The document discusses forced convection heat transfer and drag forces in external fluid flows. It covers key concepts like drag force, lift force, friction drag, pressure drag, boundary layers, Reynolds number, heat transfer coefficients, and flow over different body shapes like flat plates, cylinders, spheres, and tube banks. The document provides information on factors that influence drag and heat transfer for different flow configurations and the relationships between drag, pressure, velocity, fluid properties, surface roughness, and body geometry.

1. Forced-Convection
HeatTransfer

2. Drag and Heat
Transfer
in External
Flow
 Fluid flow over bodies causes: - drag force – lift – upward draft –
cooling
 Reliance on experimental data – using computers
 Free-stream velocity - far
 Upstream velocity / approach velocity – uniform and steady
 Thin bodies vs blunt bodies
 Fluid velocity – 0 at surface to free-stream velocity

3. Friction and
Pressure Drag
1
 Drag is the force a flowing fluid exerts on a body in the flow direction.
 Normal pressure and tangential shear forces on fluids
 Lift is the sum of the components of the pressure and wall shear forces
in the normal direction to flow which tend to move the body in that
direction.
 Drag and lift – pressure and shear (skin friction) forces
 Forces vs body positioning :parallel & normal flat plate , slender body
(wings)
 Drag force depends on: density of fluid, upstream velocity, size, shape,
orientation of body
 Drag coefficient, 𝐶𝐷;
 Where A – frontal area, 𝜌 – density, - - upstream velocity, 𝐹𝐷 - Drag
Force
 Drag coefficient - Shape of body or Reynolds No. + surface roughness

4. Friction and
Pressure Drag
2
 The drag force is the net force exerted by a fluid on a body in the direction
of flow due to the combined effects of wall shear and pressure forces.
 Skin friction drag / friction drag (shear stress) vs pressure / form drag
(shape of body)
 𝐶𝐷 = 𝐶𝐷,𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛+ 𝐶𝐷, 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒
 Friction drag vs Normal surface ; Friction drag vs Parallel surfaces
 Parallel flow over flat plate, 𝐶𝐷 = 𝐶𝐷,𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛= 𝐶𝑓
 Drag coefficient; - Area of both surfaces
 Friction drag vs viscosity : Pressure drag = 0 for steady flow/horizontal flow
 Total drag, inviscid fluids = 0; friction & Pressure drag = 0 at steady flow
 Friction drag vs surface area vs Reynolds number – lamina/turbulent flow
 Pressure drag – blunt bodies vs streamlined bodies + thin (P Δ with depth)
 Pressure (high vs low): Separation area vs pressure drag : velocity : wake
region – velocity : viscous effects

5. Parallel Flow
Over Flat
Plates
 Upstream velocity
 Temperature 𝑇∞
 Boundary layer (velocity or thermal)
 Factors affecting lamina to turbulent flow: surface geometry, surface
roughness, upstream velocity, surface temperature, and the type of
fluid
 Reynolds number
 𝑅𝑒𝑐𝑟 = 5 × 105
; 105
𝑡𝑜 3 × 106
 Friction coefficient
 Heat transfer coefficient – Nusselt Number (Cond + Conv)
 Film temperature – The arithmetic average of the surface and the
free-stream temperatures.
 𝑄 = ℎ𝐴𝑠 𝑇𝑠 − 𝑇∞
 𝑻𝒇 =
𝑇𝑠+𝑇∞
𝟐

6. FlowAcross
Cylinders and
Spheres
 Shell-and-tube heat exchangers
 Sports – tennis, soccer, golf etc.
 Reynolds number, lamina, turbulent flow
 where x is D (external diameter)
 Pressure difference vs fluid velocity (front and behind)
 Nature of flow – total drag coefficient –(friction & pressure)
 Drag force = Friction drag – low Re ; Pressure drag – high Re
 Flow separation at 80 and 140 degrees; wake; pressure drag
 Decrease in friction drag increases velocity - flying
 Effect of surface roughness (Streamlined bodies, increases drag; Blunt
bodies e.g. cylinder, sphere, decreases drag coefficient) narrow wake;
reduces pressure drag * mind the Re
 Heat transfer coefficient vs flow – (Nuθ decreases with increasing θ,
min at 80 degrees then increases with increase in θ, then decreases) -
film temperature

7. FlowAcross
Tube Banks  Condensers and evaporators of power plants, refrigerators, air
conditioners
 Shell-and-tube heat exchanger
 Flow through
 Flow over
 In-line or staggered arrangement
 Pressure drop

8. Ref:
 Yunus A. Cengel, (2000). HeatTransfer,A PracticalApproach,
Second Edition.
 Chapter 7