The objective of this problem is to design a low-temperature oven (heated box) with interior air temperature of 100°C. The interior dimensions of the box are to be Imxlmx 1 m. The outside surface of the box will be exposed to ambient air at 20°C with an average convection heat transfer coefficient of 5 W/m2-K. The average temperature of the surroundings is also 20°C. The box will sit on a flat surface that is well-insulated (adiabatic). An electric heating device is mounted inside the box to provide the necessary energy. The box also contains an electric circulation fan that mixes the air, yielding an average heat transfer coefficient of 15 W/m2-K along the interior surface. The fan dissipates 15W of heat.
Your job is to select an electric heater and insulation wall material(s) needed to achieve a steady-state air temperature of at least 100°C inside the box. The electric heater will be a finned ceramic type from Omega Engineering. For the walls, you must specify the material type(s) and calculate the required thickness(es). You may use more than one type of material for the wall but keep each wall section identical for construction simplicity. Use standard, available thicknesses for wall materials. Pay attention to the maximum service temperature of the materials that you choose. You may also get material property information from other sources, but be sure to provide references or copies of data sheets.
Of course, the cost of the heated box is very important. Your design should minimize the total cost while satisfying all other requirements. Total cost consists of the initial expenditures for the heater, fan ($30), and wall materials, plus the present-value operating cost (electricity). The present-value operating cost is based on the heater power rating, 360 hr/month operation, $0.15/kWh, a 10-year lifetime, and an 8% annual rate of return compounded monthly.
You may assume that i) all material properties are constant, ii) conduction through each wall section (top plus four sides) is identical, iii) conduction is one-dimensional and comer/edge effects can be ignored as long as the total wall thickness does not exceed 10 cm, iv) steady-state conditions prevail, v.) the surroundings are large compared to the box, vi) the given heat transfer coefficient (15 W/m2-K) inside the box accounts for any internal radiation effects, and vii) the box is air-tight.
Submit a report that clearly shows your heat transfer and cost analyses leading to your final design. All property values and costs must be specified and referenced for the material(s) that you have chosen.
1. Title page
2. Wall Material Summary Table
3. Results Summary Table