6. (20pts) Find and derive the energy balance equation at the interface for a ma

Question

6. (20pts) Find and derive the energy balance equation at the interface for a material that is poured in a cylind temperature above the fusion point, and the outer boundary is held at a constant temperature below the fusion point. rical cavity of radius R. The z-axis of the cylinder is a hot wire at a constant a) (1Opts) Use energy conservation to find the energy balance equation at the interface Answer b) (10pts) Write the finite difference formulation of the equation you found in the previous part. Answer

Explanation / Answer

Solution (a):

Energy balance calculation is often done for designing a heat exchanger to determine operating parameters for hot and cold fluids such as - inlet / outlet temperatures and flow rates.

For hot fluid side of a heat exchanger let,

mH : mass flow rate of the hot fluid in kg/hr
CpH : mass heat capacity of the hot fluid in Joules/kg0C
TiH and ToH : Respectively inlet and outlet temperatures on exchanger hot side in 0C

mC : mass flow rate of the cold fluid in kg/hr
CpC : mass heat capacity of the cold fluid in Joules/kg0C
TiC and ToC : Respectively inlet and outlet temperatures on exchanger cold side in 0C

Heat lost by the hot fluid = -Q = mH × CpH × (ToH - TiH) … (1)

Heat gained by the cold side = Q = mC × CpC × (ToC - TiC) … (2)

Comparing equations (1) and (2),

mH × CpH × (TiH - ToH) = mC × CpC × (ToC - TiC) … (3)

This energy balance equation can be solved for one variable for any given case. Out of total six variables in the equation (3), five should be fixed to determine the unknown variable.

Solution (b):

It should also be noted that the mass balance equation is already applied in this case to develop equation (3).

The fact that mHin = mHout = mH and mCin = mCout = mC is already considered while writing equations (1) and (2). Hence application of mass balance equation for heat exchanger does not present any new information here.

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.