Description

EX_HEATTRANSFER11 Design optimization for cooling with target temperature.

[ FEA, OUT ] = EX_HEATTRANSFER11( VARARGIN ) Heat transfer example for cooling of a heated block using cooling pipes. An optimization problem is defined and set up to reach (but not exceed) a target temperature, Tstar, with n=1-9 number of cooling pipes with variable diameter, D = 5-18 mm.

+--------------------------------+
|        Heated Top Block        |
+--------------------------------+   T(x,n,D) <= Tstar
|  Cooling Plate with n x Pipes  |
|    (D)  ( )  ( )  ( )  ( )     |
+--------------------------------+

Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
npipes      array {[1, 9]}         Minimum and maximum number of pipes
diam        array {[0.005, 0.018]} Minimum and maximum pipe diameter
Tstar       scalar {358.15}        Target temperature [K]
iplot       scalar 0/{1}           Plot solution and error (=1)
                                                                                  .
Output      Value/(Size)           Description
-----------------------------------------------------------------------------------
fea         struct                 Problem definition struct
out         struct                 Output struct

See also: fminbnd

Code listing

 cOptDef = { 'npipes',   [1, 9];
             'diam',     [0.005, 0.019];
             'Tstar',    358.15;
             'iplot',    1;
             'tol',      0.1;
             'fid',      1 };
 [got,opt] = parseopt( cOptDef, varargin{:} );

 feaCache = containers.Map( 'KeyType', 'char', 'ValueType', 'any' );  % Handle (in-place) cache.


% Outer loop: evaluate all integer n (starting D from previous result).
 if( ~isempty(opt.fid) )
   fprintf(opt.fid, '%-4s %-10s %-12s %-12s %-10s\n', 'n', 'D (m)', 'Tmax (K)', 'Cost', 'FEA calls');
   fprintf(opt.fid, '%s\n', repmat('-', 1, 51));
 end

 penaltyWeight = 1e4;
 D0 = (opt.diam(1) + opt.diam(2)) / 2;
 nValues = opt.npipes(1):opt.npipes(2);
 res = struct('n', {}, 'D', {}, 'cost', {}, 'ff', {});

 for it = 1:length(nValues)
   n = nValues(it);
   [Dopt, cost, ff] = innerOpt(n, opt.Tstar, opt.diam(1), opt.diam(2), penaltyWeight, D0, feaCache);
   res(it) = struct('n', n, 'D', Dopt, 'cost', cost, 'ff', ff);
   D0 = Dopt;   % Warm start next n.


   if( ~isempty(opt.fid) )
     fprintf(opt.fid, '%-4d %-10.4f %-12.2f %-12.4f %-10d\n', ...
             n, Dopt, opt.Tstar+ff.Ineq, cost, feaCache.Count);
   end
 end


% Select best feasible result.
 costs    = [res.cost];
 [~, idx] = min(costs);
 best     = res(idx);
 Tmax     = opt.Tstar + best.ff.Ineq;

 if( ~isempty(opt.fid) )
   fprintf(opt.fid, '\n--- Optimal solution ---\n');
   fprintf(opt.fid, 'Number of pipes : %d\n', best.n);
   fprintf(opt.fid, 'Pipe diameter   : %.4f m\n', best.D);
   fprintf(opt.fid, 'Max temperature : %.2f K (%.2f C)\n', Tmax, Tmax - 273.15);
   fprintf(opt.fid, 'Objective value : %.4f K\n',  best.ff.Fval);
   yn = 'No'; if( ff.Ineq <= 0 ), yn = 'Yes'; end
   fprintf(opt.fid, 'Feasible        : %s\n', yn);
   fprintf(opt.fid, 'Total FEA calls : %d\n', feaCache.Count);
 end

 [~,fea] = l_run_fea_optimization_problem([best.n; best.D], opt.Tstar);


% Error checking.
 out.err = abs(opt.Tstar - Tmax);
 out.pass = out.err < opt.tol;


% Postprocessing.
 if( opt.iplot )
   postplot( fea, 'surfexpr', 'T' )

% Mirror solution.
   fea_mirror = fea;
   fea_mirror.geom = l_block_cooling_geometry( best.n, best.D, 3 );  % 3D geometry for plotting.
   fea_mirror.grid.p(1,:) = 0.2 - fea_mirror.grid.p(1,:);  % Offset and mirror grid points.
   postplot( fea_mirror, 'surfexpr', 'T' )

   title(sprintf('Optimal solution: n=%d pipes, D=%.4f m | T_{max}=%.2f K', ...
                 best.n, best.D, Tmax));
 end


 if( ~nargout )
   clear fea out
 end


%

ex_heattransfer11.m File Reference

Description

Code listing