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The mass transfer from two spheres in tandem to an incompressible fluid flow accompanied by chemical reactions (first-order and second-order irreversible) into the fluid was analysed numerically. Creeping flow was assumed. The spheres have the same diameter, initial concentrations and physical properties. The concentration of the transferring species inside the spheres is considered: (1) constant and (2) spatially uniform and varying in time. The mathematical model equations were solved numerically in bi-spherical coordinates system. The computations focused on the conditions when the interaction between spheres does not influence the mass transfer rate. [ABSTRACT FROM AUTHOR]

The unsteady, conjugate, forced convection heat transfer from a fluid sphere to a surrounding fluid flow in the presence of viscous dissipation has been analysed. The fluid flow inside and outside the sphere was considered laminar, axisymmetric, steady and incompressible. The heat balance equations were solved numerically in spherical coordinates system by a splitting finite difference method. The influence of the Reynolds, Brinkman and Peclet numbers on the heat transfer mechanism and rate was analysed for different values of the physical properties ratios (thermal conductivity ratio, heat capacity ratio, viscosity ratio and density ratio). [ABSTRACT FROM AUTHOR]

The unsteady, conjugate, forced convection heat transfer from a porous sphere embedded in another porous medium has been analysed. Both porous media are fluid saturated. Local thermal equilibrium between the two phases is assumed. The fluid flow inside and outside the sphere was considered axisymmetric, steady and incompressible (Darcy and Brinkman flows). The heat balance equations were solved numerically in spherical coordinates system by an implicit alternating direction finite difference method. The influence of the porous media permeability and sphere Peclet numbers on the heat transfer mechanism and rate was analysed for different values of the physical properties ratios (thermal conductivity ratio and heat capacity ratio). [ABSTRACT FROM AUTHOR]

Abstract: The transient mass transfer from a binary gas bubble to an incompressible liquid accompanied by a chemical reaction into the liquid phase is analysed numerically. Only one of the bubble components transfers into the liquid phase where a first-order, irreversible chemical reaction occurs. The concentration of the transferring species inside the bubble is considered spatially uniform but not constant in time. Creeping flow was assumed. The mathematical model equations were solved numerically in spherical coordinates system. The computations focused on the influence of the Damkohler number and Henry number on the mass transfer rate for Pe =10, 100, 1000 and Da/Pe =0.1, 1, 10. [Copyright &y& Elsevier]

Abstract: Numerical methods are used to investigate the transient mass transfer from a binary gas bubble to an incompressible liquid. The bubble has two components: A – soluble and B – insoluble in the surrounding fluid. The concentration of A inside the bubble is considered spatially uniform but not constant in time. The maximum value of the initial volumetric fraction of A is 0.3. The mathematical model equations were solved numerically in spherical coordinates system. Creeping flow, moderate Re number flow, 10⩽ Re ⩽100, and potential flow around the bubble were assumed. The computations focused on the influence of the initial fraction of A and Henry number on the mass transfer rate for Pe ⩽104. [ABSTRACT FROM AUTHOR]

Abstract: Numerical methods are used to investigate the transient heat transfer from an oblate/prolate spheroid to a steady stream of viscous, incompressible fluid. The temperature of the spheroid is considered spatially uniform but not constant in time. The momentum and heat balance equations were solved numerically in oblate/prolate spheroidal coordinates system. The solutions span the parameter ranges 10⩽ Re ⩽100 (for the oblate spheroid), 10⩽ Re ⩽200 (for the prolate spheroid), Pr =1, 10 and axis ratio ε, 0.1⩽ ε ⩽0.9. The computations were focused on the influence of the axis ratio and volume heat capacity ratio on the heat transfer rate. [Copyright &y& Elsevier]

Abstract: Numerical methods are used to investigate the transient, forced convection heat/mass transfer inside circulating spheres at low to moderate Reynolds numbers. The heat/mass balance equations were solved numerically in spherical coordinates system by a finite difference method. The values considered for the sphere interior Reynolds number are Re int ⩽ 1000. The computations were focused on the influence of the sphere Peclet number, Pe, and Re int on heat/mass transfer rate for Pe/(1+ μ)⩽104. [Copyright &y& Elsevier]

Abstract: The unsteady, conjugate, forced convection heat/mass transfer from ensembles of mono-size Newtonian fluid spheres to Newtonian fluids has been studied at moderate Peclet and Reynolds numbers. The cell model has been used to account for the spheres hydrodynamic interactions. The momentum and heat/mass balance equations were solved numerically in spherical coordinates system by a finite difference method. The values considered for the sphere exterior Reynolds number are . The influence of the voidage and physical properties ratios on the heat/mass transfer rate was analysed for sphere Peclet numbers, Pe 1(2) ⩽104, and three fluid – fluid systems: gas–liquid, liquid–liquid and liquid–gas. [Copyright &y& Elsevier]

Abstract: Numerical methods are used to investigate the transient, conjugate, forced convection heat/mass transfer in multiparticle systems at low to moderate Reynolds numbers. The interparticle interactions have been accounted for by using the simple cell models. The momentum and heat/mass balance equations were solved numerically in spherical coordinates system by a finite difference method. The values considered for the sphere Reynolds number are Re <100. The computations were focused on the influence of the voidage and physical properties ratios on the heat/mass transfer rate for sphere Peclet number, 10⩽ Pe ⩽1000. [Copyright &y& Elsevier]

Abstract: Numerical methods are used to investigate the transient heat transfer from an elliptic cylinder to a steady stream of viscous, incompressible fluid. The temperature of the cylinder is considered spatially uniform but not constant in time. The momentum and heat balance equations were solved numerically in elliptic coordinate system. The solutions span the parameter ranges 5⩽ Re ⩽40, 1⩽ Pr ⩽100 and axis ratio ε, 0.1⩽ ε ⩽0.75. The computations were focused on the influence of the axis ratio and volume heat capacity ratio on the heat transfer rate. [Copyright &y& Elsevier]

Abstract: This work presents a computational study of the forced convection heat transfer around two circular cylinders in tandem. Axisymmetric, steady, laminar flow around the cylinders was assumed. The temperature inside the cylinders is considered spatially uniform but not constant in time. Numerical solutions have been obtained in bipolar cylindrical coordinates. The finite difference method was used to discretize the equations of the mathematical model. The influence of the model parameters on the heat transfer rate was analysed for the upstream cylinder Reynolds number, Re, varying from 1 to 30 and fluid phase Prandtl number equal to 0.1, 1, 10 and 100. [Copyright &y& Elsevier]