function [F12, A1, F21, A2] = plate2cyl(H, W, L, r) %[F12, A1, F21, A2] = plate2cyl(H, W, L, r); % % Description: % % View factor from rectangular plate to finite cylinder. % % Inputs: % % H = height of cylinder centerline above the plate % W = plate width % L = plate (and cylinder) length % r = cylinder radius % % Outputs: % % A1 = plate surface area % F12 = plate to cylinder view factor % A2 = cylinder surface area % F21 = cylinder to plate view factor % % Reference: % % E. M. Sparrow and R. D. Cess, "Radiation Heat Transfer," Hemisphere % Publishing, Washington, 1978, augmented edition, pp. 339-349. % % H. Leuenberger and R. A. Pearson, "Compilation of radiation shape % factors for cylindrical assemblies." ASME Annual Meeting, New York, % ASME Paper No. 56-A-144, 1956 % %========================================================================== if r > H error('plate2cyl: cylinder radius = %g, is greater than distance to plate = %g.\n',r,H); end A1 = W*L; % plate surface area A2 = 2*pi*r*L; % cylinder surface area X = H/r; Y = W/r; Z = L/r; F12 = (2/Y)*integral(@(zeta) fun(zeta,X,Y,Z), 0, Y/2); F21 = (A1*F12)/A2; end function f = fun(zeta, X, Y, Z) for i=1:length(zeta) A = Z^2 + X^2 + zeta(i)^2 - 1; B = Z^2 - X^2 - zeta(i)^2 + 1; f(i) = X/(X^2 + zeta(i)^2) - ... (X/(pi*(X^2 + zeta(i)^2)))*(acos(B/A) - ... (1/(2*Z))*(sqrt(A^2 + 4*Z^2)*acos(B/(A*sqrt(X^2 + zeta(i)^2))) ... + B*asin(1/sqrt(X^2 + zeta(i)^2)) - (pi*A)/2)); end end