Question

(a) Consider a flow through a circular pipe. If the fluid enters the pipe with a uniform velocity (Uin) and uniform temperature (Tin ), draw the radial temperature distribution T(r) at three distinct axial locations if the pipe is subjected to uniform heat flux along its surface. Do not forget to draw the boundary layers. Identify the developing and developed regions for this flow.

Answer 1

decout 22 O = (stordr) 36 ur [rem) + 27 de dze, in = (anodr) 14 ur). Ta into an element- (der) Rare of heat conduction dT -k (28 da). Rare of heat condction out element- - k 21 (rear) dae redr ƏT + 8т. Tuy Heat carried away by the (doc) 8u at arcp IT dze da B4 the energy balanec, | dra fluid dortar doc + - Aalto da at ar 1o afir dx d? & karir da 2T of k 27r da 8 a na a x2 & k apr da 22 doT, dhe euzminds suorat on arz an over k( 37 [ Negleeting Cart foron of lyse] ár - Since the heap flon the conface is consferde miform, the fluid temperature inor eases cinearly with asfare 27 = consfurt Boundary Condition: DT = constant roo M ARTER KIDER The boy (597) - 2012 27 / (+ 1 - 2 ) + 9 2.27

-> ОТ o 11 OT door at a YR OT = T(, 2) ( 2 - 2 R) + 9 mi to an condition Applying boundary de To a centreline ferry poration ro, T=TO C = To uo .: T (0, 2) = no T an 8 [ 4 ] Yo At ar z T2.3 Tone 4/63460] DI (44) no. s Two (2) - Tb (x) (4u) Twca) - Toens £ ; T (0, 2) formen)[+131] [) (133) Teremo Tscush AL x- & ; (1, 2) = (48) le Esterone (developing Entrace developed region IT-T) region ((Tw (n)) surface ter/ Bulk tepul (Tylnit Distance from enfrance (ng