Question

QUESTION 4 When there is heat transfer from the lateral side of an infinitely long cylinder of radius a into a surrounding medium, the temperature inside the cylinder depends upon the time t and the distance r from its longitudinal axis (i.e. the axis through the centre and parallel to the lateral side.) a. Write down the partial differential equation that models this problem. b. Suppose that the surrounding medium is at temperature zero and the initial temperature is constant at every point, derive the initial and boundary conditions. (a) [Hint: For the boundary condition use Newton’s law of cooling.] c. Solve the initial boundary value problem obtained in (a) and (b). [20 Marks] QUESTION 5 (Based on Chapter 7 of SG). Determine the steady temperature inside a 90 sector of a circular annulus ?? 0 < a r b; 0 2 , if its circular edges and the straight edge = 0; are in contact with ice (at 0oC; and the straight edge = 2 is a given function of r: [20 Marks]

Answer 1