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+clc();

+clear;

+// To find heat changes and temperature change on heating of a concrete wall

+b=9;                                 // thickness of the wall in ft

+A=5;                                 // area of wall in ft^2

+k=0.44;                               // Thermal conductivity in Btu/hr-ft-degF

+Cp=.202;                              // Specific heat in Btu/lbm-degF

+rho=136;                              // density in lb/ft^3

+

+function[t]=templength(x);

+    t = 90 - 8*x-80*x^2; 

+    funcprot(0);

+endfunction

+tgo = derivative(templength,0);      // temperature gradient at x=0ft

+tgl = derivative(templength,9/12);    // temperature gradient at x=9/12ft

+

+qo = -k*A*tgo;                        // Heat entering per unit time in Btu/hr

+printf("Heat entering per unit time is %.2f Btu/hr \n",qo);

+ql = -k*A*tgl;                        // Heat coming out per unit time in Btu/hr

+printf(" Heat coming per unit time is %.2f Btu/hr \n",ql);

+q3 = qo-ql;                           //Heat energy stored in Btu/hr

+printf(" Heat energy stored in wall is %.2f Btu/hr \n",q3);

+

+a=k/(rho*Cp);                         // Thermal diffusivity in ft^2/hr

+function[t2]=doublederivative(y);     // derivative of tempearture with respect to length in degF/ft

+  t2= -8-160*x;

+  funcprot(0);

+endfunction;

+timeder0=a*derivative(doublederivative,0);         // derivative of temperature  wrt time at x=0 in degF

+printf(" Time derivative of temperature wrt time at x=0ft is %.2f degF/hr\n",timeder0);

+timeder1=a*derivative(doublederivative,9/12);      // derivative of temperature wrt time at x=9/12 in degF 

+printf(" Time derivative of temperature wrt time at x=9/12ft is %.2f degF/hr\n",timeder1);

+printf(" Teperature at each part of wall decreases equally");