Forced convection

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