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.

Geometry:

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)

                        Nu

 Nusselt Number

GrL

 Grashof number

Pr

 Prandtl number

Ra

Rayleigh number

C

Constant Coefficient

g

 acceleration due to Earth's gravity

ß

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

Ts

 surface temperature

T∞

 Temperature bulk air

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

D

 diameter

v

 Kinematic viscosity

k

thermal conductivity of the fluid

h

convective heat transfer coefficient

ρ

Density of the fluid

T2

Temperature of the top wall

L1

length of opening

L

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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