From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

---
 905/CH2/EX2.4/2_4.sce | 62 +++++++++++++++++++++++++++++++++++++++++++++++++++
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diff --git a/905/CH2/EX2.4/2_4.sce b/905/CH2/EX2.4/2_4.sce
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+clear;
+clc;
+
+// Illustration 2.4
+// Page: 99
+
+printf('Illustration 2.4 -  Page: 99\n\n');
+
+// solution
+// Mass Transfer into a Dilute Stream Flowing Under Forced Convection in a Circular Conduit
+
+n = 6; // [number of variables]
+//   Variables                Symbols        Dimensions
+// Tube diameter                 D             L
+// Fluid density                 row           M/L^3 
+// Fluid viscosity               u             M/(Lt)
+// Fluid velocity                v             L/t
+// Mass diffusivity              D_AB          L^2/t
+// Mass-transfer coefficient     kc            L/t
+
+// To determine the number of dimensionless parameters to be formed, we must know the rank, r, of the dimensional matrix.
+// The dimensional matrix is 
+DM = [0,0,1,1,0,0;1,1,-3,-1,2,1;-1,-1,0,0,-1,-1];
+[E,Q,Z ,stair ,rk]=ereduc(DM,1.d-15);
+printf("Rank of matrix is %f\n\n",rk);
+
+//The numbers in the table represent the exponent of M, L, and t in the dimensional expression of each of the six variables involved. For example, the dimensional expression of p is M/Lt; hence the exponents are 1, -1, and -1
+
+// From equation 2.16
+i = n-rk; // [number of dimensional groups]
+// Let the dimensional groups are pi1, pi2 and pi3
+// Therefore pi1 = (D_AB)^a*(row)^b*(D)^c*kc
+//           pi2 = (D_AB)^d*(row)^e*(D)^f*v
+//           pi3 = (D_AB)^g*(row)^h*(D)^i*u
+
+// Solving for pi1
+// M^0*L^0*t^0 = 1 = (L^2/t)^a*(M/L^3)^b*(L)^c*(L/t)
+
+// Solution of simultaneous equation
+function[f]=F(e)
+    f(1) = 2*e(1)-3*e(2)+e(3)+1;
+    f(2) = -e(1)-1;
+    f(3) = -e(2);
+    funcprot(0);
+endfunction
+
+// Initial guess:
+e = [0.1 0.8 0.5];
+y = fsolve(e,F);
+a = y(1);
+b = y(2);
+c = y(3);
+printf("The coefficients of pi1 are %f %f %f\n\n",a,b,c);
+// Similarly the coefficients of pi2 and pi3 are calculated
+// Therefore we get pi1 = kc*D/D_AB = Sh i.e. Sherwood Number
+//                  pi2 = v*D/D_AB = P_ed i.e. Peclet Number
+//                  pi3 = u/(row*D_AB) = Sc i.e. Schmidt Number
+
+// Dividing pi2 by pi3 gives
+//       pi2/pi3 = D*v*row/u = Re i.e. Renoylds number
+
+printf('The result of the dimensional analysis of forced-convection mass transfer in a circular conduit indicates that a correlating relation could be of the form\n Sh = function(Re,Sc)\n which is analogous to the heat transfer correlation \n Nu = function(Re,Pr)');
\ No newline at end of file
-- 
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