PS8_sol_S08 - Problem Set 8(2.006 Spring 08 Problem 1...

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Problem Set 8 (2.006, Spring 08) Problem 1 Make a 100×101 array for hot stream and 101×100 array for cold stream to designate inlet and outlet temperatures of each cell. For convenience, the entire device’s inlet boundary conditions for hot and cold streams are placed at j=1 column and i=1 row, respectively. If we assume that flow properties are identical to every cell, we can see that , , min, , max, , min, min, min, * * max, max, max, min, min, 0.01 / , 0.011 / 100 100 /100 0.9091 /100 /10000 /100 h tot c tot cell h cell cell c cell cell tot tot cell tot cell tot tot cell tot cell cell tot C C C C W K C C W K C C C C C C C C UA UA NTU C C = = = = = = = = = = = = = = 1 , 1 100 tot tot NTU NTU = Apply the first law to the element shown by assuming that the bulk temperature of each stream is approximately an average of both inlet and outlet temperatures. Then ( ) ( ) , , ( , ) ( , 1) ( , ) ( 1, ) ( , ) ( , 1) ( 1, ) ( , ) 2 2 h h c c cell h cell h h c cell c c T i j T i j T i j T i j UA C T i j T i j C T i j T i j + + + + = + = + ( ) ( ) * ( , ) ( , 1) ( , ) ( 1, ) 100 1 100 ( , ) ( , 1) ( 1, ) ( , ) 2 2 h h c c h h c c tot tot tot T i j T i j T i j T i j T i j T i j T i j T i j NTU C NTU + + + + = + = + * * 1 100 1 1 100 1 ( , 1) ( , ) 2 2 2 2 1 1 100 1 1 100 ( 1, ) ( , ) 2 2 2 2 h h tot tot c c tot tot tot tot T i j T i j NTU NTU T i j T i j C NTU C NTU + + + = + + * * 1 1 100 1 1 100 1 ( , 1) ( , ) 2 2 2 2 1 1 100 1 1 100 ( 1, ) ( , ) 2 2 2 2 h h tot tot c c tot tot tot tot T i j T i j NTU NTU T i j T i j C NTU C NTU + + + = + + T h (1,1) =100 o C T h (2,1) =100 o C T h (100,1) =100 o C T c (1,1) =1 o C T c (1,2) =1 o C T c (1,100) =1 o C T h (1,101) T h (2,101) T h (100,101) T c (101,1) T c (101,2) T c (101,100) T c (i,j) T c (i+1,j) T h (i,j) T h (i,j+1)
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