Numerical solution of heat transfer through \(B\)-spline collocation with quasilinearization (Q2716745)

This paper deals with numerical solution of the boundary value problem NEWLINE\[NEWLINE{d^2U\over dR^2}+ \Biggl[{1\over R+\xi}- {\tan\alpha\over (1-R)\tan\alpha+ \vartheta}\Biggr] {dU\over dR}- {\beta U^4\over (1-R)\tan \alpha+\vartheta}= 0NEWLINE\]NEWLINE subject to the boundary conditions \(U(0)= 1\), \({dU\over dR}(1)= 0\). This problem is linearized by the quasilinearization technique and solved numerically by using an algorithm based on the B-spline collocation method. An example of temperature distributions for different types of fin geometry is presented.