**2. Heat loss considerations**

*Heat Transfer - Design, Experimentation and Applications*

Hardik and Prabhu [3] performed experiments to investigate the heat transfer and pressure drop of a diabatic two-phase water flow boiling in horizontal thin walled stainless steel tubes with different inner diameters under uniform wall heat flux conditions. To investigate the impact of vapor quality on the local boiling heat transfer coefficient, they measured vapor quality at the outlet of test section using a known range of uniform wall heat fluxes directly supplied by electrical heating tapes wrapped around the test sections. The effect of inlet vapor quality was not investigated in their study since a saturated liquid flow was provided at the inlet of test sections. In their study, the heat losses from the heating tapes were estimated using theoretical calculations of convective and radiative heat losses from the surface of test sections to the surroundings, and no single-phase experiments were conducted to empirically estimate heat losses at the same mass flux range of flow

*Typical variations in heat transfer coefficient with vapor quality for forced-convection flow boiling in a* 

A similar approach to measurement of outlet vapor quality was adopted by Yan *et al*. in two different studies [4, 5] to investigate the influence of crucial parameters, consisting of heat flux, mass flux, and vapor quality on the heat transfer performance of water flow boiling in a uniformly heated vertical nickel alloy tube as well as in a vertical 304 stainless steel (SS304) tube with twisted tape inserted

Although many experimental studies have been conducted to date to investigate the impact of local vapor quality on boiling heat transfer performance, majority of these studies have taken the similar approach to measure local vapor quality

**390**

boiling tests.

**Figure 1.**

*tube [1].*

under high heat flux conditions.

Measurements of local vapor quality of a saturated boiling flow can strongly be affected by accuracy in estimating the heat losses and calibrating the latent heat supplies. This is due to the existence of latent heat during a boiling process with a constant saturation temperature of fluid while enthalpy increases with the increase of local vapor quality as a result of heat acquisition [1, 2]. This is therefore evident that inaccurate estimation of heat losses and imprecise calibration of latent heat supplies would pose unreliability in collected heat transfer data and large errors in results as well.

Although different theoretical and experimental approaches have been engaged to date to estimate heat loss during flow boiling, majority of these methods are based on the estimation of heat loss from single-phase flow [6, 9–15]. Indeed, single-phase experiments were conducted to estimate heat loss percentages for a range of mass fluxes and heat fluxes. Then, the same heat loss percentages derived from the single-phase flow were directly used for two-phase flow at the same mass fluxes [6, 9–11]. Alternatively, the heat losses extracted from single-phase flow for a range of mass and heat fluxes were developed for flow boiling over another range of mass and heat fluxes using either interpolation or extrapolation [12, 13, 15].

In this commonly applied methodology, the amounts of heat experimentally supplied for the test section (*Qsuppl* ) to increase the temperature of single-phase flow from a known value of Tsp, in at the inlet to another known value of Tsp, out at the outlet are monitored and recorded for a range of flow rates. On the other hand, the actual amounts of heat transferred to the fluid (*Qtransf* ) can be calculated by the following energy balance for a range of flow rates:

$$Q\_{roauf} = \dot{m} \, \text{Cp} \left( T\_{sp,out} - T\_{sp,in} \right) \tag{1}$$

The difference between *Qsuppl* and *Qtransf* reveals the heat losses (*QQ Q loss suppl transf* = − ) . A correlation is then developed by plotting the variations of heat transferred to the fluid (*Qtransf* ) versus heat supplied (*Qsuppl*) , which can be used for calibrating the heat supplies as an imperative step to further measure vapor qualities within the flow boiling tests.
