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+clear;

+clc;

+printf("\t\t\tExample Number 7.8\n\n\n");

+// heat transfer across vertical air gap

+// Example 7.8 (page no.-345) 

+// solution

+

+L = 0.5;// [m] side length vertical square plate

+d = 0.015;// [m] distance between plates

+p = 101325;// [Pa] pressure of air

+R = 287;// [] universal gas constant

+T1 = 100;// [degree celsius] temperature of first plate

+T2 = 40;// [degree celsius] temperature of second plate

+E = 0.2;// emissivity of both surfaces

+// the properties of air is evaluated at the mean temperature

+Tf = (T1+T2)/2;// [degree celsius]

+rho = p/(R*(Tf+273));// [Kg/m^(3)] density

+k = 0.0295;// [W/m degree celsius]

+Pr = 0.70;// prandtl number

+Beta = 1/(Tf+273);// [K^(-1)]

+mu = 2.043*10^(-5);// [Kg/m s] viscosity

+g = 9.8;// [square meter/s] acceleration due to gravity

+// the Grashof-prandtl number product is now calculated as 

+Gr_into_Pr = (g*rho^(2)*Beta*(T1-T2)*(d)^(3)*Pr)/(mu^(2));

+// we may now use equation (7-64) to calculate the effective thermal conductivity, with

+L = 0.5;// [m]

+del = 0.015;// [m]

+// and the constants taken from table 7-3(page no.-344):

+Ke_by_K = 0.197*(Gr_into_Pr)^(1/4)*(L/del)^(-1/9);

+// the heat transfer may now be calculated with equation (7-54). the area is 

+A = L^(2);// [square meter]

+q = Ke_by_K*k*A*(T1-T2)/del;// [W]

+ // the radiation flux is calculated with equation(7-67), taking 

+T1 = 373;// [K]

+T2 = 313;// [K]

+E1 = E;

+E2 = E;

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

+q_A = sigma*(T1^(4)-T2^(4))/((1/E1)+(1/E2)-1);// [W/square meter]

+q_rad = A*q_A;// [W]

+printf("free-convection heat transfer across the air space is %f W",q);

+printf("\n\nradiation heat transfer across the air space is %f W",q_rad);