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+clear;

+clc;

+

+//Example2.9[Combined Convection and Radiation Condition]

+//Given:- 

+T_ball=300;//Temperature of spherical metal ball[degree Celcius]

+T_ambient=27;//Temperature of ambient air[degree Celcius]

+k=14.4;//Thermal conductivity of the ball material[W/m.K]

+h=25;//average convection heat transfer coefficient on the outer surface of the ball[W/m^2.K]

+e=0.6;//Emissivity of outer surface of the ball

+T_surr=290;//

+//This is one-dimensional transient heat transfer problem since the temperature within the ball changes with the radial distance r and the time t i.e. T=T(r,t)

+//Taking the moment the ball is removed from the oven to be t=0

+disp("The initial condition can be expressed as")

+disp("T(r,0)=T_ball")

+disp("degree Celcius",T_ball)

+//The problem possesses symmetry about the mid point(r=0) since the isotherms in this case are concentric spheres, and thus no heat is crossing the mid point of the ball.

+disp("The boundary condition at the midpoint i.e. r=0 can be expressed as dT(0,t)/dr=0")

+//The heat conducted to the outer surface of the ball is lost to the environment by convection and radiation.

+disp("Taking the direction of heat transfer to be the positive r direction, the boundary condition on the outer surface can be expressed as")

+disp("-k(dT(r_out,t)/dr)=h[T(r_out)-T_ambient]+e*sigma[(T(r_out)^4)-(T_ambient^4)]")
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