An Application of Spline and Piecewise Interpolation to Heat Transfer (Cubic Case)

Abstract

An Application of Cubic spline and piecewise interpolation formula was applied to compute heat transfer across the thermocline depth of three lakes in the study area of Auchi in Edo State of Nigeria. Eight temperature values each for depths 1m to 8m were collected from the lakes. Graphs of these temperatures against the depths were plotted. Cubic spline interpolation equation was modelled. MAPLE 15 software was used to simulate the modelled equation using the values of temperatures and depths in order to obtain the unknown coefficients of the variables in the 21 new equations. Three optimal equations were found to represent the thermocline depth for the three lakes. These equations were used to obtain the thermocline gradients......