Mitigating the requirement of poles in incompressible diffusive-advective heat transfer problems using the decomposition of derivatives and the multiple reciprocity techniques

The Derivatives Decomposition Technique is presented, applied in the context of the Direct Interpolation Boundary Element Method, to solve the incompressible diffusive-advective heat transfer equation. Despite achieving better accuracy, the primary objective is to develop an accurate model that uses the decomposition technique, aiming to mitigate the need for internal poles to solve the domain integral related to advective effects. Thus, the model is derived in conjunction with the well-known Multiple Reciprocity Method, which is first applied to the diffusive-advective equation. Within the contributions of this research, the significant role of the derivatives technique must be highlighted, as the velocity field is usually expressed in terms of Cartesian coordinates, which commonly requires radial approximations that compromise its precision. However, such components can be expressed in terms of standard and tangential components. Given that the derivatives of radial functions along the boundary are more precise than the normal derivatives, and that these normal derivatives can be included and solved directly in the matrix equation, the use of the Multiple Reciprocity Method becomes viable and advantageous, also in diffusive-advective models. This combined methodology yields a model that mitigates the requirement for internal poles for diffusive-advective problems, particularly at low Péclet numbers.