Hello everyone,

I would like to ask you a conceptual question about an indirect heater. It is not mi intention you to solve mi problem, instead of that I want you to clear me same doubt about the approach or method I used.

__Problem to solve:__

I have a present indirect heater (vapor bath) with the next variables:

· Mass Flow: 24270 kg/hr (Gas – Oil – Water)

· Q (heat flow) required to be exchange: 1426 KW

· Area: 59.88 m2

· Dt ml: 83.72 °C

· Overall heat transfer coefficient 298 W/m2°C

· Present Burner: 2.300.000 Kcal/h (2673KW)

Now, my client is asking me to verify which the maximum capacity of this heater is. How much mass flow rate can be processed?

What should I do?

I take two different approaches. *I ask you if I am making a big mistake, please let me now!!!!*

**Approach A:**

I take the Equation:

Q: U x A x DT

Q heat flow: I Asume a 65% maximum efficiency based on the capacity of the present burner so, 2.300.000 Kcal/hr * 0.65 : 1.495.000 Kcal/hr heat flow available to transfer the fluid. Converting units: 1737 KW. Then:

Q heat flow : 1737 KW

Area: 59.9 m2

Dtml: 83.64 °C

New Required U: 346 W/m2ºC

Then a raise the flowrate to raise velocity, because of that Reynolds Number increase, because of that Internal heat transfer coefficient *hi* increase and finally I GET my 346 W/m2 °C.

It is right? My final result is: 41510 Kg/h

**Aproches B:**

I take this two Equation:

Q: (H_{outlet}-H _{Inlet})*Q_{mass}

Q: U x A x DT

Then I make the next iterative calculation:

Raise Mass Flowrate by a 10% factor and the Calculate new Q_{10% Mass flowrate}

After that, take the equation:

Q: U x A x DT

Q: Q_{10% }calculated by Q: (H_{outlet}-H_{ Inlet})*Q_{10% Mass flowrate}

Dtml: 83.64 °C

U: Calculates from new Qmass flowrate

A: Check that the required area versus the present area of 59.9m2

If I have enough area I still raising mass flowrate.

If I don’t have enough area, a reduce mass flowrate.

At the end of this iterative calculation, I will find a new mass flowrate of: 26330 Kg/hr

Which of these approaches is the best? Some of them will give me an incorrect answer? I ask this because these approaches give me different results (very different) . If B is the correct one, what I am missing in approach A?

Thanks you!

Ariel