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+clear;

+clc;

+printf("\t\t\tExample Number 7.13\n\n\n");

+// combined free and forced convection with air

+// Example 7.12 (page no.-353-355) 

+// solution

+

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

+Ta = 27;// [degree celsius] temperature of air

+d = 0.025;// [m] diameter of tube

+u = 0.3;// [m/s] velocity of air

+Tw = 140;// [degree celcius] temperature of tube wall

+L = 0.4;// [m] length of tube

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

+// the properties of air are evaluated at the film temperature:

+Tf = (Tw+Ta)/2;// [degree celcius]

+// the properties of interest are thus

+kf = 0.0305;// [W/m degree celcius]

+Pr = 0.695;// prandtl number

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

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

+mu_f = 2.102*10^(-5);// [Kg/m s]

+mu_w = 2.337*10^(-5);// [Kg/m s]

+rho_f = p/(R*(Tf+273));// [Kg/cubic meter]

+// let us take the bulk temperature as 27 degree celsius for evaluating mu_b;then

+mu_b = 1.8462*10^(-5);// [Kg/m s]

+// the significant parameters are calculated as 

+Re_f = rho_f*u*d/mu_f;

+Gr = rho_f^(2)*g*Beta*(Tw-Ta)*d^(3)/mu_f^(2);

+Z = Gr*Pr*d/L;// constant

+// according to figure(7-14)(page no.-354), the mixed convection flow regime is encountered. thus we must use equation(7-77).

+// The graetz number is calculated as 

+Gz = Re_f*Pr*d/L;

+// and the numerical calculation for equation(7-77) becomes

+Nu = 1.75*(mu_b/mu_w)^(0.14)*[Gz+0.012*(Gz*Gr^(1/3))^(4/3)]^(1/3);

+// the average heat transfer coefficient is calculated as 

+h_bar = Nu*kf/d;// [W/square meter degree celsius]

+printf("heat transfer coefficient is %f W/square meter degree celsius",h_bar);

+