I k,l,J 



kiln AT 



then AT = AT,U+T-rf °r AT, - 1~ i • (9) 



Mi 



Then (7) becomes: d(Q l + Q T ) k I AT (10) 



1 jj^ 



Substituting Q|=/o-Kl. into ( 10 ) ^o denotes ice density) 



p,k£u^L s _J^L_ (11) 



' dt dt l.hSJk] 



^ K { l + ^} 1 ? dl ' + { 1 + ^} 1 S dQ T ==k J ATdf (12) 



/»l|(h) A Kk, A (h) r Q T (h) 



P] k[ '^(zjdiiiz)^ r 'i s di,(z)+ r T i,(z)dQ T (z) + 



•'o s "'0 "'O 



ii- r T i s dQ T (z)=k r r Mdt 



K s ^0 "'t,, 



(13) 



,Qjh) 



^l^(h)/^l s l.(h) + r T l 1 (Z)dQ T (Z) + 4 L l s Q T (h) = k i / et (T F -T)dt.( U) 



*- s »0 S </f 



