(25 p) 1) In the wall of a hollow spherical container, internal thermal energy is generated...

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(25 p) 1) In the wall of a hollow spherical container, internal thermal energy is generated as non- uniformly according to the given relation where q (r) (W/m) is the local rate of energy generation per unit volume, . (W/m) is a constant, and r, and ro are the inner and outer radius of the container. The inner surface of the container is ideally insulated. Steady-state conditions are maintained by submerging the container in a liquid that is at T. and provides a uniform convection coefficient h. Start reducing given general heat conduction equation (r)=. for spherical coordinates, Too, h ttt (1)= 9, (-1) Ii Ideally insulated" T, h fff a) Determine expression of 1-dimensional (in r direction) temperature distribution, T(r), in the wall. Express your result in terms of, qo, ri, ro, Too, h, and the thermal conductivity of the sphere, k. b) Determine expression of the location of the highest temperature, temperature in the wall, Tmax.. c) Determine expression of the total heat transfer rate through this sphere, q. and expression of the highest 1 12 ar kr2 Or + 1 a 1 a k + k sin 0- 2 sin 0 do r sine de 00 +q=pcp at (25 p) 1) In the wall of a hollow spherical container, internal thermal energy is generated as non- uniformly according to the given relation where q (r) (W/m) is the local rate of energy generation per unit volume, . (W/m) is a constant, and r, and ro are the inner and outer radius of the container. The inner surface of the container is ideally insulated. Steady-state conditions are maintained by submerging the container in a liquid that is at T. and provides a uniform convection coefficient h. Start reducing given general heat conduction equation (r)=. for spherical coordinates, Too, h ttt (1)= 9, (-1) Ii Ideally insulated" T, h fff a) Determine expression of 1-dimensional (in r direction) temperature distribution, T(r), in the wall. Express your result in terms of, qo, ri, ro, Too, h, and the thermal conductivity of the sphere, k. b) Determine expression of the location of the highest temperature, temperature in the wall, Tmax.. c) Determine expression of the total heat transfer rate through this sphere, q. and expression of the highest 1 12 ar kr2 Or + 1 a 1 a k + k sin 0- 2 sin 0 do r sine de 00 +q=pcp at