Supposedly a cylinder is heated to very high temperature and is quenched into a quenchant where the surrounding temperature is at non zero temperature i.e., T0 and initial temperature of cylinder is Ti.
The equation is to find out the temperature of a point anywhere between surface and center at a given time t, for a given thermal conductivity and heat transfer coefficient.
T(r,t)=T0+2/b(Ti-T0)* summation of (1/beta(m))*(J1(beta(m)*b)*J0(beta(m)*r))/(J0 square(beta(m)*b)+J1 square(beta(m)*b))* exp-(beta(m) square *alpha* t) where summation is m=1 to infinity.
J0 is the bessels function of first kind and J1=-d(J0)/dz
Where the eigen values beta(m) are obtained from the roots of transcendental equation
beta*b*J1(beta*b)-Bi*J0(beta*b)=0 where Bi is the biot number.
How do I draw a cooling curve using the above equation?
I'm new to matlab and this is completely out of my league. I have seen nothing like this in any other questions. Thanks for any help.