Development of modern technology in microelectronics and power engineering necessitates the creation of effective cooling systems. This is made possible by the use of the special fins technology within the cavity or special heat transfer liquids in order to intensify the heat removal from the heat-generating elements. The present work is devoted to the mathematical modeling of thermogravitational convection of a non-Newtonian fluid in a closed square cavity with a local source of internal volumetric heat generation. The behavior of the fluid is described by the Ostwald-de Waele power law model. The defining Navier–Stokes equations written using the dimensionless stream function, vorticity and temperature are solved using the finite difference method. The effects of the Rayleigh number, power-law index, and thermal conductivity ratio on heat transfer and the flow structure are studied. The obtained results are presented in the form of isolines of the stream function and temperature, as well as the dependences of the average Nusselt number and average temperature on the governing parameters.
Purpose This paper aims to study the mathematical modeling of passive cooling systems for electronic devices. Improving heat transfer is facilitated by the correct choice of the working fluid and the geometric configuration of the engineering cavity; therefore, this work is devoted to the analysis of the influence of the position of the heat-generating element and the tilted angle of the electronic cabinet on the thermal convection of a non-Newtonian fluid. Design/methodology/approach The area of interest is a square cavity with two cold vertical walls, while the horizontal boundaries are adiabatic. An element of constant volumetric heat generation is placed on the lower wall of the chamber. The problem is described by Navier–Stokes partial differential equations using dimensionless stream function and vorticity. The numerical solution is based on the developed computational code using the finite difference technique and a uniform rectangular grid. Findings The key conclusions of this work are the results of a detailed analysis of streamlines and isotherms, the average Nusselt number and profiles of the average heater temperature. It was found that more intensive cooling of the heat-generating element occurs when the cavity is filled with a pseudoplastic fluid (n < 1) and not inclined (α = 0). The Rayleigh number of Ra = 105 and the thermal conductivity ratio of k = 100 are characterized by the most positive effect. Originality/value The originality of the research lies in both the study of thermal convection in a square chamber filled with power-law fluid under the influence of a volumetric heat production element and the analysis of the influence of geometric and thermophysical parameters characterizing the considered process.
Optimization of cooling systems for electronic devices is one of the crucial challenges in the modern engineering world. Inclusion of nanosized particles to working heat transfer liquids can enhance the heat removal from the heated elements in electronics. Taking into account these data, the present research is devoted to numerical analysis of natural convection in a cavity filled with a non‐Newtonian nanosuspension under an influence of a heat‐generating wall section. The paper contains the simulation outcomes for two different cases, namely, a heat‐generating wall section with constant heat flux and a heat‐generating wall section with constant temperature. The considered phenomenon has been described using the single‐phase nanofluid model where the base liquid is a pseudoplastic fluid. The rheological parameters of the host liquid including the coefficient of flow density and an indicator of fluid behavior are the empirical data of MWCNT nanofluids. The non‐Newtonian nature of the nanoliquid has been described by the Ostwald‐de‐Waele power law. Detailed analysis has been carried out for different governing parameters including the Rayleigh number, the volume fraction of nanoparticles, and the size of the heater using the non‐primitive dimensionless variables and the finite difference method. Obtained results illustrate different temperature patterns for various boundary conditions. Moreover, in the case of heat‐generating element, the average Nusselt number is greater than for the isothermal heater. It should be noted that the considered nanofluid model reflects the energy transference degradation with a growth of the nanoparticles concentration.
In this paper, a time-dependent natural convective heat transfer in a closed square cavity filled with non-Newtonian fluid was considered in the presence of an isothermal energy source located on the lower wall of the region under consideration. The vertical boundaries were kept at constant low temperature, while the horizontal walls were completely insulated. The behavior of a non-Newtonian fluid was described by the Ostwald de Ville power law. The process under study was described by transient partial differential equations using dimensionless non-primitive variables "stream function-vorticity-temperature". This method allows excluding the pressure field from the number of unknown parameters, while the non-dimensionalization allows generalizing the obtained results to a variety of physical formulations. The considered mathematical model with the corresponding boundary conditions was solved on the basis of the finite difference method. The algebraic equation for the stream function was solved by the method of successive lower relaxation. Discrete analogs of the vorticity equation and energy equation were solved by the Thomas algorithm. The developed numerical algorithm was tested in detail on a class of model problems and good agreement with other authors was achieved. Also during the study, the mesh sensitivity analysis was performed that allows choosing the optimal mesh. As a result of numerical simulation of unsteady natural convection of a non-Newtonian power-law fluid in a closed square cavity with a local isothermal energy source, the influence of governing parameters was analyzed including the impact of the Rayleigh number in the range 10 4-10 6 , power-law index n = 0.6-1.4, and also the position of the heating element on the flow structure and heat transfer performance inside the cavity. The analysis was carried out on the basis of the obtained distributions of streamlines and isotherms in the cavity, as well as on the basis of the dependences of the average Nusselt number. As a result, it was established that pseudoplastic fluids (n < 1) intensify heat removal from the heater surface. The increase in the Rayleigh number and the central location of the heating element also correspond to the effective cooling of the heat source.
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