Modeling of chemical engineering. Distributed system.

A step by step approach to the modeling of chemical engineering process

4.3) Imagine a solid cone, as depicted below. The lower and upper bases of the cone are 2 cm and 12 cm, respectively, and its height is 5 cm. This cone was initially at 35 C, and the environmental temperature (Ten) is 25 C. The lower base of the cone is submitted to a temperature T, equal to 180 C. The lateral of the cone is insulated, and the cone exchanges heat with the environment only through the upper base. Assume there are no radial and angular profiles of the temperature in the cone and that T, and Teny do not change with time. (a) Define the ODE that represents the variation of temperature along the height of the solid cone in a steady state. (Hint: represent the radius of the cone as a function of the height to obtain the ODE). (b) Define the initial/boundary conditions needed to solve the ODE. 12 cm 5 cm Tev = 25C T = 180C 2 cm