# Write a Matlab code..) equation for the steady-state temperature distribution across the metal ro…

Consider a 25 m-long metal rod after a while agricultural spheres (300K and 350K, respectively) at twain ends, as shown in the likeness adown.A finite-difference discretization (after a while 25 equally-spaced intervals) is overlain on the metal rod.The earliest and the developed nodes are the article nodes.The metal rod is presumably well-insulated throughout, save at its entrance and vent boundaries, and as-well at the 6th and 16th nodes.A ebullition fountain (q) of 600 Watt/m3 is applied to the rod at the 6th.200 Watt/ m3 of ebullition occurs atthe 16th part. The fervent diffusivity (a) of the metal rod is 2 m2 /sec for the earliest 10 parts (for i=2 to i=11th discretized parts) and 4 m2 /sec for the quiet.Thermal (material) conductivity of the metal rod (k) is 3 m/sec throughout. Write a Matlab rule to: 1. Solve the forthcoming (1D convective-plentiful ebullition convey) equation for the steady-state sphere classification despite the metal rod using the accessible finite-difference adit to the plentiful message (the earliest message on the RHS) and backward-FD adit to the convective message (the succor message on the RHS). ? ? ? ? ? ? ? ? ? ? ? q x T k x T t T 2 2 in which T is the sphere (°C), t is period (sec), x is the spatial changeable (m),ais the fervent diffusivity (m2 /sec), k is the embodied conductivity (m/sec), and q is the ebullition fountain (W/ m3 ), andß= 10 Joule/(kg·K) .
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ME 2173 Test 2 Question 1 (50 apex): Consider a 25 m-long metal rod after a while agricultural spheres (300K and 350K, respectively) at twain ends, as shown in the likeness adown. A finite-difference discretization (after a while 25 equally-spaced intervals) is overlain on the metal rod. The earliest and the developed nodes are the article nodes. The metal rod is presumably well-insulated throughout, save at its entrance and vent boundaries, and as-well at the 6th and 16th nodes. A ebullition fountain (q) of 600 Watt/m3 is applied to the rod at the 6th. 200 Watt/m3 of ebullition occurs at the 16th part. The fervent diffusivity (a) of the metal rod is 2 m2/sec for the earliest 10 parts (for i=2 to i=11th discretized parts) and 4 m2/sec for the quiet. Fervent (material) conductivity of the metal rod (k) is 3 m/sec throughout. Write a Matlab rule to: 1. Solve the forthcoming (1D convective-plentiful ebullition convey) equation for the steady-state sphere classification despite the metal rod using the accessible finite-difference adit to the plentiful message (the earliest message on the RHS) and backward-FD adit to the convective message (the succor message on the RHS). ? ? ?? ? ?? ? ? ? ? q xk T xT t T 2 2 in which T is the sphere (°C), t is period (sec), x is the spatial changeable (m), a is the fervent diffusivity (m2/sec), k is the embodied conductivity (m/sec), and q is the ebullition fountain (W/m3), and ß= 10 Joule/(kg· K) . Note that for a steady-state elucidation, ?T ?t ?0 . Hint: You conciliate possess to weigh coefficients of Ti, Ti-1, and Ti+1. Note that, twain the convective and plentiful messages conciliate give to the coefficients. 2. Plot sphere variations despite the rod as a employment of space from the earliest article node. Article node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 T=300K T=350K Article node q=600Watt/m L=25mq=200Watt/m Question 2 (50 apex): (a) Write a MATLAB rule that conciliate fit a third-order (cubic) polynomial to the forthcoming postulates set X = [0.0 0.30 0.53 0.80 1.10...