In the case o f a real plate of finite thickness, a pressure gradient will exist but this should only be significant in the immediate vicinity o f the leading edge. Therefore, in obtaining the boundary layer solution for flow over a flat plate, it will be assumed that the velocity outside the boundary is equal to U l and that the pressure gradient is everywhere equal to zero. But the conditions outside the boundary layer are assumed to b e those that exist in inviscid flow over the body considered and the pressure gradient in the boundary layer is assumed to be equal to that existing in this/outer inviscid flow. As a result, the pressure gradient, d p /dx, is everywhere zero. pl~te o f zero thickness is that the velocity is everywhere the same and equal to the undisturbed free stream velocity, U l, i.e., that, i f the effects o f viscosity are ignored, a f lat plate aligned with the flow will have no effect on the flow. In writing these equations it has been noted that the solution for inviscid flow over a flat. As a result o fthese assumptions, the equations governing the problems are:Īu + av = 0 ax ay au au u -+vax ay aT aT u a x + v ay I t will further be assumed that the flow is two-dimensional which means that the plate is assur,ned to b e wide compared to its longitudinal dimension. I t will be assumed that the Reynolds number is large enough for the boundary layer assumptions to be applicable. 83Ĩ 4 Introduction to Convective Heat Transfer Analysisį low whose size is large compared to the dimensions o f the body T he flow situation 'lis thus as shown in: Fig. S IMILARITY SOLUTION F OR F LOW OVER AN I SOTHERMAL PLATEĬonsider the flow o f a fluid at a velocity o ( U l over a flat plate whose entire surface is held at a uniform temperature o f Tw whidh is different from that o f t he fluid a head. Also, solution~ to the full Navier-Stokes and energy equations wi~l b e d ealt with only relatively tmefly, t he majority o f the solutions considered being based on the use o f the boundary layer equations. In addition, dissipation effecfs in the energy equation will b e neglected in most o f this chapter, these effects being briefly considered in a last section o f this chapter. In all the solutions given in the present chapter, the fluid properties will b e assumed to b e constant a nd the flow will b e assumed to b e two-dimensional. This flow is good model o f m any situations involving flow over fins that are relatively widely spaced. For example, flow pver a flat plate aligned with the flow will b e extensively considered. Some o f the flows considered, although apparently highly i dealized,are, however, good models o f situations that are o f great practical importance. The problems chosen to illustrate the methods o f solution are not directly, in most cases, o f great practical significance but they serve to illustrate t4~ basic ideas involved in the solution procedures. External flows involve a flow, which i s essentially infinite in extent, over the outer surface o f a body as shown in Fig. T he purpose o f this chapter is to illustrate some o f the ways in which the equations derived in the previous chapter can b e u sed to obtain heat transfer rates for situations involving external laminar flows. Some Solutions for External Laminar Forced Convection
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |