, ▁among ▁others ▁in ▁the ▁ 1 9 6 0 s , ▁began ▁to ▁investigate ▁heat ▁transfer ▁as ▁a ▁couple d ▁problem . ▁At ▁that ▁time , ▁many ▁other ▁research ers ▁▁▁▁▁ ▁started ▁to ▁solve ▁simple ▁problems ▁using ▁different ▁approaches ▁and ▁joining ▁the ▁solutions ▁for ▁body ▁and ▁fluid ▁on ▁their ▁interface . ▁A ▁review ▁of ▁early ▁conjug ate ▁solutions ▁may ▁be ▁found ▁in ▁the ▁book ▁by ▁Dorf man . ▁ ▁Con j ug ate ▁problem ▁form ulation ▁The ▁conjug ate ▁con ve ct ive ▁heat ▁transfer ▁problem ▁is ▁govern ed ▁by ▁the ▁set ▁of ▁equations ▁consisting ▁in ▁conform ity ▁with ▁physical ▁pattern ▁of ▁two ▁separate ▁systems ▁for ▁body ▁and ▁fluid ▁domains ▁which ▁incorpor ate ▁the ▁following ▁equations : ▁ ▁Body ▁domain ▁Un st ead y ▁or ▁steady ▁( L ap lace ▁or ▁Po isson ) ▁two - or ▁three - dimensional ▁condu ction ▁equations ▁or ▁simplified ▁one - dimensional ▁equations ▁for ▁thin ▁bodies ▁ ▁Fl uid ▁domain ▁ ▁For ▁l amin ar ▁flow : ▁Nav ier – Sto kes ▁and ▁energy ▁equations ▁or ▁simplified ▁equations : ▁boundary ▁layer ▁for ▁large ▁and ▁cre eping ▁flow ▁for ▁small ▁Reyn olds ▁numbers , ▁respectively . ▁ ▁For ▁tur bul ent ▁flow : ▁Reyn olds ▁average ▁Nav ier – Sto kes ▁and ▁energy ▁equations ▁or ▁boundary ▁layer ▁equations ▁for ▁large ▁Reyn olds ▁numbers ▁ ▁Initial , ▁boundary ▁and ▁conjug ate ▁conditions ▁ ▁Cond itions ▁specifying ▁the ▁spatial ▁distributions ▁of ▁variables ▁for ▁dynamic ▁and ▁thermal ▁equations ▁at ▁initial ▁time ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁▁▁▁▁▁▁ ▁No - s lip ▁condition ▁on ▁the