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+clear;

+clc;

+printf("\t\t\tExample Number 8.21\n\n\n");

+// influence of convection on solar equilibrium temperature 

+// Example 8.21 (page no.-455) 

+// solution

+

+T_surr = 25+273;// [K] surrounding temperature

+sigma = 5.669*10^(-8);// [W/square meter K^(4)]

+h = 10;// [W/square meter] heat transfer coefficient

+// in this case the solar energy absorbed must equal the sum of the radiation and convection transfers to the surroundings

+// (q_by_A_sun)*alpha_sun = alpha_low_temp*sigma*(T^4-T_surr^4)+h*(T-T_surr)         (a)

+q_by_A_sun = 700;// [W/m^(2)] solar flux

+

+// for the white paint, using the same surface properties as in example 8-20 gives 

+

+alpha_sun = 0.12;

+alpha_low_temp = 0.9;

+// so that equation (a) becomes

+deff('[y] = f(T)','y = (q_by_A_sun)*alpha_sun-alpha_low_temp*sigma*(T^4-T_surr^4)-h*(T-T_surr)');

+T = fsolve(1,f);

+printf("the radiation-convection equillibrium temperatures for case (a) is %f degree celsius",T-273);

+

+//for flat black lacquer we obtain

+

+alpha_sun = 0.96;

+alpha_low_temp = 0.95;

+// so that equation (a) becomes

+deff('[y] = f2(T1)','y = (q_by_A_sun)*alpha_sun - alpha_low_temp*sigma*(T1^4-T_surr^4)-h*(T1-T_surr)');

+T1 = fsolve(1,f2);

+printf("\n\n the radiation-convection equillibrium temperatures for case (b) is %f degree celsius",T1-273);

+printf("\n\n where case (a)     surface is coated with white paint");

+printf("\n\n       case (b)     surface is coated with flat black lacquer");

+

+