Heat Transfer Coefficients Parker Williams Tristan Grieves Lucas Vacca

Outline Apparatus/Procedure Calculations Results Discussion of Results Conclusions/Questions

Apparatus Figure 1: The heat exchanger system used for conducting the experiment.

Calculations Logarithmic-mean temperature-difference (1.) ∆𝑇𝑙𝑛= (𝑇 𝑤𝑖 − 𝑇 𝑓𝑖 )−( 𝑇 𝑤2 − 𝑇 𝑓2 ) ln⁡ 𝑇 𝑤𝑖 − 𝑇 𝑓𝑖 𝑇 𝑤2 − 𝑇 𝑓2 Twi = water initial temperature Tw2 = water final temperature Tfi = steam initial temperature Tf2 = steam final temperature Heat transfer coefficient (2.) h = ( 𝑇 𝑓2 − 𝑇 𝑓𝑖 ) 𝑙𝑛( 𝑇 𝑤 − 𝑇 𝑓 ) ∗ 2𝑅 𝐿 ∗ 𝜌<𝑣>𝐶𝑝 4 = 𝑚∗𝐶𝑝∗∆𝑇 𝐴∗𝑇𝑙𝑛 L = length of exchanger tube R = Radius of exchanger tube 𝜌 = Density of fluid m = mass flow of fluid A = cross sectional area

Calculations Reynolds number (Re) (3.) Turbulent Nusselt Number (5.) 𝑅𝑒= 𝐷𝑉𝜌 𝜇 D = pipe diameter V = fluid velocity 𝜌 = fluid density 𝜇= fluid viscosity Turbulent Nusselt Number (5.) Nusselt number (Nu) (4.) 𝑁𝑢= ℎ𝐷 𝑘 h = heat transfer coefficient k = thermal conductivity of fluid Prandtl number (Pr) (6.) Pr = 𝐶𝑝 ∗ 𝜇 𝑘 Cp = Specific heat capacity

Results Figure 2: The relationship between heat transfer coefficients and fluid velocity and pipe diameter.

Figure 3: The relationship between heat transfer coefficient, log mean temperature, and pipe diameter.

Figure 4: Relationship between Nusselt number, Reynolds number, and diameter.

Table 1: Relation of Nusselt numbers using our chosen equation and an equation representing turbulent flow (Mills). Table 2: Representation of similar Reynolds numbers from different tubes and the corresponding Nusselt numbers.

Conclusions The heat transfer coefficient increases as radius decreases. The heat transfer increases as the velocity of the water increases and becomes more turbulent. As the log mean temperature increases, the heat transfer coefficient increases. The convective heat transfer increases with increasing radius. The Nusselt number increases with increasing turbulent flow.

References Bird, Robert Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena. 2nd ed. New York: Wiley, 2002. Crosby, E. J. "Experiment 7.a Heat-Transfer Coefficients in Circular Tubes." Experiments in Transport Phenomena. New York: John Wiley & Sons, 1961. 88-107. Mills, Anthony. F. Heat Transfer. CRC Press, 1992.