Spring 2002, METBD452 - FEA Heat Transfer Applications

Prof. Dave Johnson, dhj1@psu.edu, Penn State - Erie, The Behrend College

Conduction, Convection, & Radiation Homework or Project

Concepts:

• Conduction, Convection, and Radiation Heat Transfer
• approximation for "stagnant" air space
• Heat generation loading
• Convection and Radiation (Outside) using Surface Effect finite elements
• Radiation (Inside) using the Radiation Matrix Utility

Reference:  J. P. Holman, Heat Transfer, 8th ed., p. 482

The figure above shows the cross-section of a flat-plate solar collector.  All dimensions are given in meters.  A glass plate covers and air space above a blackened surface which is insulated.  Solar energy at the rate of 75000 W/m³ is absorbed by the aluminum collector.  The black surface heats up and radiates to the glass and side walls.  It also loses heat by conduction and convection across the air gap .  

The outside surface of the glass loses heat by radiation and convection to the environment which is at 30^oC with h = 20 W/m²-^oC.  (Use SURF151 with both convection and radiation to the extra node.  For the simple radiation in SURF151, define the proper EMIS material property and a real constant with the Stefan-Boltzmann constant and form factor.)

It is assumed that the glass does not transmit any of the thermal radiation.  (Radiant energy is absorbed and emitted at the the glass surfaces).  

Initially, assume that all the outside surfaces of the insulation are adiabatic.  

The air inside is assumed NOT to flow for the model, but instead is treated with an enhanced conductivity, k_e, which lumps the conduction and convection  within the air space into a simpler, linear conduction behavior, using an effective thermal conductivity of k_e = 1.4 k_air.

• The insulation is a fiber insulating board, k_insulation = 0.048 W/m-^oC, surface emissivity = 0.95
• The aluminum with the blackened surface has k_aluminum = 204 W/m-^oC, and emissivity = 1.0
• The glass top has k_glass = 0.78  W/m-^oC, and  emissivity = 0.9
• "effective" k_air = ( 0.03 W/m-^oC) * 1.4

Perform a steady-state, nonlinear heat transfer analysis of this structure.  

Repeat the analysis, but consider that all the outside faces of the insulation may convect (h =  20 W/m²-^oC) and radiate (insulation with emissivity = 0.95) to the surroundings at 30^oC.  Create more SURF151 elements to handle this behavior.  (You will need to define a different EMIS material property).

Turn In:

• Plots showing the model (materials) and boundary conditions (convection and heat flux) for both simulations.
• A plot showing you have proper orientation of the radiating surface skin elements (LINK32).
• A plot showing that you have different emissivities on the radiating surface skin elements.
• Results plots of the temperatures on  model for both simulations.
• A comparison of the FEA results to theory.  (Only the first simulation can be compared to theory: 1D heat flow).
• For both simulations, report the total heat flow out of the system from the outside convection/radiation together, i.e., at the extra node.
• For both simulations, report the amount of heat loss by convection and radiation separately (you must use ETABLE data, HFCTOT and HRTOT for all of the SURF151's followed by SSUM)
• Compare the original model (temperature extremes & heat loss data) to the more realistic (second) analysis.
• Include the annotated log file, showing the initial model generation and solution.

Reminder: All project reports will be typed, and include:

• a cover page with course name, project name, team names, and date
• a brief objective statement (2-3 sentences, maximum, of engineering objectives)
• a summary of procedures (bulleted items)
     a complete list of:
  • assumptions, 
  • given data, 
  • modeling and analysis steps
• a conclusion statement (what was learned about the part or device, an evaluation of the design, validation of the model, and an interpretation of the results)
• a copy of the project statement (this web page) may be attached.