Reconsider Problem 3–78E. Using EES (or other) software, investigate the effects of the thermal conductivity of the pipe material and the outer diameter of the pipe on the length of the tube required. Let the thermal conductivity vary from 10 Btu/h · ft · °F to 400 Btu/h · ft · °F and the outer

Question

Reconsider Problem 3–78E. Using EES (or other) software, investigate the effects of the thermal conductivity of the pipe material and the outer diameter of the pipe on the length of the tube required. Let the thermal conductivity vary from [latex]10 Btu / h \cdot ft \cdot{ }^{\circ} F[/latex] to [latex]400 Btu / h \cdot ft \cdot{ }^{\circ} F[/latex] and the outer diameter from 0.5 in. to 1.0 in. Plot the length of the tube as functions of pipe conductivity and the outer pipe diameter, and discuss the results.

Accepted Answer

"GIVEN"

T_infinity_1=100 "[F]"

T_infinity_2=70 "[F]"

k_pipe=223 "[Btu/h-ft-F], parameter to be varied"

D_i=0.4 "[in]"

"D_o=0.6 [in], parameter to be varied"

r_1=D_i/2

r_2=D_o/2

h_fg=1037 "[Btu/lbm]"

h_o=1500 "[Btu/h-ft^2-F]"

h_i=35 "[Btu/h-ft^2-F]"

m_dot=120 "[lbm/h]"

"ANALYSIS"

L=1 "[ft], for 1 ft length of the tube"

A_i=pi*(D_i*Convert(in, ft))*L

A_o=pi*(D_o*Convert(in, ft))*L

R_conv_i=1/(h_i*A_i)

R_pipe=ln(r_2/r_1)/(2*pi*k_pipe*L)

R_conv_o=1/(h_o*A_o)

R_total=R_conv_i+R_pipe+R_conv_o

Q_dot=(T_infinity_1-T_infinity_2)/R_total

Q_dot_total=m_dot*h_fg

L_tube=Q_dot_total/Q_dot

[latex] k _{ ext {pipe }} ext { [Btu/h \cdot ft \cdot F] }[/latex]	[latex] L _{ ext {tube }}[ f t ][/latex]
10	1176
30.53	1158
51.05	1155
71.58	1153
92.11	1152
112.6	1152
133.2	1151
153.7	1151
174.2	1151
194.7	1151
215.3	1151
235.8	1150
256.3	1150
276.8	1150
297.4	1150
317.9	1150
338.4	1150
358.9	1150
379.5	1150
400	1150

[latex] D _{ o }[ i n ] [/latex]	[latex] L _{ ext {tube }} ext { [ft] }[/latex]
0.5	1154
0.525	1153
0.55	1152
0.575	1151
0.6	1151
0.625	1150
0.65	1149
0.675	1149
0.7	1148
0.725	1148
0.75	1148
0.775	1147
0.8	1147
0.825	1147
0.85	1146
0.875	1146
0.9	1146
0.925	1146
0.95	1145
0.975	1145
1	1145

Question 3.80: Reconsider Problem 3–78E. Using EES (or other) software, inv...

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