The objective of the research is to empirically develop correlations between convection heat transfer and these above mentioned nondimensional 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)

T_{s}

surface temperature

T∞

Temperature bulk air

L

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

T_{2}

Temperature of the top wall

L_{1}

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. Ra_{L}^{x}_{ }. Pr^{y }. (L_{1}/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 {Gr_{L}. Pr} (Nusselt Number is a function of Grash of & Prandtl number)
Ra = Gr_{L}. Pr