The control volume formulation to model the convective–diffusive unsteady heat transfer over the 1-D semi-infinite domain

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];…”

“…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].…”

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

“…The principal novelty of the method proposed here is the introduction of non-physical thermal conductivity k * and heat source q * in order to prevent the non-physical specific heat capacitance c * from becoming non-realisable (i.e. non-positive), which is possible for the methods proposed in references [14,15]. The approach proposed here couples transport control volume theory and the central difference scheme to ensure integral conservation of energy over each nodal-control volume.…”

“…The work builds on the ideas underpinning the control volume capacitance method (CVCM) [14] applied to the FEM and those in Ref. [15] applied to central finite difference scheme. The principal novelty of the method proposed here is the introduction of non-physical thermal conductivity k * and heat source q * in order to prevent the non-physical specific heat capacitance c * from becoming non-realisable (i.e.…”