The　laminar　heat　transfer　in　the　thermal　entrance　region　in　round　tubes,　which　has　a　variable　surface　heat　flux　boundary　condition,　is　analytically　studied.　The　results　show　that　the　heat　transfer　coefficient　is　closely　related　to　the　wall　temperature　gradient　along　the　tube　axis.　The　greater　the　gradient,　the　higher　the　heat　transfer　rate.　Furthermore,　the　coordination　of　the　velocity　and　the　temperature　gradient　fields　is　also　analysed　under　different　surface　heat　fluxes.　The　validity　of　the　field　coordination　principle　is　verified　by　checking　the　correlation　of　heat　transfer　coefficient　and　the　coordination　degree.　The　results　also　demonstrate　that　optimizing　the　thermal　boundary　condition　is　a　way　to　enhance　heat　transfer.