Updated 2014-11-13 10:17:01 by gold

Historical Kelvin Earth Cooling and eTCL Slot Calculator Demo Example , numerical analysis  edit

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gold Here is some eTCL starter code for calculations on cooling of the earth from Lord Kelvin.

Lord Kelvin calculated the age of the earth by approximating the cooling of an molten iron sphere. Lord Kelvin's calculation is of historical interest. Modern calculations estimate the age of the earth as 4.2 billion years based on radioactive decay. While Lord Kelvin published two estimates in his lifetime, no overt statements on the age of the earth were found in the Kelvin papers. Rather, these estimates were used in academic circles to counter the theory that the earth was 6000 years old. The first published estimate was 100 million years and the second published estimate was 25 million years. Heating of radioactive elements in earth's crust was not considered in Lord Kelvin's calculation.

As an initial testcases, some one line formulas or procs below can be pasted into the eTCL console. Following assumptions are givens, crust thermal defusivity $cc is 1.5E-6 meters/sec*sec. As a alternate defusivity estimate, sandstone is about 1.1E-6 meters/sec*sec. Alpha $dd is 0.04 degrees centigrade per meter. Initial temperature $aa was 2500 centgrade degrees. Final temperature $bb was near zero degrees centigrade. The time constant $ee was number seconds in year as 3156000 seconds.
    proc pi {} {expr acos(-1)}  ; #AMG
    proc kelvinearthtempage {aa bb cc dd ee} { return [ expr (($aa - $bb)*($aa - $bb)/ ( $cc * [pi]* $dd* $dd*$ee))]} 
    set age_of_earth  [ kelvinearthtempage 5100 .1 .0000015 .04 31536000. ] 
    set age_of_earth2   [ kelvinearthtempage 2500 .1 .0000015 .04 31536000. ] 
    puts " first estimate  $age_of_earth    first estimate  $age_of_earth    "
    #usage: low estimate: set age_of_earth " [ kelvinearthtempage 2500 .1 .0000015 .04 31536000. ] ";
    #answer 26 million years
    #usage: high estimate could be: set age_of_earth " [ kelvinearthtempage 5100 .1 .0000015 .04 31536000. ] ";
    #answer 110 million years

Pseudocode and Equations

 expr (($aa - $bb)*($aa - $bb)/ ( $cc * [pi]* $dd* $dd*$ee))]} 

Testcases Section

Testcase 1

table 1printed in tcl wiki format
quantity value comment, if any
testcase number:1
5100.0 :t1 initial temperature degrees centigrade
0.1 :t2 final temperature degrees centigrade
1.5e-6 :thermal defusivity meters/sec*sec
0.04 :alpha degrees centigrade per meter
109384453.042 :optional
109384453.042 :answers: time years
109384453.042 : time years
109.384 : time million years


Testcase 2

table 2printed in tcl wiki format
quantity value comment, if any
testcase number:2
2500.0 :t1 initial temperature degrees centigrade
0.1 :t2 final temperature degrees centigrade
1.5e-6 :thermal defusivity meters/sec*sec
0.04 :alpha degrees centigrade per meter
26283158.359 :optional
26283158.359 :answers: time years
26283158.359 : time years
26.283 : time million years


Testcase 3

table 3printed in tcl wiki format
quantity value comment, if any
testcase number:3
5100.0 :t1 initial temperature degrees centigrade
0.1 :t2 final temperature degrees centigrade
1.1e-6 :thermal defusivity meters/sec*sec sandstone value
0.04 :alpha degrees centigrade per meter
149160617.784 :optional
149160617.784 :answers: time years
149160617.784 : time years
149.160 : time million years


References:

  • Stat

Appendix Code edit

appendix TCL programs and scripts

        # pretty print from autoindent and ased editor
        # Historical Kelvin Earth Cooling Calculator 
        # written on Windows XP on eTCL
        # working under TCL version 8.6.x and eTCL 1.0.1
        # gold on TCL WIKI, 10oct2014
        package require Tk
        namespace path {::tcl::mathop ::tcl::mathfunc}
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} {t1 initial temperature degrees centigrade :} }
        lappend names {t2 final temperature degrees centigrade:}
        lappend names {thermal defusivity meters/sec*sec: }
        lappend names {alpha degrees centigrade per meter :}
        lappend names {optional :}
        lappend names {answers: time years : }
        lappend names {time years : }
        lappend names {time million years :}
        foreach i {1 2 3 4 5 6 7 8} {
            label .frame.label$i -text [lindex $names $i] -anchor e
            entry .frame.entry$i -width 35 -textvariable side$i
            grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
      proc pi {} {expr acos(-1)}
      proc kelvinearthtempage {aa bb cc dd ee} { return [ expr (($aa -  $bb)*($aa -  $bb)/ ( $cc * [pi]*  $dd* $dd*$ee))]}
      proc about {} {
            set msg "Calculator for Historical Kelvin Earth Cooling 
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg }       
       proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global testcase_number
            incr testcase_number 
            set side1 [* $side1 1. ]
            set side2 [* $side2 1. ]
            set side3 [* $side3 1. ]
            set side4 [* $side4 1. ]
            set side5 [* $side5 1. ]
            set side6 [* $side6 1. ]
            set side7 [* $side7 1. ]
            set side8 [* $side8 1. ] 
            set temp_1  $side1
            set temp_2  $side2
            set defusivity $side3
            set alpha $side4
            set seconds [* 1. 365. 24. 60. 60. ] 
            #set age_of_earth [  kelvinearthtempage 5100 .1 .0000015 .04  31536000.  ]
            set age_of_earth [  kelvinearthtempage $temp_1 $temp_2 $defusivity $alpha  $seconds  ]
            set side5 $age_of_earth
            set side6 $age_of_earth
            set side7 $age_of_earth
            set side8 [* $age_of_earth 1.E-6 ]
                  }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$aa"
            .frame.entry2 insert 0 "$bb"
            .frame.entry3 insert 0 "$cc"
            .frame.entry4 insert 0 "$dd"
            .frame.entry5 insert 0 "$ee"
            .frame.entry6 insert 0 "$ff" 
            .frame.entry7 insert 0 "$gg"
            .frame.entry8 insert 0 "$hh" 
             }
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7 8 } {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 side8 
            global testcase_number
            console show;
            puts "%|table $testcase_number|printed in| tcl wiki format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| testcase number:|$testcase_number | |&"
            puts "&| $side1 :|t1 initial temperature degrees centigrade|   |&"
            puts "&| $side2 :|t2 final temperature degrees centigrade| |& "
            puts "&| $side3 :|thermal defusivity meters/sec*sec| |& "
            puts "&| $side4 :|alpha degrees centigrade per meter |  |&"
            puts "&| $side5 :|optional  |  |&"
            puts "&| $side6 :|answers: time years |  |&"
            puts "&| $side7 :| time years|  |&"
            puts "&| $side8 :| time million years|  |&"
         }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 5100. .1  1.5E-6 .04 100.E6 100.E6 100.E6 110.}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 2500.0 .1 1.5E-6 .04   25E6  25E5 25E5 26. }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 5100.00 .1  1.1E-6 .04 150E6  150E6  150E6 150. }
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command about
        ::ttk::button .cons -text report -command { reportx }
        ::ttk::button .exit -text exit -command {exit}
        pack .calculator  -in .buttons -side top -padx 10 -pady 5
        pack  .clearallx .cons .about .exit .test4 .test3 .test2   -side bottom -in .buttons
        grid .frame .buttons -sticky ns -pady {0 10}
        . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
        wm title . "Historical Kelvin Earth Cooling Calculator "


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Comments Section edit

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