Figure 9 depicts the influence of

Prandtl number Pr.

where [[sigma].sub.[epsilon]] is the

Prandtl number of turbulent kinetic energy dissipation rate, [C.sub.[epsilon]1] and [C.sub.[epsilon]2] the constants of turbulent model, respectively.

In the case of convective heat transfer, there are several dimensional parameters that are important, namely Nusselt number, Reynolds number

Prandtl number, and Rayleigh number.

This situation happens when the frequencies' ratio is equal to six in the case of low

Prandtl number or is equal to three in the case of high

Prandtl number, which can be more convenient to be reproduced experimentally, since one can look only for small natural integer frequencies' ratio.

Here Tfr is the freezing point of the base liquid (273.16K).kb is the Boltzmann constant(kb[approximately equal to] 1.38*1023J/K),df is the fluid molecular diameter ,dp is the diameter of nanoparticles (10 nm [less than or equal to] dp [less than or equal to] 150 nm), T is the nanofluid temperature (294[less than or equal to]T(K) [less than or equal to]324), x is the particle volume concentration which is valid for 0.2%[less than or equal to]x[less than or equal to]9%, prf is these

prandtl number of the base fluid, [rho]f and uf are the density and the dynamic viscosity of the base fluid respectively and uB is the nanopr article Brownian velocity which is calculated as the ratio between dp and the time TD= dp2/6D BY assuming the absence of agglomeration.

The P-function of Jayatilleke is expected to be a suitable model for higher

Prandtl number flows (10 and 20), as long as a proper wall [Y.sup.+] (within the logarithmic layer) is ensured.

To solve the governing nondimensional unsteady equations (4) subject to initial and boundary conditions (5), we apply Laplace transform technique for the case of unit

Prandtl number and Schmidt number, as for arbitrary

Prandtl number or Schmidt number, the Laplace transform technique leads to a difficult inverse transformation step (integrand of the Bromwich integral becomes a complicated multivalued function).

The results for velocity and temperature distribution reveal the flow kinematics under the effects of key physical parameters of the problem namely non linear shrinking parameter s, magnetic parameter M, porosity parameter K, mixed convection parameter and

Prandtl number Pr .

Thakare, Parekh (2014) have published a paper aimed towards presenting the CFD study of vortex tube carried out to gain an understanding about influence of thermophysical properties such as thermal diffusivity,

Prandtl number, specific gas constant and thermal conductivity of different gases and turbulence models on its performance.

The Rayleigh number (Ra) is defined as the product of the Grashof number (Gr), which describes the relationship between buoyancy and viscosity within a fluid, and the

Prandtl number (Pr), which describes the relationship between momentum diffusivity and thermal diffusivity.

According to a study by Brethouwer (2011), the turbulent

Prandtl number associated with heat transfer in rotating channels is lower than the typical value of 0.9 for a stationary channel.

In order to investigate the influence of solid particles volume fraction [phi] on the heat transfer characteristics, the Reynolds and

Prandtl number of the nanofluids can be expressed as: