models/johnpye/radialheatloss.a4c

(*	ASCEND model library
	Copyright (c) 2006 Carnegie Mellon University

	This program is free software; you can redistribute it
	and/or modify it under the terms of the GNU General Public
	License as published by the Free Software Foundation; either
	version 2 of the License, or (at your option) any later
	version.

	This program is distributed in the hope that it will be
	useful, but WITHOUT ANY WARRANTY; without even the implied
	warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
	PURPOSE.  See the GNU General Public License for more
	details.

	You should have received a copy of the GNU General Public
	License along with this program; if not, write to the Free
	Software Foundation, Inc., 59 Temple Place, Suite 330,
	Boston, MA 02111-1307  USA
*)(**
	This is a simple model for computing the
	steady-state temperature and heat loss profile 
	of a multi-layered pipe-plus-insulation
	
	by John Pye
*)

REQUIRE "atoms.a4l";
REQUIRE "johnpye/thermo_types.a4c";

MODEL radial_loss;
	D_1 IS_A distance;
	D_2 IS_A distance;
	q IS_A energy_rate;
	L IS_A distance;
	T_1, T_2 IS_A temperature;
METHODS
METHOD specify;
	FIX D_1, D_2;
END specify;
END radial_loss;

(*
	Wall conduction
*)
MODEL wall_conduction REFINES radial_loss;
	k IS_A thermal_conductivity;
	
	q = 2 * 1{PI} * L * k *(T_1 - T_2) / ln(D_2/D_1);

END wall_conduction;

(*
	Convection boundary
*)
MODEL convection_boundary REFINES radial_loss;
	h IS_A heat_transfer_coefficient;
	D_1, D_2 ARE_THE_SAME;
	
	q = h * 1{PI} * D_1 * (T_1 - T_2);

END convection_boundary;

MODEL pipe_test REFINES radial_loss;

	n IS_A integer_constant;
	n:==5;

	loss[1..5] IS_A radial_loss;

	loss[1] IS_REFINED_TO convection_boundary;
	loss[2] IS_REFINED_TO wall_conduction;
	loss[3] IS_REFINED_TO wall_conduction;
	loss[4] IS_REFINED_TO wall_conduction;
	loss[5] IS_REFINED_TO convection_boundary;

	L, loss[1..5].L ARE_THE_SAME;
	
	FOR i IN [2..n] CREATE
		(* layers are touching *)
		loss[i].D_1, loss[i-1].D_2 ARE_THE_SAME;

		(* steady state: heat rate is uniform *)
		loss[i].q,loss[i-1].q ARE_THE_SAME;

		loss[i].T_1, loss[i-1].T_2 ARE_THE_SAME;
	END FOR;

	loss[i].D_1, D_1 ARE_THE_SAME;
	loss[n].D_2, D_2 ARE_THE_SAME;

	loss[i].T_1, T_1 ARE_THE_SAME;
	loss[i].T_2, T_2 ARE_THE_SAME;

	loss[i].q, q ARE_THE_SAME;

METHODS
METHOD default_self;
	RUN reset; RUN values;
END default_self;

METHOD specify;
	FIX loss[1].h;
	FIX loss[2..4].k;
	FIX loss[5].h;
	
	FIX loss[2].D_1, loss[2].D_2;
	FIX loss[4].D_1, loss[4].D_2;
END specify;

METHOD values;
	L = 1 {m};

	loss[1].h := 1000 {W/m^2/K};
	loss[2].k := 40 {W/m/K}; (* 'alloy steel', Ashby & Jones, Eng Matls 2, p.11 *)
	loss[3].k := 0.05 {W/m/K}; (* Masud's figure for lagging *)
	loss[4].k := 240 {W/m/K}; (* aluminium, Ashby & Jones, Eng Matls 2, p.11 *)
	loss[5].h := 50 {W/m^2/K};
	
	loss[1].D_1 := 0.05 {m}; (* pipe interior *)
	loss[1].D_2 := 0.07 {m}; (* pipe exterior *)
	loss[4].D_1 := 0.17 {m}; (* cover interior *)
	loss[4].D_2 := 0.19 {m}; (* cover exterior *)
END values;
END pipe_test;
1	johnpye	611	(* ASCEND model library
2			Copyright (c) 2006 Carnegie Mellon University
3
4			This program is free software; you can redistribute it
5			and/or modify it under the terms of the GNU General Public
6			License as published by the Free Software Foundation; either
7			version 2 of the License, or (at your option) any later
8			version.
9
10			This program is distributed in the hope that it will be
11			useful, but WITHOUT ANY WARRANTY; without even the implied
12			warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
13			PURPOSE. See the GNU General Public License for more
14			details.
15
16			You should have received a copy of the GNU General Public
17			License along with this program; if not, write to the Free
18			Software Foundation, Inc., 59 Temple Place, Suite 330,
19			Boston, MA 02111-1307 USA
20			)(*
21			This is a simple model for computing the
22			steady-state temperature and heat loss profile
23			of a multi-layered pipe-plus-insulation
24
25			by John Pye
26			*)
27
28			REQUIRE "atoms.a4l";
29			REQUIRE "johnpye/thermo_types.a4c";
30
31			MODEL radial_loss;
32			D_1 IS_A distance;
33			D_2 IS_A distance;
34			q IS_A energy_rate;
35			L IS_A distance;
36			T_1, T_2 IS_A temperature;
37			METHODS
38			METHOD specify;
39			FIX D_1, D_2;
40			END specify;
41			END radial_loss;
42
43			(*
44			Wall conduction
45			*)
46			MODEL wall_conduction REFINES radial_loss;
47			k IS_A thermal_conductivity;
48
49			q = 2 * 1{PI} * L * k *(T_1 - T_2) / ln(D_2/D_1);
50
51			END wall_conduction;
52
53			(*
54			Convection boundary
55			*)
56			MODEL convection_boundary REFINES radial_loss;
57			h IS_A heat_transfer_coefficient;
58			D_1, D_2 ARE_THE_SAME;
59
60			q = h * 1{PI} * D_1 * (T_1 - T_2);
61
62			END convection_boundary;
63	johnpye	612
64			MODEL pipe_test REFINES radial_loss;
65
66			n IS_A integer_constant;
67			n:==5;
68
69			loss[1..5] IS_A radial_loss;
70
71			loss[1] IS_REFINED_TO convection_boundary;
72			loss[2] IS_REFINED_TO wall_conduction;
73			loss[3] IS_REFINED_TO wall_conduction;
74			loss[4] IS_REFINED_TO wall_conduction;
75			loss[5] IS_REFINED_TO convection_boundary;
76
77			L, loss[1..5].L ARE_THE_SAME;
78
79	johnpye	615	FOR i IN [2..n] CREATE
80	johnpye	611	(* layers are touching *)
81			loss[i].D_1, loss[i-1].D_2 ARE_THE_SAME;
82	johnpye	612
83			(* steady state: heat rate is uniform *)
84	johnpye	615	loss[i].q,loss[i-1].q ARE_THE_SAME;
85
86			loss[i].T_1, loss[i-1].T_2 ARE_THE_SAME;
87	johnpye	612	END FOR;
88
89	johnpye	615	loss[i].D_1, D_1 ARE_THE_SAME;
90			loss[n].D_2, D_2 ARE_THE_SAME;
91
92			loss[i].T_1, T_1 ARE_THE_SAME;
93			loss[i].T_2, T_2 ARE_THE_SAME;
94
95			loss[i].q, q ARE_THE_SAME;
96
97	johnpye	612	METHODS
98			METHOD default_self;
99			RUN reset; RUN values;
100			END default_self;
101	johnpye	611
102			METHOD specify;
103			FIX loss[1].h;
104			FIX loss[2..4].k;
105			FIX loss[5].h;
106
107	johnpye	615	FIX loss[2].D_1, loss[2].D_2;
108			FIX loss[4].D_1, loss[4].D_2;
109	johnpye	611	END specify;
110
111	johnpye	615	METHOD values;
112			L = 1 {m};
113
114	johnpye	611	loss[1].h := 1000 {W/m^2/K};
115			loss[2].k := 40 {W/m/K}; (* 'alloy steel', Ashby & Jones, Eng Matls 2, p.11 *)
116			loss[3].k := 0.05 {W/m/K}; (* Masud's figure for lagging *)
117			loss[4].k := 240 {W/m/K}; (* aluminium, Ashby & Jones, Eng Matls 2, p.11 *)
118			loss[5].h := 50 {W/m^2/K};
119
120			loss[1].D_1 := 0.05 {m}; (* pipe interior *)
121			loss[1].D_2 := 0.07 {m}; (* pipe exterior *)
122			loss[4].D_1 := 0.17 {m}; (* cover interior *)
123			loss[4].D_2 := 0.19 {m}; (* cover exterior *)
124			END values;
125	johnpye	612	END pipe_test;