Impact of porous complicated fin and sinusoidal-heated wall on thermogravitational convection of different nanofluids in a square domain

https://doi.org/10.1016/j.ijthermalsci.2021.107053Get rights and content

Abstract

Porous fins due to high extended heat transfer surface are widely used in different engineering devices including heat exchangers, solar collectors, and chemical reactors. Location of these fins within the working area can be very manifold. Therefore, the present research deals with computational analysis of complicated porous fin influence on nanofluid flow and heat transfer within the heated/cooled cabinet where one vertical wall is kept at non-uniform sinusoidal temperature. The considered fin consists of the mounted porous part at the bottom adiabatic wall and inner porous zone. Investigation has been performed using the boundary-value problem for the partial differential equations formed on the basis of the conservation laws using the experimentally-based correlations for thermal properties of nanofluid. Employing the finite difference techniques the useful results have been obtained illustrating an impact of the inner porous part penetration, location of this part and nanoparticles concentration. It has been ascertained that vertical position and penetration of internal porous block can be efficacious characteristics for the heat transfer augmentation. Moreover, an addition of alumina nanoparticles suppresses the heat transfer and convective flow.

Introduction

Analysis of convective heat transfer in closed cabinets having heated/cooled parts and different solid/porous obstacles is very important due to a wide range of applications in various engineering fields including electronics, heat exchangers, solar collectors, chemical reactors and others. It is well-known that the heat transfer enhancement can be achieved by using the extended heat transfer surface or nanofluids. At the same moment, it is necessary to understand the fluid flow and heat transfer in the case of non-uniform wall temperature distributions.

There are many published papers devoted to analysis of non-uniform (sinusoidal) wall temperature distributions on flow structures and heat transport within the closed regions. Thus, the influence of Lorentz force on the thermal convection of nanofluid in a square closed space with isothermal obstacles and sinusoidal wall temperature distribution was numerically scrutinized by Pordanjani et al. [1]. They used finite volume method and their data revealed that by growing Ha, the Nusselt number is decreased for all volumetric fractions of nanoparticles. Wu et al. [2] reported a computational analysis of thermal convection in a chamber saturated with a heat-producing porous material under the non-uniform temperature wall profiles on sidewalls. Their results showed that the periodic changes with various magnitudes appear in the thermal patterns for liquid and solid phases. Wang et al. [3] developed a computational basis on the spectral element technique for electro-heat-hydrodynamics. Then, they applied the electro-heat-convection in a closed space having various temperature distributions. 3D numerical simulations were performed by Lee et al. [4] on natural convection with internal circular cylinder located in a cooled cubical closed space under the non-uniform temperature conditions. They observed that flow and heat transfer in the closed region depend on the change of heat wall restrictions on the lower surface of the closed space. Umadevi and Nithyadevi [5] studied the free convection in a chamber saturated with Ag−water nanofluid and a heat conducting solid square body by employing the finite volume technique and taking into account of non-uniform thermal boundary conditions. Cheong et al. [6] used the sinusoidal temperature boundary conditions in an inclined rectangular closed space to investigate the natural convection. They found that growing the aspect ratio demonstrates a reducing trend of the heat transfer for all Ra.

The transient free convection for a cooled outer closed space and a hot internal circular cylinder under the non-uniform temperature distribution was studied by Roslan et al. [7]. They ascertained that the heat transfer rate rises by oscillating the source temperature signal. Varol et al. [8] performed a steady free convection analysis in a porous region under sinusoidal varying temperature profile. They revealed that the heat transfer strength rises with growing of amplitude and reduces with growing of aspect ratio. Bilgen and Yedder [9] performed a numerical simulation of natural convection in a rectangular enclosure with a non-uniform temperature distribution on vertical wall. They ascertained that the penetration achieves 100% at high Ra when the bottom zone is warmed. Bouhalleb and Abbassi [10] performed numerically for thermal convection study in a tilted rectangular cabinet saturated with nanofluid heated under spatial temperature boundary conditions. They demonstrated that the strength of heat transfer increases with growing of concentration of nanoparticles. Khandelwal et al. [11] dealt with thermal convection in a rectangular cabinet under sinusoidal temperature profile, numerically by employing spectral element technique. It is revealed that, various periodicities of thermal wall conditions have essential influence on the flow and heat transfer. Mejri et al. [12] performed a work on thermal convection and entropy production in a square closed space with a water–Al2O3 nanofluid under magnetic field and sinusoidal heating. They used the lattice Boltzmann method (LBM) to solve the coupled equations. They showed that for Ra = 5 × 104 and Ha = 20 the heat transfer and entropy production rise and reduce with the increasing of φ. A computational study has been performed by Malik and Nayak [13] on MHD nanofluid heat transfer and entropy production in a closed space with saturated porous medium. They worked on effects of different parameters for energy flux vectors. Unsteady thermal convection in an isosceles triangular cabinet saturated with nanofluid is studied by Rahman et al. [14] by employing the finite element method. They showed that the heat transfer strength increases with an addition of nanoparticles and a growth of Ra number. Also, different parameters for sinusoidal temperature boundary condition become effective on natural convection. Other useful results on non-uniform heating influence on heat transfer and fluid flow can be found in Refs. [[15], [16], [17], [18], [19], [20], [21], [22], [23]].

An introduction of extended heat transfer surfaces allows to intensify the heat transfer. Thus, He et al. [24] conducted computational simulation of double diffusive thermal convection of nanofluids in a closed space having heat partitions vertically attached to the horizontal walls. They applied sinusoidal boundary conditions to the right sidewall of the closed space. Their results showed that the position of partitions is a major factor in controlling the heat and mass transfer rates of nanofluids. Waseem et al. [25] performed a computational study on analysis of the impacts of temperature profiles on heat transfer by using a porous fin model. They observed that porous pins manufactured of aluminum can transport more energy than Si3N4. Swain et al. [26] made a comparison between straight triangular pin and porous pin in the presence of thermal convection. They showed that better heat transfer is observed in the case of using of porous pin fin. Porous substrates can find an application on renewable energy such as solar energy to control heat transfer as studied by Alkam and Al-Nimr [27]. Another experimental work on natural convection from a vertical cylinder by using porous fins is studied by Kiwan et al. [28]. Other similar applications on porous fins effects of heat transfer can be found in Refs. [[29], [30], [31], [32]].

The performed brief review illustrates the importance and necessity of analysis of heat transfer and fluid flow in closed chambers under an influence of porous fins, non-uniform temperature distributions and nano-sized solid particles. It should be noted that nowadays the numerical analysis of nanofluid flow and heat transfer can be performed using the single-phase models [[33], [34], [35], [36], [37], [38]] and two-phase models [[37], [38], [39], [40], [41], [42], [43]]. Employing these models demands understanding the used assumptions and limitations. The single-phase model is the simplest one, but this model can be used for practical analysis if the experimentally-based correlations for thermal properties of the nanofluid are introduced in the model. In the present research such correlations have been employed. Therefore, the obtained results allow to evaluate the possible heat transfer enhancement for the considered complicated system.

The objective of this research is a computational study of thermogravitational heat transfer in a square alumina-water nanofluid region with sinusoidal-heated wall in the presence of mounted porous fin and internally-located porous block employing the single-phase mathematical nanofluid approach having experimentally-based formulae for effective thermophysical parameters of working fluid. The main aim is to see the effects of two porous intermittent body on heat transfer and fluid flow for different conditions. Alumina is just chosen working flow. Such combination of boundary mounted porous fin and a porous block placed within the chamber over the porous fin can be considered as a complex porous fin. The influence of complex solid fin was studied previously [44].

Section snippets

Mathematical formulation

The considered model of momentum, mass and heat transport in a square nanofluid domain is schematically demonstrated in Fig. 1a. The region consists of nanofluid differentially heated cabinet (see Fig. 1a) with a porous fin mounted on the bottom wall and a porous insertion located over this fin. The walls parallel to x -coordinate are adiabatic, while the left wall has the non-uniform thermal pattern and the right surface has low temperature Tc. It is supposed that the physical characteristics

Computational procedure

The control equations (18), (19), (20), (21), (22), (23), (24), (25), (26) with restrictions were worked out by employing the finite differences [[44], [45], [46]].

The developed numerical program was verified using experimental and numerical results of other researchers. The complicated verification of the present code can be found in Refs. [[44], [45], [46]].

A grid independency study was conducted employing three various mesh sizes (50 × 50, 100 × 100, and 200 × 200) for Ra = 105, Pr = 6.82, Da

Results and analysis

In the present research, we study thermal convection of an alumina-water nanofluid in a heated/cooled cabinet having complicated porous fin. It should be noted that the base of this fin is aluminum foam with Da1 = 10−3 and ε1 = 0.9, while the inner porous block is a copper foam with ε2 = 0.8 and Da2 = 10−5 – 10−3. The effects of the Darcy number of inner porous block (Da2 = 10−5 – 10−3), nanoparticles volume fraction (φ = 0.0–0.04), and inner porous block vertical location (δ = 0.1–0.4) on the

Conclusions

Free convective heat transfer of alumina/water nanofluid in a heated/cooled cabinet under an influence of non-uniform left vertical surface temperature pattern with a complex porous fin with wall-mounted part and inner block is examined computationally. Experimental correlations for the nanofluid heat conductivity and efficacious viscosity are employed. Formulated PDEs are worked out by employing the finite difference approach. Investigation of the influence of the internal porous block

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The work was supported by the Russian Science Foundation (Project No. 17-79-20141). Authors also wish to express their thank to the very competent Reviewers for the valuable comments and suggestions.

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