Empirical correlation, Chemical Engineering

The objective of the research is to empirically develop correlations between convection heat transfer and these above mentioned non-dimensional in numbers. The simple empirical correlation of Nusselt Number with Grashof/Rayleigh numbers in natural convection from a surface is given by following equation.


Geometric model of cubicle and enclosures with an opening of following dimensions would be constructed using CAD software SolidWorks. Five different sizes of openings (one at a time) are evaluated for convection heat loss. The dimensions of the enclosure, openings and its locations are as follows.

Cubical Enclosure - 5m x 5m x 5m

Opening sizes        - (1mx 5m), (2m x 5m), (3m x 5m) and (4m x 5m)


 Nusselt Number


 Grashof number


 Prandtl number


Rayleigh number


Constant Coefficient


 acceleration due to Earth's gravity


 volumetric thermal expansion coefficient (equal to approximately 1/T, for ideal fluids, where T is absolute temperature)


 surface temperature


 Temperature bulk air

 Distance between hot and cold surface in our case bottom and top surface




 Kinematic viscosity


thermal conductivity of the fluid


convective heat transfer coefficient


Density of the fluid


Temperature of the top wall


length of opening


Total length of the enclosure

Location of opening- On one wall of the enclosure the opening starting from the bottom of the wall

Heat - Bottom surface uniformly heated by a source with 2000W of heat

CFD will be done by ANSYS or Solidworks FlowWorks

Mathematical model:

The target equation is Nu= C. RaLx . Pry . (L1/L)

The value of Nu and Ra obtained for the simulation will be plotted. From this equation we can find the values of C, x and y which will give us the required relation.

The simple empirical correlation of Nusselt Number with Grashof/Rayleigh numbers in natural convection from a surface is given by following equation.

     Nu= f {GrL. Pr} (Nusselt Number is a function of Grash of & Prandtl number)

                        Ra = GrL. Pr

2028_empirical correlation 1.png

632_empirical correlation 2.png

Posted Date: 3/9/2013 2:22:21 AM | Location : United States

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