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Math
Forced Laminar Flow Over an Isothermal Plate
Air (or any other fluid) forced over a hot plate will remove heat from the plate according to the rules of forced convection. If the air's velocity is slow enough and the plate length short enough, we can expect the flow in the boundary layer near the plate to be laminar.

Use this calculator to calculate the heat rate removed from the plate under such a laminar flow assumption. We also assume that the plate is maintained at a constant temperature (i.e. isothermal). (The default calculation is for a relatively hot, small rectangular plate immersed in a medium velocity air stream at room temperature, with answers rounded to 3 significant figures.)

Inputs
  Length of plate, L:    
  Area of plate, A:    
  Temperature (constant) of plate, Tw:    
  Fluid free-stream velocity, uinf:    
  Fluid free-stream temperature, Tinf:    
  Fluid viscosity, m:    
  Fluid density, r:    
  Fluid specific heat, cp:    
  Fluid conductivity, k:    
Answers
  Reynolds Number, Re:  3.04 × 104  
  Prandtl Number, Pr:  0.683  
  Nusselt Number, Nu:  102  
  Heat Transfer Coefficient, h:  12.7  W/m^2-K
  Heat Transfer Rate to Air, Q:  22.9  W
  Film Temperature, Tf:  47.5  C
 
Equations Behind the Calculator
The heat tranferred from a hot isothermal plate to a forced laminar air stream is given by Newton's Law,
where Tw and are the wall and fluid free-stream temperatures, respectively. The convection heat transfer coefficient for the plate hplate is related to the plate Nusselt Number NuL by,
In this equation, k is the fluid's thermal conductivity, and L is the length of the plate. The Nussult Number for this problem is given by,
where Pr is the fluid Prandtl Number, and ReL is the fluid/plate Reynolds Number.

See the theory page for more information on this problem's development.

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Metal 3D Printing Design Guide

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Optimize your designs, reduce machining time, and lower your costs.

Mechanical Engineers Outlook

Guide for those interested in becoming a mechanical engineer. Includes qualifications, pay, and job duties.

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