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For simplicitys sake, it is assumed that the panel is in shadow with no incident heat flux of any kind. It is losing heat by radiation to the surroundings at 0K. Using the finite difference method, model the panel. Provide the following
The temperature distribution within the panel
A list of equations for each type of node
The average value of hrad on the surface of the panel
The heat transfer from the panel.
Typical radiators may dissipate between 100 and 350 W/m2. Is your calculated dissipation rate reasonable? Note that you can use typical finite difference equations, substituting h (for convection) with hrad and Tsurr=T "= 0 . Y o u w i l l n e e d t o i t e r a t e y o u r r e s u l t . S t a r t w i t h a n i n i t i a l g u e s s o f h r a d . C a l c u l a t e t h e t e m p e r a t u r e d i s t r i b u t i o n , a n d t h e n c a l c u l a t e h r a d b a s e d o n t h e s u r f a c e t e m p e r a t u r e . I t e r a t e a s n e e d e d . ( T h e i t e r a t i o n p r o c e s s s h o u l d b e v e r y f a s t . I f i t s n o t , a s k your instructor because you may be making it harder than it should be.)
Hints if you use Excel:
1) Set up Excel to perform the iterations under Options, Formulas. Set the calculation to manual, the maximum number of iterations to 10,000, and the maximum change to 0.00001. Check the iteration box. Turn off Recalculate before save. When you wish to calculate your results, hit F9 (or whatever it is on your computer).
2) Save often! If you mistakenly enter an undefined number, it will spread throughout your spreadsheet once you hit F9, forcing you to start over. After making a change to an equation, save before you start to iterate.
3) Before you start entering your formulas, outline your solution space on the spreadsheet. Enter a rough estimate of the final temperature in each cell (make sure your guess temperature is above your air and water temperatures). In some versions of Excel, i f h j l $ 6 W X $
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3 mm thickness. (If there are nodes on each corner, will you have 3 or 4 nodes across the 3 mm width?
Other surfaces adiabatic
Radiation to surroundings at 0 K on this side
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