VM126

VM126
Heat Transferred to a Flowing Fluid

Overview

Reference:	W. M. Rohsenow, H. Y. Choi, Heat, Mass and Momentum Transfer, 2nd Printing, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1963, pg. 168, ex. 7.5
Analysis Type(s):	Thermal (fluid flow) Analysis (ANTYPE = 0)
Element Type(s):	Coupled Thermal-Fluid Pipe Elements (FLUID116)
Input Listing:	vm126.dat

Test Case

Heat is transferred to air at 14.7 psi, and temperature T_i, flowing at a rate w inside a round tube of length and diameter d having a uniform tube wall temperature T_w. Determine the heat flow in terms of the inlet (q_in) and outlet (q_out) heat transport rates. Also determine the air outlet temperature T_o. The convection coefficient is given by the expression Nu = 0.08 Re^0.7 Pr^0.35 + 1.63. The tube is nearly frictionless.

Figure 178: Flowing Fluid Problem Sketch

Material Properties

Geometric Properties

k = 0.017 BTU/hr-ft-°F

c = 1.002 x 18⁸ BTU -ft/lb_f-hr^2-°F

μ = 1.17418 x 10^-10 lb_fhr/ft²

ρ = 1.4377 x 10^-10 lb_f-hr²/ft⁴

f = 0.001 for 0 < Re < 5 x 10⁴

d = 1 in = (1/12) ft

= 5 in = (5/12) ft

T_i = 100°F

T_w = 200°F

w = 1.131 x 10^{-8 lb} _f hr/ft

Analysis Assumptions and Modeling Notes

The convection node locations are arbitrarily selected as coincident. The flow rate (w) is input as a real constant, so MU is not required to be input. The nonlinear material property table is used to input the friction factor table and the flow-dependent film coefficient. Since the heat transport rate is calculated at the element inlet, an extra element is extended beyond the tube exit to obtain q_out. POST1 is used to report the required quantities.

Results Comparison

	Target	Mechanical APDL	Ratio
T_o , °F	123.0	122.55[1]	0.996
q_in , Btu/hr	113.28	113.44[2]	1.001
q_out , Btu/hr	139.33	139.02[2]	0.998

Temperature at Node 17.
q_in and q_out are obtained from the heat transport rates of elements 1 and 9, respectively.