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EMTH271 Mathematical Modelling and Computation

Qeustion:
We wish to model the dynamic temperature profile within a heating fin in order to assess how the fin responds to temperature or heat flow changes of the element, the amount of heat stored in the fin and transferred to the oil flow.

Physical and system properties you will need are:

• The heating fin is made of Aluminium with thermal conductivity coefficient, k = 205 W/mK, density, = 2700 kg/m3 and specific heat, cp = 910 J/kgK

• The convective heat transfer co-efficient on the outer surfaces of the heating fin is determined to be h =1200 W/m2K

• Consider an Aluminium fin that is 20mm thick and 40mm in length. We will use a resolution of x= y=1mm.

• Consider a 100mm section of the depth of the fin (along the axis of the tube) and assume the temperature of the fluid flow is constant along its surface. Assume the fluid flow is at Tflu = 20°C.

• Initially the heating element has been turned off for a long period of time and the heating fin is in thermal equilibrium with the its environment i.e. at t=0s all nodes are at 20°C.

The heating element is turned on at time t = 0.5s, its temperature with respect to time Tele(t) (in °C) can be expressed by the function: