Gus Omer • Randy Hurd

Determining the most economic

method

for heating diesel fuel in a reservoir

from 20 to 100 °C in under 90

minutes.

PROBLEM

• Three different power heaters are available from the

chosen manufacturer: 1500 W, 2500 W and 3750 W.

• The 3750 W heater will obviously heat the fuel the fastest,

but because our target heat-up time is 90 minutes it may

make more sense economically to choose a smaller heater

that will cost less to purchase and run long-term.

INITIAL THOUGHT

• Steel tank filled with diesel fuel

• Wall thickness = 0.003038m

• k = 50 W/m∙K

RESERVOIR

0.2413m

0.6604m

0.4064m

• Uniform heating

• Bottom of tank is insulated (q=0)

• Thin walled tank (fuel and reservoir at same temperature)

• Quiescent air (no forced convection)

• Lumped capacitance for natural convection

ASSUMPTIONS

• Mild Steel

• k = 50 W/m • k

• C = 500 J/kg • K

• ρ = 7,850 kg / m3

• Diesel Fuel

• C = 1,800 J/kg • K

• ρ = 875 kg / m3

Mathematic Model Material Properties

APPROACH

• The coefficient h was calculated assuming all heat transfer

through convection was due to natural convection in quiescent air.

• Separate Rayleigh, Nusselt, and h values were calculated for the

top of the fuel reservoir and the sides.

• The weighted average is h ≈ 7

• The total heat transfer q was then calculated:

− q = Ash(Ts – T∞ )

CONVECTION

RADIATION

• Properties:

− ε = 0.08

• Heat Transfer:

− q = Asεσ(Ts4 - Tsur

4)

• The calculated heat transfer through radiation was comparatively

small and could safely be considered insignificant in calculating

temperature increase with respect to time.

RESULTS

90

100

• Assuming the fuel reservoir heater was run for 16 hours a

day, 300 days per year at a cost of 8.51¢/kWh, the annual

cost to run one unit would be:

− 1500 W: $612.72

− 2500 W: $1021.20

− 3750 W: $1531.80

• In addition, smaller power heaters require a smaller initial

investment.

FINANCES

• According to our calculation only the 2500W and 3750 W

heaters were capable of accomplishing the proposed task.

The initial cost of the heaters is relatively insignificant when

compared to energy costs over long periods of time. When

energy costs are considered the 2500W heater proves ideal

because it performs the proposed task for the cheapest

energy cost.

CONCLUSION

QUESTIONS