### Heat Transfer in HRSG

Heat transfer is the transfer of energy that occurs due to temperature differences between objects or materials. In thermodynamics, the moving energy is heat. Analysis on heat transfer rate should be considered. Generally, heat transfer in HRSG that occurs there are three kinds:
1. Conduction heat transfer
2. Convection heat transfer
3. Radiation heat transfer

In this case, the heat transfer which is used is conduction heat transfer, convection and combination of conduction and convection. In the HRSG boiler is assumed does not use additional fuel and heat sources only from exhaust gases of gas turbine. So it does not analyze the radiation heat transfer in this HRSG boiler.

1. Conduction Heat Transfer
Conduction heat transfer is the transfer of heat from one part of solid objects to other parts of same solid object without any movement of solid molecules itself. Generally, equation used in the conduction heat transfer is:

1. Convection Heat Transfer
Convection heat transfer is the heat transfer which is performed by molecules of fluid (liquid or gas). Generally, the equation of convection heat transfer is:

where Tw is temperature of solid object while T∞ is temperature of fluid.

Convection heat transfer consists of two types of heat transfer. I.e., free convection heat transfer in which the air velocity is assumed does not exist. As for air that has flow is type of forced convection where the effect occurred at Nuselt number for every condition is different.

2.a. Free Convection Heat Transfer
Free convection heat transfer in HRSG as follow:

-          On horizontal cylinder:

Multiplication between the Grashof number and Prandtl numbers is called Rayleigh number:

Ra = Gr . Pr

Where the Rayleigh number can be calculated as follow:

where:
Tw = temperature of surface
T∞ = ambient air temperature
υ = kinetic viscosity
g = gravity (9.8 m/s2)
δ = D = characteristic dimension
β = coefficient of volume expansion

-          On the ball

The equation above can be changed by entering Prandalt number, thus can be obtained following formula:

Then the value of free convection can be obtained as follow:

-          Through inner cylinder

-          Through bank of tubes

where:
C = flow coefficient across bank of tubes
Re = Reynolds Number
Pr = Prandlt Number
do = outside diameter of cylinder / tubes
di = inside diameter of cylinder

1. Combination of Conduction and Convection Heat Transfer
Heat transfer that occurs in HRSG is a combination of conduction and convection, such as the following figure where on one side there is hot fluid A and on the other side fluid B has cooler temperature.
 Figure 1: Heat Transfer on Flat Plane (Source: Heat Transfer Book - Holman JP)

Heat transfer can be expressed as:

Heat transfer can be described in the network above, so that the overall heat transfer is calculated by dividing overall temperature difference by the amount of thermal resistance:

Overall heat flow as a result of the combined conduction and convection can be expressed by thorough heat transfer coefficient (U), formulated in relationship:

where A is the area of ​​heat flow field, in accordance with the above equation then the overall heat transfer coefficient is: