Transient Heat Transfer

There are 3 forms of heat transfer: conduction, convection and radiation. The main form of heat transfer focused on within this experiment is conduction; convection can also be considered however radiation has little effect within heat exchangers except as a method of energy loss. Conduction is the transfer of heat through direct contact, in this case the hot water fed to the water jacket has contact with the vessel walls and transfers heat through conduction. The heat energy is further transferred to the water contained within the vessel through contact with the vessel wall. The energy transfer occurs due to the vibration of surface molecules in contact with the hotter medium. The amount of energy gained by the water in the vessel can be calculated by:

Q=Mc_p (T-T_0) (1)

Where Q is the energy gained, M is the mass of water, cp is the specific heat capacity of the water, T is the final temperature and T0 being the waters initial temperature. Equation 1, can be reformed by differentiating with respect to time to display the rate of change of energy of the water.

dQ/dt=Mc_p dT/dt (2)

The rate of energy gained by the water is provided by the hot water supplied to the jacket.

dQ/dt=UA(T_h-T) (3)

Where U is the overall heat transfer coefficient, A is the heat transfer area, Th is the temperature at the jacket inlet and T is the temperature at the jacket outlet. Equation 2 and Equation 3 can be combined to form an energy balance:

Mc_p dT/dt=UA(T_h-T) (4)

Equation 4 shows that that the rate of energy acquired by the water in the vessel is equal to the rate of energy lost by the hot water in the jacket.