Design a plate and frame heat exchanger for the following problem:
Hot water at 0.0063 m^3/s, 82.2°C, enters a plate and frame heat exchanger and is cooled to 57.2°C. Cold water enters this same exchanger at 0.00756 m^3/s, 37.8°C. The plates are made of stainless steel (316SS) with a heat transfer area of 0.316 m^2 per plate. The plate spacing is 5.08 mm, the plate width is 381 mm, and the plate thickness is 1.016 mm.
Hint: You should use iteration method to solve this problem. Assume a value for number of plates and solve the problem to find q_c, q_h and q_by LMTD. If q_c = q_h = q_by LMTD, your assumption is good. Otherwise repeat the procedure with a new guess for number of plates.

See explaination and attachment.

Explanation:

Iteration method is a repetitive method applied until the desired result is achieved.

Let the given equation be f(x) = 0 and the value of x to be determined. By using the Iteration method you can find the roots of the equation. To find the root of the equation first we have to write equation like below

x = pi(x)

Let x=x0 be an initial approximation of the required root α then the first approximation x1 is given by x1 = pi(x0).

Similarly for second, thrid and so on. approximation

x2 = pi(x1)

x3 = pi(x2)

x4 = pi(x3)

xn = pi(xn-1).

please go to attachment for the step by step solution.

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(b)

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