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Need help with MATLAB finite element Consider the following differential equation in cylindrical coordinates With the boundary conditions dT dr 0 This equation governs the
Need help with MATLAB finite element
Consider the following differential equation in cylindrical coordinates With the boundary conditions dT dr 0 This equation governs the heat flow in a long circular cylinder of inner radius Riand outer radius Ro. The thermal conductivity is k and the internal heat generated (for example, due to the passage of an electric current) is known as f Heat is dissipated from the outer surface of the cylinder by convection in the surrounding air, which is at a temperature For this problem, the weak formulation gives the following expressions for the FEM model (I have simplified by 2rfor convenience) Given this information, use MATLAB to compute the temperature distribution along the radial coordinate using four linear elements. The values needed are Ro 0.05m k 40W/(m C) f = 4 106W/ -400W/(m2 . c) Too = 20C HINT Don't forget to apply the boundary condition after assembling your element matrices. Notice that Q1 = 0 except for Q5. which is given by the convection condition above The general values are (these come from the weak formulation) dr dr rb For your reference, the correct answer for this problem is 34.6825 329.4742 317.3214 297.5298 270.0000 Consider the following differential equation in cylindrical coordinates With the boundary conditions dT dr 0 This equation governs the heat flow in a long circular cylinder of inner radius Riand outer radius Ro. The thermal conductivity is k and the internal heat generated (for example, due to the passage of an electric current) is known as f Heat is dissipated from the outer surface of the cylinder by convection in the surrounding air, which is at a temperature For this problem, the weak formulation gives the following expressions for the FEM model (I have simplified by 2rfor convenience) Given this information, use MATLAB to compute the temperature distribution along the radial coordinate using four linear elements. The values needed are Ro 0.05m k 40W/(m C) f = 4 106W/ -400W/(m2 . c) Too = 20C HINT Don't forget to apply the boundary condition after assembling your element matrices. Notice that Q1 = 0 except for Q5. which is given by the convection condition above The general values are (these come from the weak formulation) dr dr rb For your reference, the correct answer for this problem is 34.6825 329.4742 317.3214 297.5298 270.0000Step by Step Solution
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