-
Refer to Assignment Problem 25. a. Illustrate the (transformed) data in a graph. Add means and error bars showing standard errors of means. b. The table at the bottom of the page shows partial...
-
4. Solve the differential equation. (Hint: Use an appropriate substitution) dy (4x y+ 1)? dx
-
Critically consider the purpose of calculating production overhead absorption rates.
-
Explain how the apportionment of those costs incurred up to the separation point of two or more joint products could give information which is unacceptable for (i) stock valuation and (ii)...
-
Blade and disk vibration a. can cause failure of turbines and aircraft engines b. cause discomfort in human activity during metal cutting c. can cause wheels of locomotives to rise off the track d....
-
Imbalance in diesel engines a. can cause failure of turbines and aircraft engines b. cause discomfort in human activity during metal cutting c. can cause wheels of locomotives to rise off the track...
-
Rayleigh (1877) a. published a book on the theory of sound b. first person to investigate musical sounds on a scientific basis c. wrote a treatise called Introduction to Harmonics d. founder of...
-
A dependency diagram is shown below, Identify the partial dependencies and transitive dependencies. Normalise the given scenarios to Third normal form 1. XYZ school stores student information as...
-
Find the market equilibrium point for the following demand and supply functions. Demand: 2p = - q + 56 Supply: 3p - q = 34
-
Refer to the information presented in PA-33. Data from PA-33 VHL reported income before income taxes of $400,000. Current income tax expense was $40,000; deferred income tax expense was $10,000....
-
Refer to the facts set out in P7-13 above and consider the following additional information: a. On July 1, 2018, ICI received a $43,750 interest payment on the Zoe Corp. bonds. The next interest...
-
Charlie Company purchased a building for $5 million. The building has a 20-year useful life and zero residual value. The company uses the straight-line method to depreciate buildings. After using and...
-
Assume that Boardmaster sold skateboards to a department store for \($35,000\) cash. How would this transaction affect Boardmasters accounting equation? a. Increase both assets and stockholders...
-
Generally Accepted Accounting Principles (GAAP) are created by the a. Securities and Exchange Commission (SEC). b. Financial Accounting Standards Board (FASB). C. Institute of Management Accountants...
-
Boardmaster is famous for custom skateboards. At the end of a recent year, Boardmasters total assets added up to \($622\) million, and stockholders equity was \($487\) million. How much did...
Study smarter with the SolutionInn App