Empirical Co - Relations approach for solving problems of convection 10:06:43

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Empirical Corelations for Free Convection

Use T f or T b for getting various properties like Re = VL c / ν β = thermal expansion coefficient α = thermal diffusivity v = kinematic viscosity C p = Specific heat at const press. k = thermal conductivity of air P r = Prendtle Number 10:06:44

An uninsulated steam pipe of diameter 0.5 m is used to transport high temperature steam from one building to another. The pipe outside surface temperature is 150 C and it is exposed to ambient air at 4 C. Air moves over the pipe in cross flow with a velocity of 5 m/s. What is the heat loss per unit length of the pipe? Properties of Air (350 K, 1 atm): = 20.9 10-6 m 2 /s, k = 0.030 W/m-K, Pr = 0.70. V, T Ts Nu 0.3 0.62 Re Given: D = 0.5m, T s = 4 o C, T = 150 o C, v = 5m/s Uninsulated steam pipe find q per unit length =? 0.5 Pr 1/3 (1 (Re / 282000) 1176 0.4 Pr 5/8 2/3 ) 4/5 10:06:44

Assumptions: Steady flow Constant property evaluated at 77deg C Steam pipe outside surface temp is constant Properties: At T f = (T s + T ) / 2 = 77 C, Pr = 0.7; ρ = 0.995kg/m 3 ; C p = 1009 J/kgK; μ = 208.2* 10-7 Pa.s; ν = 20.92*10-6 m 2 /s; k = 0.03W/mK Re = VD/ ν = 5 X 0.5 / (20.92*10-6 ) = 119502.9 Nu = 0.3+0.62 Re0.5 Pr 1/3 (1+ (Re / 282000) 5/8 ) 4/5 / (1176+0.4/(Pr) 2/3 ) = 241.52 Nu = h D/ k = 241.52 h = 241.52 x 0.03 / 0.5 = 14.4912 W/m 2 K q = h П D (T s -T ) = 14.4912 x П x 0.5 x (150-4) = 3323.35 W/m..Ans 10:06:44

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Case 1

Case 2

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Forced Convection. Fluid flow over solid bodies frequently occurs in practice, and it is responsible for numerous physical phenomena such as the drag force acting on the automobiles, power lines, trees, and underwater pipelines; the lift developed by airplane wings; upward draft of rain, snow and dust particles in high winds; and the cooling of metal or plastic sheets, steam and hot water pipes, and extruded wires. Therefore, developing good understanding of external flow and external forced convection is important in the mechanical and thermal design of many engineering systems such as aircraft, automobiles, buildings, electronic components, and turbine blades.

The force a flowing fluid exerts on a body in the flow direction is called drag. A stationary fluid exerts only normal pressure forces on the surface of a body immersed in it. A moving fluid, however, also exerts tangential shear forces on the surface because of the no-slip condition caused by viscous effects. Both of these forces, in general, have components in the direction of flow, and thus the drag force is due to the combined effects of pressure and wall shear forces in the flow direction. The components of the pressure and wall shear forces in the normal direction to flow tend to move the body in that direction, and their sum is called lift. In general, both the skin friction (wall shear) and pressure contribute to the drag and the lift. 10:06:50

The Drag Force F D depends on the density ρ of the fluid, the upstream velocity v, and the size, shape, and orientation of the body, among other things. The drag characteristics of a body is represented by the dimensionless drag coefficient C D. C D F D 1 v 2 2 A where A is the frontal area (the area projected on a plane normal to the direction of flow) ; e.g. The frontal area of a cylinder of diameter D and length L, for example, is A = LD. The drag coefficient is primarily a function of the shape of the body, but it may also depend on the Reynolds number and the surface roughness. The part of drag that is due directly to wall shear stress Ʈ w is called the skin friction drag (or just friction drag) since it is caused by frictional effects, and the part that is due directly to pressure P is called the pressure drag (also called the form drag because of its strong dependence on the form or shape of the body).

The friction drag is zero for a surface normal to flow, and maximum for a surface parallel to flow. Therefore, for parallel flow over a flat plate, the drag coefficient is equal to the friction drag coefficient, or simply the friction coefficient. C D = C f C D = C d pressure 10:06:50

The experimental data for heat transfer is often represented conveniently with reasonable accuracy by a simple power-law relation of the form

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Constant properties evaluated at 140 F by assuming there is no temperature drop in plastic sheet.

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Constant properties evaluated at mean film temperature. Radiation losses is negligible.

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