Question

If two ends of a bar of length l is insulated then what are the conditions to solve the heat flow equation?

(a) ux(0,t) = 0 = ux(l,t)

(b) ut(0,t) = 0 = ut(l,t)

(c) u(0,t) = 0 = u(l,t)

(d) uxx(0,t) = 0 = uxx(l,t)

This question was posed to me by my college professor while I was bunking the class.

This is a very interesting question from Solution of 1D Heat Equation in portion Applications of Partial Differential Equations of Engineering Mathematics

Answer 1

Correct answer is (a) ux(0,t) = 0 = ux(l,t)

For explanation I would say: Since the ends are insulated no heat can flow through the ends of the bar. Therefore ux(0,t) = 0 = ux(l,t).