A non-probabilistic approach to study the effect of imprecisely defined parameters on heat transfer in a conical porous cylinder

ABSTRACTTo improve the computing precision and efficiency of temperature field analysis in tangential clearance of scroll compressor, the ridgelet finite element method is combined with fuzzy finite element method to construct the fuzzy ridgelet finite element method of analyzing temperature field in tangential clearance. First, the related research progresses on heat transfer of scroll compressor, wavelet finite element method, and fuzzy finite element method are summarized. Second, the leakage flow model of tangential clearance in scroll compressor is studied in depth. Third, the heat transfer model of leakage flow in tangential clearance of scroll compressor is established, and then the fuzzy ridgelet finite element model is constructed, the fuzzy finite element model is transformed to the random model based on information entropy, the corresponding calculating procedure is designed. Finally, the simulation analysis is performed based on fuzzy finite element method, fuzzy Daubechies wavelet finite element method, and the fuzzy ridgelet finite element model, respectively, comparing analysis between simulation and test results shows that the fuzzy ridgelet finite element method has best computing effectiveness on temperature field analysis of tangential clearance of scroll compressor. In addition, the tangential clearance temperature of scroll compressor with and without water cooling has been analyzed based on the fuzzy ridgelet finite element method, and the results show that the water cooling system can reduce the temperature in tangential clearance greatly.

ABSTRACTHeat transfer of leakage flow in tip clearance will reduce the working performance, and therefore it is necessary to study it in depth. To improve the computing effectiveness of heat transfer of leakage flow in the tooth tip clearance of the single-screw compressor, the fuzzy contourlet finite element model is constructed by combining the contourlet finite element method and fuzzy finite element method. First, the related research progresses are summarized. Second, heat transfer model of leakage flow in the tip clearance of single-screw compressor is constructed. Third, the fuzzy contourlet wavelet finite element model is established. Finally, heat transfer simulation of leakage flow in the tip clearance of single-screw compressor is performed, and the variables with fuzziness are chosen, which are transformed to random variables based on information entropy theory. The comparing analysis among simulation analysis and test results is performed, and results show that the contourlet finite element method has highest computing precision and efficiency. In addition, the temperature of leakage flow in the tip clearance (L1) is also obtained, and results show that the fuzzy contourlet wavelet finite element method can effectively obtain the temperature distribution rules with fuzziness.

Effects of imprecisely defined parameters on heat and mass transfer in a vertical annular porous cylinder

A numerical approach to study heat and mass transfer in porous medium influenced by uncertain parameters

In order to optimize structure of twin screw compressor, and improve the working efficiency of twin screw refrigeration compressor, the heat transfer rules of cavity in twin screw refrigeration should be obtained correctly. Because the coupling of clearance leakage flow and heat transfer has a significant effect on heat transfer of cavity medium of twin screw refrigeration compressor, the heat transfer model of cavity medium under clearance leakage-heat coupling is constructed. To promote the computation accuracy and efficiency, the fuzzy beamlet finite element model is constructed by considering fuzzy affecting parameters and taking beamlet transform as interpolating function of element. The heat transfer laws of medium in cavity are obtained based on the theoretical an experimental analysis. Based on the simulation results, the computation error of fuzzy beamlet finite element method has least computation error and diversity than the other two methods for comparison, and the running time of fuzzy beamlet finite element method is least. Heat transfer analysis of medium in cavity under three conditions is carried out, and results show that temperature of cavity medium of twin screw refrigeration compressor is highest when the clearance leakage-heat coupling is considered and agrees better with reality; therefore, the proposed method has higher computing precision and efficiency than selected numerical methods according to computing results and running time. The impact of different clearances on heat transfer of medium in cavity is analyzed based on fuzzy beamlet finite element method, results show that the temperature of cavity medium increases accordingly as tooth top clearance, clearance between teeth, suction end clearance and exhaust end clearance increase, and the suction end clearance and exhaust end clearance have less effect on temperature of cavity medium.

This work presents the effects of variable wall permeability on two-dimensional flow and heat transfer in a leaky narrow channel containing water-based nanoparticles. The nanofluid is absorbed through the walls with an exponential rate. This situation arises in reverse osmosis, ultrafiltration, and transpiration cooling in industry. The mathematical model is developed by using the continuity, momentum, and energy equations. Using stream function, the transport equations are reduced and solved by using regular perturbation method. The expressions for stream function and temperature distribution are established, which helps in finding the components of velocity, wall shear stress, and heat transfer rate inside the channel. The results show that velocity components, temperature, wall shear stress, and rate of heat transfer are minimum at the entrance region due to the reabsorption of fluid containing nanoparticles. Additionally, with increasing volume fraction of nanoparticles, the rate of heat transfer enhances at all positions inside the channel. Titanium dioxide (TiO 2 ) nanoparticles show higher wall shear stress compared to copper and alumina. The streamlines confirms that all the fluid is reabsorbed before reaching the exit region of the channel for high reabsorption.

Low Rayleigh number flow in a heat generating porous media

This paper reports a numerical investigation of highly coupled system of partial differential equations, simulating the fluid flow and heat transfer in a large-scale enclosure with time-periodic heat generation. The bottom wall of the enclosure is insulated, and heat exchange with the environment is modeled at other external boundaries. The heater with time-periodic heat generation is located at the bottom of the enclosure. The internal surfaces of both the heater and walls are assumed to be gray. Air is the working fluid and the Rayleigh number is 109. To solve the governing equations with dimensionless vorticity – stream function – temperature variables, the finite difference method has been used. The developed model has been validated through a comparison with data of other authors. The effect of surface emissivity and periodic heat generation on Nusselt numbers and both stream function and temperature distributions has been investigated. The results showed that the influence of the thermal radiation on total thermal transmission increases with surface emissivity of walls and heater surfaces. The present numerical method can be applied in several engineering problems, such as designing passive cooling systems and the simulation of heat transfer in building constructions.

A numerical study of heat transfer problem by natural convection of a fluid inside a square cavity with two inner bodies is presented. This subject is of great interest in the engineering area, mainly in applications involving development of heat exchangers and cooling or heating systems of bodies by natural convection mechanism. Two cases have been studied. The inner bodies are square in case 1 and circular in case 2. In both cases, the bodies are solid and thermally conductive, the cavity lower and upper horizontal surfaces are isothermal with high temperature Th and low temperature Tc, respectively. Both vertical surfaces are adiabatic. A FORTRAN code using Finite Element Method (FEM) is developed to simulate the problem and solve the governing equations. The distributions of stream function, ψ, dimensionless temperature, θ, and vorticity, ω, are determined. Heat transfer is evaluated by analyzing the behavior of the average Nusselt number.

A numerical analysis has been performed for the steady-state temperature and stream function distributions in a finite vertical cylinder, having an isothermal side and top and an insulated bottom, for a uniform heat generating porous medium. The analysis uses the stream function formulation of Darcy's equation in cylindrical coordinates and the Boussinesq approximation. A single energy equation was used for the fluid and solid. The non-dimensionalized momentum and energy equations were solved for a wide range of Rayleigh numbers (10 to 10 x 10^6) and solutions for the streamlines and isotherms were obtained using a transient explicit finite-difference approximation. The isotherms and streamlines were followed while varying the heat generation rate, bulk thermal conductivity, permeability, boundary temperature and cylinder size. Conduction was prominent at low Rayleigh numbers and convection predominated at high Rayleigh numbers. Within the convective heat transfer realm, several different flow patterns were observed.

This study numerically investigates double-diffusive natural convection of non-Newtonian power-law fluids inside an inclined square cavity in the presence of Soret effect. This complex phenomenon can play an important role in real-life applications, and the interaction of the pertinent parameters can affect the characteristics of the flow and heat and mass transfers. The simulations emphasize the effects of different governing parameters, including Lewis number, Le, buoyancy ratio, N, power-law index, n, Soret parameter, Sr, inclination angle, θ , and the thermal Rayleigh number, Ra T . Numerical predictions of the heat and mass transfers along the heated boundary are presented in terms of Nusselt and Sherwood numbers in addition to contours of concentration, temperature and stream function distributions. The outcomes demonstrated the existence of angles of inclination θ max for which the Nusselt and Sherwood numbers present a maximum and it was shown to depend on n, Ra T , Le, N and Sr. An interesting transition phenomenon occurring at particular inclination angles ( θ Tr ) tends to change the flow structure from the horizontal monocellular flow to vertical one in the case of the pseudoplastic fluids. In contrast, for dilatant fluids, the flow transforms into a major clockwise vortex extending from the left-top corner to the right-bottom corner, with two small cells appearing in the other two corners. Streamlines are shown to give greater understanding of the transition mechanism at θ Tr showing different flow structures. Heat and mass transfers improved by increasing Ra T , |N| and Sr or by decreasing n. The increase in Le affects heat transfer negatively compared to mass transfer.

ABSTRACTThis paper presents the reliability analysis on the basis of the foundation failure against bearing capacity using the concept of fuzzy set theory. A surface strip footing is considered for the analysis and the bearing capacity is estimated using the conventional Finite Element Method (FEM). The spatial variability of the variables is taken into consideration to capture the physical randomness of the soil parameters for an isotropic field. A variation of the probability of failure (Pf) against a varying limiting applied pressure (q) is presented for different Coefficient of Variation (COV) of the variables and different scale of fluctuation (θ). The results reveal that the friction angle of soil (ϕ) is the most influencing parameter among the other variables. Further, the influence of the scale of fluctuation (θ) on the probability of failure (Pf) is also examined. It is observed that for a particular COV of ϕ, higher value of θ predicts higher Pf whereas, Pf increases as COV of ϕ increases for a particular θ value. Later, a comparison study is accomplished to verify the viability of the present method and it can be noticed that the present method compares well with the other reliability method (First Order Reliability Method) to a reasonably good extent.

In this research work natural convection in two dimensional cavity is studied numerically for differently heated air filled square and rectangular cavity. Vertical cavity with two adiabatic and hot and cold wall with different aspect ratio of 1, 2.5, 5, 7.5 and 10 has taken for investigation. the heat transfer was investigated over the wide range of Rayleigh number from 103 to 106 . Solutions are obtained for several Rayleigh numbers with Prandtl number Pr = 0.70 and aspect ratio 1, 2.5, 5, 7.5 and 10. The Pressure-Velocity Coupling Method used with Non-Iterative Time Advancement (NITA) scheme used to solve the problem. Flow patterns and isotherm plots were used to display the results, and for every case, local and mean Nusselt values were also produced. The results show that an increase in Rayleigh numbers greatly increases heat transfer, natural convection intensity, and average Nusselt number at a particular aspect ratio. The distribution of temperature and stream function are taken as a function of thermal and geometrical output parameter for given problem. Two stage investigations have been performed to find out the variation in the result between different approaches. Keyword: ANN (average Nusselt number), AR (aspect ratio), LNN (local Nusselt number), Nu (Nusselt number), Pr (Prandtl number), Ra (Rayleigh number).

The Shannon wavelet function and its scale function are used as interpolating functions to establish the Shannon wavelet finite element. The temperature and velocity of every leakage path are calculated based on fuzzy Shannon wavelet finite element method, fuzzy Daubechies wavelet finite element model, fuzzy finite element method and experiment, and comparisons between numerical analysis results and experimental results show that fuzzy Shannon-cosine wavelet finite element method can get highest computing precision and accuracy. The coupling relationships between the flow and heat transfer of clearance leakage flow are analyzed based on fuzzy Shannon-cosine finite element method, and numerical results show that the Nusselt number of every leakage path decreases with increase of Mach number, the flow has great influence on heat transfer of clearance leakage flow of single screw compressor.

Inverse approach for calculating temperature in EHL of line contacts