Consider a quasi-one-dimensional steady advection-diffusion flow with the boundary conditions as illustrated in Figure 1: u(x)...

  

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Consider a quasi-one-dimensional steady advection-diffusion flow with the boundary conditions as illustrated in Figure 1: u(x) x=0 p=0 in = puA = 1 x 10-4 -4 kg/s Figure 1 In Figure 1, the velocity u is given in the form of constant mass flow rate, m = puA = 1 x 10-* kg/s, with density p = 1.0 kg/m³ and A = 1 x 104 m² is the cross-sectional area at the entrance of the flow path. The cross-sectional area A at the (x₂.) range, A₂, is two times bigger that the area at the (0, x₁) range, which is A₁ = A, with a linearly gradual change from A₁ to A2₂ in the (x₁,x₂) range, i.e., A₂ = 2A₁. Other data and parameters include path length = (0.5 +0.1g) and diffusivity coefficient I = 0.05 kg/m-s. Given that the source term S(x) forms a linear relation with the x-coordinate as shown in Figure 2, where So= 10f, x₁ = 0.6€ and x₂ = 0.8l. (i) the central-differencing scheme; (ii) the upwind-differencing scheme; the hybrid method. (iii) S(x) So u(x) By using a one-dimensional grid system containing at least 10 computational nodes or cells: a) develop the algebraic formulation that can be used to compute the solution of along the x-axis from the corresponding transport equation; (8 marks) x = l dø/dx = 0 b) obtain the distribution of the value at steady state condition using one of the appropriate schemes or methods depending on the Peclet number: (12 marks) X₁ with area A₁ x₂ with area A₂ = A₁ Figure 2 x = l For variables f and g, they are based on the last two digits of the student registration number, i.e., P1234fg. If f is zero, use f = 10 instead. If the student registration number is not readily available, use the second last and last digits of the passport number used to register as the UKM student for the value of f and g, respectively. Use appropriate graphs or charts to illustrate the distribution of along the x-axis. In addition, students are encouraged to present the answers for (a) and (b) using appropriate office applications such as Microsoft Word and Microsoft Equation to write the answers for (a) and Microsoft Excel or any other numerical tools or spreadsheet applications for (b). For submission of the assignment files containing the workouts, analysis and results, please use the link below to upload the files. Each student can upload up to two files in form of documents (e.g., .docx), spreadsheets (e.g., .xlsx), PDF or image files. All the calculations need to be shown in numerical forms and formula in the relevant files, such as the spreadsheet file. Consider a quasi-one-dimensional steady advection-diffusion flow with the boundary conditions as illustrated in Figure 1: u(x) x=0 p=0 in = puA = 1 x 10-4 -4 kg/s Figure 1 In Figure 1, the velocity u is given in the form of constant mass flow rate, m = puA = 1 x 10-* kg/s, with density p = 1.0 kg/m³ and A = 1 x 104 m² is the cross-sectional area at the entrance of the flow path. The cross-sectional area A at the (x₂.) range, A₂, is two times bigger that the area at the (0, x₁) range, which is A₁ = A, with a linearly gradual change from A₁ to A2₂ in the (x₁,x₂) range, i.e., A₂ = 2A₁. Other data and parameters include path length = (0.5 +0.1g) and diffusivity coefficient I = 0.05 kg/m-s. Given that the source term S(x) forms a linear relation with the x-coordinate as shown in Figure 2, where So= 10f, x₁ = 0.6€ and x₂ = 0.8l. (i) the central-differencing scheme; (ii) the upwind-differencing scheme; the hybrid method. (iii) S(x) So u(x) By using a one-dimensional grid system containing at least 10 computational nodes or cells: a) develop the algebraic formulation that can be used to compute the solution of along the x-axis from the corresponding transport equation; (8 marks) x = l dø/dx = 0 b) obtain the distribution of the value at steady state condition using one of the appropriate schemes or methods depending on the Peclet number: (12 marks) X₁ with area A₁ x₂ with area A₂ = A₁ Figure 2 x = l For variables f and g, they are based on the last two digits of the student registration number, i.e., P1234fg. If f is zero, use f = 10 instead. If the student registration number is not readily available, use the second last and last digits of the passport number used to register as the UKM student for the value of f and g, respectively. Use appropriate graphs or charts to illustrate the distribution of along the x-axis. In addition, students are encouraged to present the answers for (a) and (b) using appropriate office applications such as Microsoft Word and Microsoft Equation to write the answers for (a) and Microsoft Excel or any other numerical tools or spreadsheet applications for (b). For submission of the assignment files containing the workouts, analysis and results, please use the link below to upload the files. Each student can upload up to two files in form of documents (e.g., .docx), spreadsheets (e.g., .xlsx), PDF or image files. All the calculations need to be shown in numerical forms and formula in the relevant files, such as the spreadsheet file.

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a Formulation in algebra We must create the algebraic formulation based on the transport equation in order to calculate the solution for the given adv... View the full answer