scholarly journals Estimation of the Biot Number Using Genetic Algorithms: Application for the Drying Process

Energies ◽  
2019 ◽  
Vol 12 (14) ◽  
pp. 2822 ◽  
Author(s):  
Krzysztof Górnicki ◽  
Radosław Winiczenko ◽  
Agnieszka Kaleta

The Biot number informs researchers about the controlling mechanisms employed for heat or mass transfer during the considered process. The mass transfer coefficients (and heat transfer coefficients) are usually determined experimentally based on direct measurements of mass (heat) fluxes or correlation equations. This paper presents the method of Biot number estimation. For estimation of the Biot number in the drying process, the multi-objective genetic algorithm (MOGA) was developed. The simultaneous minimization of mean absolute error (MAE) and root mean square error (RMSE) and the maximization of the coefficient of determination R2 between the drying model and experimental data were considered. The Biot number can be calculated from the following equations: Bi = 0.8193exp(-6.4951T−1) (and moisture diffusion coefficient from D/s2 = 0.00704exp(-2.54T−1)) (RMSE = 0.0672, MAE = 0.0535, R2 = 0.98) or Bi = 1/0.1746log(1193847T) (D/s2 = 0.0075exp(-6T−1)) (RMSE = 0.0757, MAE = 0.0604, R2 = 0.98). The conducted validation gave good results.

Author(s):  
Cristiano Bigonha Tibiric¸a´ ◽  
Gherhardt Ribatski ◽  
John Richard Thome

Experimental flow boiling heat transfer results are presented for horizontal 1.0 and 2.2 mm I.D. (internal diameter) stainless steel tubes for tests with R1234ze, a new refrigerant developed as a substitute for R134a with a much lower GWP (Global Warming Potential). These two tube diameters were chosen due the necessity to a better investigation the macro to microchannel transition boundary. The experimental campaign includes mass velocities ranging from 50 to 1500 kg m−2s−1, heat fluxes from 10 to 300 kW m−2, exit saturation temperatures of 25, 31 and 35 °C, vapor qualities from 0.05 to 0.99 and heated lengths of 180 mm and 361 mm. Flow pattern characterization was performed using high-speed videos. Data for heat transfer coefficients, critical heat fluxes and flow pattern transitions were obtained. R1234ze demonstrated similar thermal performance to R134a data when running at similar conditions. For critical heat flux the correlation of Katto and Ohno (1984) best predicted the database with a mean absolute error of 6.3%. For the heat transfer coefficients, the Thome et al. (2004) three-zone model predicted the data for slug flow with 15.9% and Saitoh et al. (2007) predicted data for other flow regimes with mean absolute error of 19.4%.


Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 830
Author(s):  
Viktor Vajc ◽  
Radek Šulc ◽  
Martin Dostál

Heat transfer coefficients were investigated for saturated nucleate pool boiling of binary mixtures of water and glycerin at atmospheric pressure in a wide range of concentrations and heat fluxes. Mixtures with water mass fractions from 100% to 40% were boiled on a horizontal flat copper surface at heat fluxes from about 25 up to 270kWm−2. Experiments were carried out by static and dynamic method of measurement. Results of the static method show that the impact of mixture effects on heat transfer coefficient cannot be neglected and ideal heat transfer coefficient has to be corrected for all investigated concentrations and heat fluxes. Experimental data are correlated with the empirical correlation α=0.59q0.714+0.130ωw with mean relative error of 6%. Taking mixture effects into account, data are also successfully correlated with the combination of Stephan and Abdelsalam (1980) and Schlünder (1982) correlations with mean relative error of about 15%. Recommended coefficients of Schlünder correlation C0=1 and βL=2×10−4ms−1 were found to be acceptable for all investigated mixtures. The dynamic method was developed for fast measurement of heat transfer coefficients at continuous change of composition of boiling mixture. The dynamic method was tested for water–glycerin mixtures with water mass fractions from 70% down to 35%. Results of the dynamic method were found to be comparable with the static method. For water–glycerin mixtures with higher water mass fractions, precise temperature measurements are needed.


Author(s):  
Ann-Christin Fleer ◽  
Markus Richter ◽  
Roland Span

AbstractInvestigations of flow boiling in highly viscous fluids show that heat transfer mechanisms in such fluids are different from those in fluids of low viscosity like refrigerants or water. To gain a better understanding, a modified standard apparatus was developed; it was specifically designed for fluids of high viscosity up to 1000 Pa∙s and enables heat transfer measurements with a single horizontal test tube over a wide range of heat fluxes. Here, we present measurements of the heat transfer coefficient at pool boiling conditions in highly viscous binary mixtures of three different polydimethylsiloxanes (PDMS) and n-pentane, which is the volatile component in the mixture. Systematic measurements were carried out to investigate pool boiling in mixtures with a focus on the temperature, the viscosity of the non-volatile component and the fraction of the volatile component on the heat transfer coefficient. Furthermore, copper test tubes with polished and sanded surfaces were used to evaluate the influence of the surface structure on the heat transfer coefficient. The results show that viscosity and composition of the mixture have the strongest effect on the heat transfer coefficient in highly viscous mixtures, whereby the viscosity of the mixture depends on the base viscosity of the used PDMS, on the concentration of n-pentane in the mixture, and on the temperature. For nucleate boiling, the influence of the surface structure of the test tube is less pronounced than observed in boiling experiments with pure fluids of low viscosity, but the relative enhancement of the heat transfer coefficient is still significant. In particular for mixtures with high concentrations of the volatile component and at high pool temperature, heat transfer coefficients increase with heat flux until they reach a maximum. At further increased heat fluxes the heat transfer coefficients decrease again. Observed temperature differences between heating surface and pool are much larger than for boiling fluids with low viscosity. Temperature differences up to 137 K (for a mixture containing 5% n-pentane by mass at a heat flux of 13.6 kW/m2) were measured.


1962 ◽  
Vol 84 (4) ◽  
pp. 365-371 ◽  
Author(s):  
H. S. Swenson ◽  
J. R. Carver ◽  
G. Szoeke

In large, subcritical pressure, once-through power boilers heat is transferred to steam and water mixtures ranging in steam quality from zero per cent at the bottom of the furnace to 100 per cent at the top. In order to provide design information for this type of boiler, heat-transfer coefficients for forced convection film boiling were determined for water at 3000 psia flowing upward in a vertical stainless-steel tube, AISI Type 304, having an inside diameter of 0.408 inches and a heated length of 6 feet. Heat fluxes ranged between 90,000 and 180,000 Btu/hr-sq ft and were obtained by electrical resistance heating of the tube. The operation of the experimental equipment was controlled so that nucleate boiling, transition boiling, and stable film boiling occurred simultaneously in different zones of the tube. The film boiling data were correlated with a modified form of the equation Nu = a a(Re)m(Pr)n using steam properties evaluated at inside surface temperature. Results of a second series of heat-transfer tests with tubes having a helical rib on the inside surface showed that nucleate boiling could be maintained to much higher steam qualities with that type of tube than with a smooth-bore tube.


Author(s):  
Todd M. Bandhauer ◽  
Taylor A. Bevis

The principle limit for achieving higher brightness of laser diode arrays is thermal management. State of the art laser diodes generate heat at fluxes in excess of 1 kW cm−2 on a plane parallel to the light emitting edge. As the laser diode bars are packed closer together, it becomes increasingly difficult to remove large amounts of heat in the diminishing space between neighboring diode bars. Thermal management of these diode arrays using conduction and natural convection is practically impossible, and, therefore, some form of forced convective cooling must be utilized. Cooling large arrays of laser diodes using single-phase convection heat transfer has been investigated for more than two decades by multiple investigators. Unfortunately, either large fluid temperature increases or very high flow velocities must be utilized to reject heat to a single phase fluid, and the practical threshold for single phase convective cooling of laser diodes appears to have been reached. In contrast, liquid-vapor phase change heat transport can occur with a negligible increase in temperature and, due to a high enthalpy of vaporization, at comparatively low mass flow rates. However, there have been no prior investigations at the conditions required for high brightness edge emitting laser diode arrays: >1 kW cm−2 and >10 kW cm−3. In the current investigation, flow boiling heat transfer at heat fluxes up to 1.1 kW cm−2 was studied in a microchannel heat sink with plurality of very small channels (45 × 200 microns) using R134a as the phase change fluid. The high aspect ratio channels (4.4:1) were manufactured using MEMS fabrication techniques, which yielded a large heat transfer surface area to volume ratio in the vicinity of the laser diode. To characterize the heat transfer performance, a test facility was constructed that enabled testing over a range of fluid saturation temperatures (15°C to 25°C). Due to the very small geometric features, significant heat spreading was observed, necessitating numerical methods to determine the average heat transfer coefficient from test data. This technique is crucial to accurately calculate the heat transfer coefficients for the current investigation, and it is shown that the analytical approach used by many previous investigations requires assumptions that are inadequate for the very small dimensions and heat fluxes observed in the present study. During the tests, the calculated outlet vapor quality exceeded 0.6 and the base heat flux reached a maximum of 1.1 kW cm−2. The resulting experimental heat transfer coefficients are found to be as large a 58.1 kW m−2 K−1 with an average uncertainty of ±11.1%, which includes uncertainty from all measured and calculated values, required assumptions, and geometric discretization error from meshing.


2021 ◽  
Vol 2119 (1) ◽  
pp. 012172
Author(s):  
T G Gigola ◽  
V V Cheverda

Abstract The process of the liquid spray impact on the heated surface is studied experimentally using the IR-transparent sapphire plate method. The spatiotemporal distribution of the temperature field on the sapphire substrate surface during impacting spray is received. The obtained experimental data are an important step in a study of the local characteristics of heat transfer in the areas of the contact lines during liquid spray impact on the heated surface. Further, the local heat fluxes and heat transfer coefficients will be determined by solving the problem of thermal conductivity in the sapphire substrate.


1986 ◽  
Vol 108 (1) ◽  
pp. 4-8 ◽  
Author(s):  
T. Kumada ◽  
T. Hirota ◽  
N. Tamura ◽  
R. Ishiguro

Some of the previously reported heat transfer coefficients with evaporation are fairly large as compared with those of a dry body under similar hydrodynamic conditions. In order to clarify this curious enhancement of heat transfer, a method of error evaluation was developed and applied to correct the experimental errors in the recently reported results. An experimental study was also made on turbulent heat and mass transfer of air flowing over a water surface. The present and the previously reported experimental results revealed that the heat transfer coefficient with evaporation agrees with that of a dry body without evaporation, within experimental error, if the erroneous heat inputs into the liquid are properly corrected according to the proposed method.


1993 ◽  
Vol 115 (4) ◽  
pp. 998-1003 ◽  
Author(s):  
P. F. Peterson ◽  
V. E. Schrock ◽  
T. Kageyama

In turbulent condensation with noncondensable gas, a thin noncondensable layer accumulates and generates a diffusional resistance to condensation and sensible heat transfer. By expressing the driving potential for mass transfer as a difference in saturation temperatures and using appropriate thermodynamic relationships, here an effective “condensation” thermal conductivity is derived. With this formulation, experimental results for vertical tubes and plates demonstrate that condensation obeys the heat and mass transfer analogy, when condensation and sensible heat transfer are considered simultaneously. The sum of the condensation and sensible heat transfer coefficients becomes infinite at small gas concentrations, and approaches the sensible heat transfer coefficient at large concentrations. The “condensation” thermal conductivity is easily applied to engineering analysis, and the theory further demonstrates that condensation on large vertical surfaces is independent of the surface height.


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