Forward Time Center Space Algorithm for Mathematical Model Solution of Heat Transfer
Abstract
Heat transfer is a physical phenomenon that can be represented in the form of a mathematical model. In this study, heat transfer occurs in a viscoelastic fluid through an elliptic cylinder surface with free convection flow. The mathematical model of heat transfer is obtained from partial differential equations and solved numerically using the Forward Time Center Space (FTCS) scheme. Numerical solution is carried out based on an algorithm compiled by an iterative process according to a predetermined point. The iteration process is carried out until it produces a stable and convergent value. Furthermore, the algorithm is implemented into the Matlab programming language with the influence of a heat variable, namely the Prandtl number (Pr). Several test results that have been carried out during the iteration process have shown that the FTCS scheme is stable along the space and time grid. In addition, this scheme shows that the obtained difference equations are proven to produce consistent and convergent graphs. Based on the resulting graph, the greater the value of the Prandtl number, the smaller the resulting temperature. This is in accordance with the definition of the Prandtl number, which is the heat determining parameter which is the ratio between the kinematic viscosity value and the heat diffusivity, so that the large Prandtl number can inhibit heat transfer that occurs on the surface of the object.
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