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

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.