Numerical Study of Prandtl Number Disparity on Fluid Flow Through a Heated Pipe

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Numerical Study of Prandtl Number Disparity on Fluid Flow Through a Heated Pipe

Stephen I. Okeke1*, Chukwuka G. Ifeoma2
1Department of Mathematics/Statistics, David Umahi Federal University of Health Sciences, Uburu, Ebonyi State, Nigeria.
2Department of Mathematics/Statistics, Federal Polytechnic of Oil and Gas, Bonny Island, Nigeria.
*Corresponding Author
Received: 06 June 2023; Revised: 16 June 2023; Accepted: 22 June 2023; Published: 22 July 2023

Abstract: – This paper examined the phenomenon known as Prandtl Number disparity numerically on fluid flow through a heated pipe using a statistical technique. Prandtl Number disparity is an observed difference in the Prandtl Number of a fluid when passing through a variety of shapes as a pipe or tube. The Statistical Package for the Social Sciences (SPSS, version 20) tool simulated the data precisions by investigating the regression model for the Prandtl Number. The R values showed the relationship between the observed values and the predicted values while the R2 values indicated how much of the total disparities in the thermal conductivity, specific heat capacity, viscosity, density and Prandtl Number were described by the temperature. For the quadratics case; the R2 values were found to be: 99.8%, 99.5%, 92.1%, 100% and 90.4 % respectively. The quadratic Prandtl Number model was approximated to be Pr(T,ϵ)=0.083+4.636E-007T^2+ϵ for the bound |Pr(T,ϵ)-Pr(T)|≤M. Various plots were shown for the observed data, linearity, quadratics and interpolation lines. The significance column in the ANOVA table indicated that the regression model predicted the dependent variable significantly well. In each case, p<0.001 which highly significantly predicted the outcome variable; that it is a good fit for the data. The significance of the Prandtl Number is that when Pr<1, the conductive heat transfer is a more dominant occurrence. Hence with the numerical values of Prandtl Numbers, heat diffused faster for the fluid.

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Keywords: Prandtl Number, Fluid Flow, Temperatures, Regression Model and Interpolation.

I. Introduction

Prandtl Number is a dimensionless number that represents the ratio of kinematic viscosity coefficient to thermal diffusion coefficient of a fluid. The Prandtl Numbers of fluids range from less than 0.01 for liquid metals to more than 100,000 for heavy oils. Liquid metals are a special class of fluids with very low Prandtl Numbers. The very low Prandtl Number is due to the high thermal conductivity of these fluids, since the specific heat and viscosity of liquid metals are very comparable to other common fluids. The Prandtl Numbers of gases are about 1, which indicates that both momentum and heat dissipate through the fluid at about the same rate. Heat diffuses very quickly in liquid metals (Pr <1) and very slowly in oils (Pr >1) relative to momentum (Yunu & Afhin, 2015).

The Prandtl Number dictates the amount of heat transfer that can occur from the walls of the shape to the fluid. This research seeks to answer the question of how Prandtl Number disparity affects fluid dynamics. The method numerically showed the Prandtl Number disparity on fluid flow through a heated pipe using a statistical technique with the view of ANOVA which were not found in other related studied literatures.

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