Numerical modelling of unsteady convective–diffusive heat transfer with a control volume hybrid method

Abstract

Presented in this paper is a numerical methodology for the solution of the parabolic governing partial differential equation that describes unsteady advection-diffusion heat transfer. The formulation presented here is shown to be free from the numerical oscillation commonly associated with advection-diffusion heat transfer regardless of the value of the Peclet number. The formulation involves the absorption of the advection term in the unsteady heat equation into the capacitance term. This process is achieved with the use of a control volume methodology applied to each nodal element on a finitevolume mesh. This is shown to ensure that spurious energy losses and gains are avoided and provides for consistency between temperature and energy change. This approach provides unconditional stability and it is shown that good accuracy is achievable with relatively large time-steps.In order to highlight the features of the approach it is compared against those of benchmark numerical schemes. Detailed analysis is performed for the 1D semi-infinite moving solid problem for which an exact solution is available and for a realistic engineering heat transfer problem. Oscillation free results are achieved at good accuracy for a wide range of Peclet numbers and problems considered.

Dynamic buckling of an imperfect elastoplastic beam subjected to an impulsive load analyzed using transport equations

“…refer to a material reference system, a spatial reference system and a computational reference system coordinate respectively. The relations between the material derivative and an arbitrary Lagrangian-Eulerian derivative with respect to the spatial derivative are defined by the following expressions [1][2][3][4][5][6][7];…”

“…By considering as arbitrary space, the general form of continuity, energy and momentum equations are derived as [1][2][3][4][5][6][7] ( )…”

“…Davey used the transport equations in the field of modeling heat transfer in the presence and absence of boundary and material discontinuities [1][2][3][4][5][6][7]. The performance of the capacity control methods for convection-solidification problems was investigated by Davey [1].…”

“…The development and application of a control volume capacitance method to combined mass transport and solidification problem were studied [2][3]. Rodriguez et al [4][5] used finite difference method to solve the transfer equations governing on diffusion-convection equations and made some improvement on the standard control volume capacitance method. Application of nonphysical variables in isothermal solidification problem was studied by Davey and Mondragon [6].…”