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### CONVECTION

INTRODUCTION

• Convection is the mode of heat transfer which involves the motion of the medium that is involved.
• Convection heat transfer requires an energy balance along with the analysis of the fluCid dynamics of the problems considered.
• For basic understanding of convection heat transfer, some basic relations of fluid dynamics and boundary layer analysis are necessary. This chapter deals the concept of convection heat transfer in detail.

FLOW OVER A BODY
• The heat transfer by convection is strongly influenced by the velocity and temperature distribution of the immediate neighborhood of the surface of a body over which a fluid is flowing.
• For simple analysis of heat transfer involving convection, the velocity and temperature distribution at the boundary surface can be known by introducing the boundary - layer concept.
• Two different types of boundary layers are considered for this purpose viz., velocity boundary layer and thermal boundary layer.

VELOCITY BOUNDARY LAYER
• Consider a fluid flowing over a flat plate as shown in Figure 1. Let u∞ be the velocity of the fluid parallel to the plate surface at the leading edge of the plate at x =0.
• When there is no slip at the wall surface, the fluid moving, along the x direction that is in contact with the plate has no velocity. Thus the components of velocity   u(x, y) ≡ u retards along the x direction.
• Hence at the plate surface at y = 0 velocity u becomes zero. This retardation effect reduces considerably on the fluid moving at a sufficiently higher level (y - direction) and at one point the retardation effect is completely negligible.
• The velocity of the fluid at distance y = δ(x) from the surface of the plate where the axial velocity component u is 99 percent of the free stream velocity u∞.
• The locus of such points where u =0.99 u∞ is known as velocity boundary layer δ(x).
• The flow over the plate results in separation of flow field into two distinct regions.

Boundary layer region:

In this region the velocity gradients and shear stress are large due to the rapid variation of the axial velocity component u(x, y) with the distance y from the plate.
Potential flow region:

In this region the velocity gradient and shear stress are negligible. This region is the region outside the boundary layer.

•     This value is dependent on the surface roughness and the turbulence level of the free stream. In the turbulent boundary layer next to the wall, there is a very thin layer called viscous sub-layer in which the viscous flow character is retained by the flow.
•     The region adjacent to the viscous sub-layer is known as buffer layer. In this layer exists fine-grained turbulence and the mean axial velocity increases rapidly with the distance from the wall. The buffer layer is followed by turbulent layer with large scale turbulence.
•     The change in relative velocity with the distance from the wall is very little in this layer. Curved body Consider a curved body on the surface of which the fluid flows.
•     For a curved body the x co-ordinate is measured along the curved surface of the body starting from the stagnation point as shown in Fig. 2. The y co-ordinate is normal to the surface of the body.

•     In the above case, the free stream velocity is not constant but varies with distance along the curved surface. The thickness of boundary layer θ(x) increases with distance x along the surface. After some distance x, the velocity profile u(x, y) exhibits a point of inflection in which a y =0 at the wall surface.
•     This behavior is attributed purely to the curvature of the surface. Beyond this point flow reversal takes place and the boundary layer is detached from the surface. Beyond this point of flow reversal, boundary layer analysis is not applicable and flow patterns become very complicated.

DRAG COEFFICIENT

• Consider a boundary layer having a velocity profile u(x, y). The viscous shear stress 1"x acting on the wall at any given position x is given by,