Academia.eduAcademia.edu

Figure 6 – uploaded by Sergio Nardini

See full PDFdownloadDownload figure
It is shown that contrary to effectiveness, by increasing of Re number the effectiveness factor of both cases increase. Also with decrease of Darcy number a considerable increase is shown in amount of the effectiveness and with the same Re the BPC case increases more in effectiveness factor than the HPC case. Fig.9. Variation of effectiveness factor (Eff/EffC) in the HPC case with Darcy and Reynolds numbers for Rk = | and Pr = 0.69.

Figure 9 It is shown that contrary to effectiveness, by increasing of Re number the effectiveness factor of both cases increase. Also with decrease of Darcy number a considerable increase is shown in amount of the effectiveness and with the same Re the BPC case increases more in effectiveness factor than the HPC case. Fig.9. Variation of effectiveness factor (Eff/EffC) in the HPC case with Darcy and Reynolds numbers for Rk = | and Pr = 0.69.

Related Figures (15)

uniform temperature T;,, with a uniform velocity U, from left and the cold fluid enters the low channel at uniform temperature T,; with the same velocity from right of the two channels where contain an |, length and R height aluminum plate. The lengths of 1; and 1, have been chosen to eliminate outlet boundary effects at the exits. In different cases of study up and down of aluminum plate filled with porous structures and results of these cases reported. The porous medium is considered to be homogeneous, isotropic, non-deformable, saturated with fluid and in local therma equilibrium with the fluid. To neglect the channeling effect, fibrous media are considered which have a relatively constan’ porosity and permeability even close to the walls [10]. Also he effects of thermal dispersion, natural convection and hermal radiation are neglected. According to [11], the effective viscosity of porous medium can be considered equa o that of the fluid in higher porosities. The general forms o mass, momentum and energy balance governing equations, used in this study are [12]: channel. Both channels walls are insulated except between Where the non-dimensional parameters are given as bellow [13]:
uniform temperature T;,, with a uniform velocity U, from left and the cold fluid enters the low channel at uniform temperature T,; with the same velocity from right of the two channels where contain an |, length and R height aluminum plate. The lengths of 1; and 1, have been chosen to eliminate outlet boundary effects at the exits. In different cases of study up and down of aluminum plate filled with porous structures and results of these cases reported. The porous medium is considered to be homogeneous, isotropic, non-deformable, saturated with fluid and in local therma equilibrium with the fluid. To neglect the channeling effect, fibrous media are considered which have a relatively constan’ porosity and permeability even close to the walls [10]. Also he effects of thermal dispersion, natural convection and hermal radiation are neglected. According to [11], the effective viscosity of porous medium can be considered equa o that of the fluid in higher porosities. The general forms o mass, momentum and energy balance governing equations, used in this study are [12]: channel. Both channels walls are insulated except between Where the non-dimensional parameters are given as bellow [13]:
In Figs. 3 and 4 the numerical result of this work i: compared with the relevant available experimental data of G Hetsroni [15], which is in a rectangular channel with a porou: block made of 316LSS and mounted heat source. (i.e., W=1/5 Ly= 15, 200 < Re < 2800, (1) Da = 8.610", C = 1.24 and R, = 18.8 (2) Da = 3.84x10°, C = 3.07 and Ry= 15.65). As it is shown both of the calculated pressure drop and the mear Nusselt number are in good agreement with the experimenta results. The maximum difference is less than 5 percent anc therefore, the numerical code is reliable and can be used fot the analysis of varying permeability effect. Fig.4. Comparison of the calculated Nusselt number, with the experimental results of G. Hetsroni [15].
In Figs. 3 and 4 the numerical result of this work i: compared with the relevant available experimental data of G Hetsroni [15], which is in a rectangular channel with a porou: block made of 316LSS and mounted heat source. (i.e., W=1/5 Ly= 15, 200 < Re < 2800, (1) Da = 8.610", C = 1.24 and R, = 18.8 (2) Da = 3.84x10°, C = 3.07 and Ry= 15.65). As it is shown both of the calculated pressure drop and the mear Nusselt number are in good agreement with the experimenta results. The maximum difference is less than 5 percent anc therefore, the numerical code is reliable and can be used fot the analysis of varying permeability effect. Fig.4. Comparison of the calculated Nusselt number, with the experimental results of G. Hetsroni [15].
Fig.3. Comparison of the calculated pressure drop, with the experimental results of G. Hetsroni [15].
Fig.3. Comparison of the calculated pressure drop, with the experimental results of G. Hetsroni [15].
Dt) eeathes! Fig.6. Variation of effectiveness in the BPC case with Darcy and Reynolds numbers for Rk = | and Pr= 0.69.
Dt) eeathes! Fig.6. Variation of effectiveness in the BPC case with Darcy and Reynolds numbers for Rk = | and Pr= 0.69.
In the other hand As the Darcy number decreases, there is a small increase in effectiveness and this effect in BPC case is more visible than the HPC case. Finally according to the results it is observed that in special Darcy and Re numbers, the effectiveness of BPC is slightly more than HPC case. Fig.7. Variation of effectiveness in the HPC case with Darcy and Reynolds numbers for Rk = | and Pr= 0.69.
In the other hand As the Darcy number decreases, there is a small increase in effectiveness and this effect in BPC case is more visible than the HPC case. Finally according to the results it is observed that in special Darcy and Re numbers, the effectiveness of BPC is slightly more than HPC case. Fig.7. Variation of effectiveness in the HPC case with Darcy and Reynolds numbers for Rk = | and Pr= 0.69.
Eff/Eff. Factor shows the ratio of effectiveness of porous heat exchanger to the effectiveness of nonporous heat exchanger. Variations of this factor in BPC and HPC cases are indicated in Figs .8 and 9, respectively. Fig.8. Variation of effectiveness factor (Eff/EffC) in the BPC case with Darcy and Reynolds numbers for Rk = | and Pr = 0.69.
Eff/Eff. Factor shows the ratio of effectiveness of porous heat exchanger to the effectiveness of nonporous heat exchanger. Variations of this factor in BPC and HPC cases are indicated in Figs .8 and 9, respectively. Fig.8. Variation of effectiveness factor (Eff/EffC) in the BPC case with Darcy and Reynolds numbers for Rk = | and Pr = 0.69.
Fig.11. Total dimensionless pressure drop in the HPC case versus Darcy numbers at various Reynolds number. Also the pressure drop in BPC case at the same Darcy numbers is approximately two times of the HPC case and this is due to negligible pressure drop in the nonporous channel compared with the porous channel. As expect in both cases pressure drop increases as Reynolds number increases.
Fig.11. Total dimensionless pressure drop in the HPC case versus Darcy numbers at various Reynolds number. Also the pressure drop in BPC case at the same Darcy numbers is approximately two times of the HPC case and this is due to negligible pressure drop in the nonporous channel compared with the porous channel. As expect in both cases pressure drop increases as Reynolds number increases.
Fig.10. Total dimensionless pressure drop in the BPC case versus Darcy numbers at various Reynolds number.
Fig.10. Total dimensionless pressure drop in the BPC case versus Darcy numbers at various Reynolds number.
The effects of thermal conductivity ratio on the effectiveness of BPC and HPC cases are shown in Figs. 12 and 13, respectively. These figures show that the effectiveness of heat exchangers will increase with the decrease of Darcy number. But, the amount of this increase is not considerable. On the other hand with increase of Rx, significant increase effectiveness is obtained. Fig.12. Variation of effectiveness in the BPC case with thermal conductivity ratio and Darcy number for Re = 200 and Pr = 0.69.
The effects of thermal conductivity ratio on the effectiveness of BPC and HPC cases are shown in Figs. 12 and 13, respectively. These figures show that the effectiveness of heat exchangers will increase with the decrease of Darcy number. But, the amount of this increase is not considerable. On the other hand with increase of Rx, significant increase effectiveness is obtained. Fig.12. Variation of effectiveness in the BPC case with thermal conductivity ratio and Darcy number for Re = 200 and Pr = 0.69.
T/Tc, is defined to indicate the ratio of local temperature of hot and cold fluids in the centerline of porous channels to the cold fluid inlet temperature. Fig. 14 show this ratio versus X, for different R, in Re=200, Da=10° and Pr=0.69 for BPC case. With increasing thermal conductivity ratio, the rate of decrease and increase of the hot and cold fluids temperature is increased and their temperatures faster get closer. But this phenomenon dose not leads to more decline of hot fluid temperature and hence effectiveness does not increase.
T/Tc, is defined to indicate the ratio of local temperature of hot and cold fluids in the centerline of porous channels to the cold fluid inlet temperature. Fig. 14 show this ratio versus X, for different R, in Re=200, Da=10° and Pr=0.69 for BPC case. With increasing thermal conductivity ratio, the rate of decrease and increase of the hot and cold fluids temperature is increased and their temperatures faster get closer. But this phenomenon dose not leads to more decline of hot fluid temperature and hence effectiveness does not increase.
Fig.13. Variation of effectiveness in the HPC case with thermal conductivity ratio and Darcy number for Re = 200 and Pr = 0.69.
Fig.13. Variation of effectiveness in the HPC case with thermal conductivity ratio and Darcy number for Re = 200 and Pr = 0.69.
Fig.16. Variation of effectiveness in the HPC case with Darcy and Prandtl numbers for Re = 200 and Rk = 1.
Fig.16. Variation of effectiveness in the HPC case with Darcy and Prandtl numbers for Re = 200 and Rk = 1.
Fig.15. Variation of effectiveness in the BPC case with Darcy and Prandtl numbers for Re = 200 and Rk = 1. Effectiveness of BPC and HPC cases in different Prandt numbers are displayed in Figs. 15 and 16 respectively.
Fig.15. Variation of effectiveness in the BPC case with Darcy and Prandtl numbers for Re = 200 and Rk = 1. Effectiveness of BPC and HPC cases in different Prandt numbers are displayed in Figs. 15 and 16 respectively.
In order to investigate the effects of using porous medium on flow structure and the heat transfer in parallel channel with a joint aluminum plate, a study of laminar forced convection was performed. Hydrodynamic and heat transfer results are reported for three cases of nonporous channels (NPC) , both channels filled by porous structure (BPC), the channel contains hot fluid, filled by porous structure and the other one is nonporous (HPC). Subscripts The results show that the more the Darcy, Reynolds or Prandtl number decreases, the more effectiveness of heat exchanger increases. But increase of thermal conductivity ratio causes to different effects on effectiveness of BPC and HPC cases. But in all cases significant increase in effectiveness is obtained.
In order to investigate the effects of using porous medium on flow structure and the heat transfer in parallel channel with a joint aluminum plate, a study of laminar forced convection was performed. Hydrodynamic and heat transfer results are reported for three cases of nonporous channels (NPC) , both channels filled by porous structure (BPC), the channel contains hot fluid, filled by porous structure and the other one is nonporous (HPC). Subscripts The results show that the more the Darcy, Reynolds or Prandtl number decreases, the more effectiveness of heat exchanger increases. But increase of thermal conductivity ratio causes to different effects on effectiveness of BPC and HPC cases. But in all cases significant increase in effectiveness is obtained.
Related topics:
Mechanical EngineeringAerospace EngineeringApplied MathematicsGeologyGeophysicsFinite Volume MethodsMesh generationThermal SciencesPipe FlowGroundwater flow
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved