Page 110 - Modelling in Transport Phenomena A Conceptual Approach

90 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

Churchill-Bernstein correlation

Churchill and Bernstein (1977) proposed a single comprehensive equation that
covers the entire range of Reo for which data are available, as well as for a wide
range of Pr, which is in the form

(4.48)

where all properties are evaluated at the film temperature. Equation (4.4-8) is
recommended when
Reo Pr > 0.2
4.4.2.1 Calculation of the heat transfer rate

Once the average heat transfer coefficient is estimated by using correlations, the
rate of heat transferred is calculated as
(4.49)

Example 4.10 Assume that a person can be approximated as a cylinder of 0.3 m
diameter and 1.8m height with a surface temperature of 30°C. Calculate the rate
of heat loss fmm the body while this person is subjected to a 4 m/ s wind with a
temperature of - 10 "C.
Solution

Physical properties
The film temperature is (30 - 10)/2 = 10 "C

p = 16.7 x kg/ m. s
u = 12.44 x m2/s
For air at -10°C (263K) :
= 23.28
Pr = 0.72
u = 14.18 x m2/ s
For air at 10 "C (280 K) : k = 24.86 x W/ m. K
Pr = 0.714

p = 18.64 x kg/ m. s
For air at 30°C (303K) :

Assumption
1. Steady-state conditions prevail.