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+clear;
+clc;
+printf("\t\t\tExample Number 7.1\n\n\n");
+// constant heat flux from vertical plate  
+// Example 7.1 (page no.-330-331) 
+// solution
+
+q_w = 800;// [W/square meter] radiant energy flux
+H = 3.5;// [m] height of metal plate surface
+W = 2;// [m] width of metal plate
+Ta = 30;// [degree celsius] surrounding air temperature 
+// we treat this problem as one with constant heat flux on the surface since we do not know the surface temperature, we must make an estimate for determining Tf and the air properties.
+// an approximate value of h for free convection problems is 
+h = 10;// [W/square meter degree celsius]
+dT = q_w/h;// [degree celsius]
+// then
+Tf = (dT/2)+Ta;// [degree celsius] approximately 
+// at Tf the properties of air are 
+v = 2.005*10^(-5);// [square meter/s]
+k = 0.0295;// [W/m degree celsius]
+Pr = 0.7;// prandtl number
+Beta = 1/(Tf+273);// [K^(-1)]
+// from equation (7-30), with
+x = 3.5;// [m]
+g = 9.8;// [square meter/s] acceleration due to gravity 
+Gr_x = (g*Beta*q_w*x^(4))/(k*v^(2));
+// we may therefore use equation (7-32) to evaluate h_x
+h_x = (k*0.17*(Gr_x*Pr)^(1/4))/x;// [W/square meter degree celsius]
+// in the turbulent heat transfer governed by equation (7-32), we note that
+// Nu_x = h*x/k ~ (Gr_x)^(1/4) ~ x
+// or h_x doest noy vary with x, and we may take this as the average value. the value of h
+h = 5.41;// [W/square meter degree celsius]
+// is less than the approximate value we used to estimate Tf, recalculating dT, we obtain
+dT1 = q_w/h_x;// [degree celsius]
+// our new film temperature would be
+Tf1 = Ta+dT1/2;// [degree celsius]
+// at Tf the properties of air are
+v1 = 2.354*10^(-5);// [square meter/s]
+k1 = 0.0320;// [W/m degree celsius]
+Pr1 = 0.695;// prandtl number
+Beta1 = 1/(Tf1+273);// [K^(-1)]
+// then 
+Gr_x1 = (g*Beta1*q_w*x^(4))/(k1*v1^(2));
+// and h_x is caalculated from
+h_x1 = (k1*0.17*(Gr_x1*Pr1)^(1/4))/x;// [W/square meter degree celsius]
+// our new temperature difference is calculated as 
+dT2 = q_w/h_x1;// [degree celsius]
+// the average wall temperature is therefore
+T_w_avg = dT2+Ta;// [degree celsius]
+printf("the average wall temperature is therefore %f degree celsius",T_w_avg);
+
+
+
+
+
+