Question

Determine the overall heat transfer coefficient (U) in a heat exchanger that uses steam to heat water to the point of vaporization (in vacuum.) The system is non-insulated, so the heat lost to the surroundings must be taken into consideration. While I know that the heat Q = mCdT and the heat transfer rate q = UAdT(Log-mean), I am struggling to equate the two due to the heat lost to the surroundings. How do I go about determining the overall heat transfer coefficient in a system like this?

Answer 1

A Brief explanation about overall heat transfer coefficiemt

The overall heat transfer coefficient is employed in calculating the rate of heat transfer from one fluid at an average bulk temperature T₁ through a solid surface to a second fluid at an average bulk temperature T₂ (where T₁ > T₂). The defining equation is generally only applicable to an incremental element of heat transfer surface dA for which the heat transfer rate is d , and the equation is strictly valid only at steady state conditions and negligible lateral heat transfer in the solid surface, conditions generally true enough in most practical applications. The defining equation is

where U is referenced to a specific surface (see below).

In the particular situation of heat transfer across a plane wall of uniform thickness, U is related to the individual film heat transfer coefficients, α₁ and α₂, of the two fluids by the equation

where δ_w is the thickness of the wall and λ_w is the thermal conductivity of the wall.

If there are fouling deposits on the wall, they have a resistance to heat transfer, R₁ and R₂, in units of m² K/W, and these resistances must be added in (see Fouling and Fouling Factors)

For the special but very important case of heat transfer through the wall of a plain round tube, the different heat transfer areas on the inside and outside surfaces of the tube need to be considered. Let dA_i be the inside incremental area and dA_o be the outside. Then (including fouling resistances R_fi and R_fo inside and out):

(4)

where U_i is termed the "overall heat transfer coefficient referenced to (or based on) the inside tube heat transfer area", and r_i and r_o the inside and outside radii of the tube.

Alternatively, the overall coefficient may be based on the outside heat transfer area, giving

where U_o is termed the "overall heat transfer coefficient based on the outside tube heat transfer area." Note that

(6)

These ideas may be extended to more complicated surfaces such as finned or composite tubes, but it is then necessary to add further resistance terms (and the area ratio corrections) for the fins or imperfect metal-to-metal contact.

I think it is quite easy. You Just need to make an energy balance.

mCpdT= UAdT (log-mean) - Energ loss through the non insulating portion.

Energy loss may be actually, depends on the thermal conductivity of the surface and convective heat transfer coefficient of ambient fluid.

We can discuss furthur, if you ask specifically about a problem.