Question

1. (25 pts) Answer the following conceptual questions. Write down full explanations and derivations on a clean piece of paper. h, 8 h(x) 80) 1 a. The effect of transition from laminar to turbulent flow on local velocity boundary layer thickness, 8(x) and local convection coefficient, h(x) for steady flow over an isothermal plate is illustrated in the following figure. Why does the convection coefficient decrease with x in the laminar region? How would the local heat flux change with x within the laminar region? How would it change in the turbulent region? MT T. Laminar Turbulent Transition 1 b. In the case of external flow convection what is the film temperature? Does it change with location in case of isothermal surfaces exposed to forced convection? 1 c. Under what conditions is the average convection heat transfer coefficient for internal flow in a pipe a constant (independent of the Reynolds and Prandtl numbers)?

Answer 1

1 a is easy to In laminar flow over flat plates fluid motion Away from the surface necessitated by the Slowing of the fluid rear the wall as the boundary layer groue 2 the a disuction, In laminas boundary layer, the fluid flow & highly ondered and it is dersity Stream - lines along which fluid moves. As the boundary layer thickness and growe that velouty gradient at g-o decalare in the stream wise direction Cie, in increasing direction. So as boundary lays thickers, the connection Coelhoone tecnici es Heat flum Convective heat transfer Coefficient at that location x 2 is directly proportional to the Q = has CTs - Ta ) Nux= hair 0.5 1/3 Pr P >0.6 LAMINAR = 0.332 Rex 0.8 TURBULENT K Nu hrix K 0.0296 Ren 2 Ps 0.6 L P L 60 5x105 a Reciot for Laminat 005 0.5 R Rexo -0.5 x are ha a and hence ie, ha is infinite at leading edge and decrease by factor a in flow direction higher in turbulent flow than laminas flow. It is due to irregular and it Characterized by random Local hat transter coefficents highly

30 motion toward the Much of the mixing of relatively large parcels of fluid. Mixing orthin the boundary byer carries high speed fluid solid surface and transta Slower moving fluid Frother into the free stream promoted by streamwise Streets, which are genoured ittently near the flat plate. So, hence the heat flux alo. & the QAT film temperature Vortius called ) intermi o 4 b. In case of enternal flow connection, is the authoretic average of the surface and the Pare-stream temperatures Ist Ta Ts 2 ie, the No, mean film temperature ducenot voory with location in case of isothermal surfaces exposed to forced to account the convection. It is Variation of fluid temporature with in the thermal boundary layer, fluid temperature Varies in the thermal Bh from Is at sus face to Ta at the outer edge of boundary. So here the feast properties vary with temperature and thus with position across the boundary layer, So to account for the Variations are evaluated at also fluid properties film temperature

TS-Tm at ar 1 c. The thomally fully developed region of a pipe shows Convective heat trarstes Constant value of local Coefficent For hy broly mamically freely developed eve: duan) U=Ula) =0 on . in the For thermally fully developed case Ts (2) - 7(aa) T(A) - Tolo) e velocity profile remains unchanged hydbodynami celly filly developed sejeon, Similarly for fully developed thermal flow : a Is-T IST is dependent of a . anlTs-Tm hence 0 Is-Tom 2 1 - 1 - 6/8) laat BBC So å = he (TST) = kar lack Then a I-I is also independent of n. 38 L TS-TmJ Is-T R=R & fex .) Torto Con K ha ОТ 28 Dorf & fom. is the [Xe]: Entry length Oi seria which is used find whetha fully developed on not.