Unsteady Conjugate Heat Transfer Associated with a Translating Spherical Droplet: A Direct Numerical Simulation

Abstract

Thermal behavior of a liquid drop moving in an incompressible fluid of infinite extent is investigated numerically. Dynamical equations describing the temporal evolution of the flow and temperature fields of dispersed and continuous phases are solved by a hybrid spectral scheme in conjunction with the influence matrix technique to resolve the lack of vorticity boundary conditions. Both Chebyshev and Legendre polynomials are employed to expand the flow variables and temperature in the radial and angular directions, respectively. With the aid of the Galerkin and collocation methods, together with the first-order backward Euler time differencing, the governing partial differential equations reduce to a nonlinear system of algebraic equations. Numerical results reveal a discrepancy between quasi-steady and fully transient analyses at high Peclet numbers.