The performance of both conservative and non-conservative formulations of the Galerkin finite ele... more The performance of both conservative and non-conservative formulations of the Galerkin finite element method for the solution of advection-diffusion problems is analyzed by considering some simple steady- and unsteady-state test cases. Comparisons concern the accuracy reached in the prediction of the scalar field and in the preservation of the physical conservation principle. The influence of the domain subdivision on the conservation error is also investigated.
ASME 2010 8th International Conference on Nanochannels, Microchannels, and Minichannels: Parts A and B, 2010
ABSTRACT As an alternative to massive CFD, a hybrid technique, which has the advantage of account... more ABSTRACT As an alternative to massive CFD, a hybrid technique, which has the advantage of accounting for all of the three-dimensional features of the flow field, but with a limited computational effort, is used for the solution of conjugate convection-conduction heat transfer problems in cross-flow micro heat exchangers. The key feature of the proposed method is represented by the separate computation of the velocity fields in single microchannels and on the subsequent mapping of such velocity fields onto the three-dimensional grid used to solve the thermal problem. The cross-flow micro heat exchangers considered in the paper consist of a number of layers of rectangular microchannels. A parametric study is carried out on the combined effect on cross-flow micro heat exchanger thermal performances due to the variation of the microchannel cross-section and of the ratio of solid to fluid thermal conductivity.
The problem of laminar flow and heat transfer in the entrance region of ducts of arbitrary cross ... more The problem of laminar flow and heat transfer in the entrance region of ducts of arbitrary cross sectiois considered. A procedure for the calculation of developing velocity and temperature fields is proposed based on the finite element method. The error in the evaluation of integral parameters, such as the local Nusselt number, is of the order of 0.5 percent or
ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels, Parts A and B, 2006
ABSTRACT The effects of viscous dissipation and temperature dependent viscosity in simultaneously... more ABSTRACT The effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels of circular cross-section are studied with reference to convective boundary conditions. Viscosity is assumed to vary linearly with temperature, in order to allow a parametric investigation, while the other fluid properties are held constant. A finite element procedure, based on a projection algorithm, is employed for the step-by-step solution of the parabolized momentum and energy equations. Axial distributions of the local overall Nusselt number and of the apparent Fanning friction factor are presented with reference to both heating and cooling conditions for three different values of the Biot number. Examples of temperature profiles at different axial locations are also shown.
Numerical Heat Transfer, Part B: Fundamentals, 1988
ABSTRACT A finite-element procedure for the prediction of laminar forced convection in three-dime... more ABSTRACT A finite-element procedure for the prediction of laminar forced convection in three-dimensional parabolic flows is presented. The procedure, based on the parabolized simplification of the complete Navier-Stokes equations, is first validated by comparing computed results with the available literature data for thermally and hydrodynamically developing flows in flat channels. Then, new results are presented for simultaneously developing flows in square duels, with $, and $ boundary conditions and Prandtl number ranging from 0.1 to 10.
Numerical Heat Transfer, Part B: Fundamentals, 1982
... by using the proper form of algorithm (39) and the values of the stream function can be ... T... more ... by using the proper form of algorithm (39) and the values of the stream function can be ... Theformulation in the preceding section is general and applicable to any type of finiteelement ... A simpleFEM generator routine was also used to speed up the preparation of geometric input ...
Numerical Heat Transfer, Part B: Fundamentals, 1981
A finite-element marching procedure is presented for the calculation of transport processes in th... more A finite-element marching procedure is presented for the calculation of transport processes in three-dimensional parabolic flows. As in corresponding finite-difference procedures, equations are solved one after the other. Similarly, longitudinal and cross-stream pressure gradients are uncoupled. Velocity fields are determined by first calculating intermediate velocity values based on estimated pressure gradient distributions and then obtaining appropriate corrections so as to
Numerical Heat Transfer, Part B: Fundamentals, 1979
This paper presents a generally applicable approach to laminar heat transfer problems in the entr... more This paper presents a generally applicable approach to laminar heat transfer problems in the entrance region of ducts. Consideration is given to the general situation in which ducts have arbitrary but constant cross sections. The finite-element method is used in the simultaneous step-by-step integration of the momentum and energy equations. Several illustrative examples demonstrate the versatility of the proposed technique and permit an evaluation of its accuracy.
Numerical Heat Transfer, Part B: Fundamentals, 1978
This paper it concerned with velocity and heat transfer characteristics in the thermal entrance r... more This paper it concerned with velocity and heat transfer characteristics in the thermal entrance region of hydrodynamically developed laminar duct flows. Consideration is given to the general situation in which ducts have arbitrary but constant cross sections. The finite-element method is used for the first time, and with good results, for the solution of this class of problems.
ABSTRACT The effects of viscous dissipation and temperature dependent viscosity in simultaneously... more ABSTRACT The effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels of arbitrary but constant cross-section are studied with reference to convective thermal boundary conditions. Viscosity is assumed to vary linearly with temperature, in order to allow a parametric investigation, while the other fluid properties are held constant. A finite element procedure, based on a projection algorithm, is employed for the step-by-step solution of the parabolized momentum and energy equations. Axial distributions of the local overall Nusselt number and of the apparent Fanning friction factor in flat microchannels are presented with reference to both heating and cooling conditions for two different values of the Biot number. Examples of temperature profiles at different axial locations are also shown. Keywords: laminar forced convection, microchannels, entrance region, temperature dependent viscosity, viscous dissipation, convective boundary conditions. 1 Introduction In several heat transfer problems concerning microchannel flows, the thermal resistance of the channel wall must be taken into account in order to obtain accurate solutions. Moreover, in many situations of practical interest, fluid velocity and temperature fields develop simultaneously, resulting in overlapping hydrodynamic and thermal entrance regions. This occurs when fluid heating or cooling begins at the microchannel inlet, where also the velocity boundary layer
The performance of both conservative and non-conservative formulations of the Galerkin finite ele... more The performance of both conservative and non-conservative formulations of the Galerkin finite element method for the solution of advection-diffusion problems is analyzed by considering some simple steady- and unsteady-state test cases. Comparisons concern the accuracy reached in the prediction of the scalar field and in the preservation of the physical conservation principle. The influence of the domain subdivision on the conservation error is also investigated.
ASME 2010 8th International Conference on Nanochannels, Microchannels, and Minichannels: Parts A and B, 2010
ABSTRACT As an alternative to massive CFD, a hybrid technique, which has the advantage of account... more ABSTRACT As an alternative to massive CFD, a hybrid technique, which has the advantage of accounting for all of the three-dimensional features of the flow field, but with a limited computational effort, is used for the solution of conjugate convection-conduction heat transfer problems in cross-flow micro heat exchangers. The key feature of the proposed method is represented by the separate computation of the velocity fields in single microchannels and on the subsequent mapping of such velocity fields onto the three-dimensional grid used to solve the thermal problem. The cross-flow micro heat exchangers considered in the paper consist of a number of layers of rectangular microchannels. A parametric study is carried out on the combined effect on cross-flow micro heat exchanger thermal performances due to the variation of the microchannel cross-section and of the ratio of solid to fluid thermal conductivity.
The problem of laminar flow and heat transfer in the entrance region of ducts of arbitrary cross ... more The problem of laminar flow and heat transfer in the entrance region of ducts of arbitrary cross sectiois considered. A procedure for the calculation of developing velocity and temperature fields is proposed based on the finite element method. The error in the evaluation of integral parameters, such as the local Nusselt number, is of the order of 0.5 percent or
ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels, Parts A and B, 2006
ABSTRACT The effects of viscous dissipation and temperature dependent viscosity in simultaneously... more ABSTRACT The effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels of circular cross-section are studied with reference to convective boundary conditions. Viscosity is assumed to vary linearly with temperature, in order to allow a parametric investigation, while the other fluid properties are held constant. A finite element procedure, based on a projection algorithm, is employed for the step-by-step solution of the parabolized momentum and energy equations. Axial distributions of the local overall Nusselt number and of the apparent Fanning friction factor are presented with reference to both heating and cooling conditions for three different values of the Biot number. Examples of temperature profiles at different axial locations are also shown.
Numerical Heat Transfer, Part B: Fundamentals, 1988
ABSTRACT A finite-element procedure for the prediction of laminar forced convection in three-dime... more ABSTRACT A finite-element procedure for the prediction of laminar forced convection in three-dimensional parabolic flows is presented. The procedure, based on the parabolized simplification of the complete Navier-Stokes equations, is first validated by comparing computed results with the available literature data for thermally and hydrodynamically developing flows in flat channels. Then, new results are presented for simultaneously developing flows in square duels, with $, and $ boundary conditions and Prandtl number ranging from 0.1 to 10.
Numerical Heat Transfer, Part B: Fundamentals, 1982
... by using the proper form of algorithm (39) and the values of the stream function can be ... T... more ... by using the proper form of algorithm (39) and the values of the stream function can be ... Theformulation in the preceding section is general and applicable to any type of finiteelement ... A simpleFEM generator routine was also used to speed up the preparation of geometric input ...
Numerical Heat Transfer, Part B: Fundamentals, 1981
A finite-element marching procedure is presented for the calculation of transport processes in th... more A finite-element marching procedure is presented for the calculation of transport processes in three-dimensional parabolic flows. As in corresponding finite-difference procedures, equations are solved one after the other. Similarly, longitudinal and cross-stream pressure gradients are uncoupled. Velocity fields are determined by first calculating intermediate velocity values based on estimated pressure gradient distributions and then obtaining appropriate corrections so as to
Numerical Heat Transfer, Part B: Fundamentals, 1979
This paper presents a generally applicable approach to laminar heat transfer problems in the entr... more This paper presents a generally applicable approach to laminar heat transfer problems in the entrance region of ducts. Consideration is given to the general situation in which ducts have arbitrary but constant cross sections. The finite-element method is used in the simultaneous step-by-step integration of the momentum and energy equations. Several illustrative examples demonstrate the versatility of the proposed technique and permit an evaluation of its accuracy.
Numerical Heat Transfer, Part B: Fundamentals, 1978
This paper it concerned with velocity and heat transfer characteristics in the thermal entrance r... more This paper it concerned with velocity and heat transfer characteristics in the thermal entrance region of hydrodynamically developed laminar duct flows. Consideration is given to the general situation in which ducts have arbitrary but constant cross sections. The finite-element method is used for the first time, and with good results, for the solution of this class of problems.
ABSTRACT The effects of viscous dissipation and temperature dependent viscosity in simultaneously... more ABSTRACT The effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels of arbitrary but constant cross-section are studied with reference to convective thermal boundary conditions. Viscosity is assumed to vary linearly with temperature, in order to allow a parametric investigation, while the other fluid properties are held constant. A finite element procedure, based on a projection algorithm, is employed for the step-by-step solution of the parabolized momentum and energy equations. Axial distributions of the local overall Nusselt number and of the apparent Fanning friction factor in flat microchannels are presented with reference to both heating and cooling conditions for two different values of the Biot number. Examples of temperature profiles at different axial locations are also shown. Keywords: laminar forced convection, microchannels, entrance region, temperature dependent viscosity, viscous dissipation, convective boundary conditions. 1 Introduction In several heat transfer problems concerning microchannel flows, the thermal resistance of the channel wall must be taken into account in order to obtain accurate solutions. Moreover, in many situations of practical interest, fluid velocity and temperature fields develop simultaneously, resulting in overlapping hydrodynamic and thermal entrance regions. This occurs when fluid heating or cooling begins at the microchannel inlet, where also the velocity boundary layer
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