Enhancement of Heat Transfer in a Liquid Metal Flow past a Thermally Conducting and Oscillating Infinite Flat Plate

Abstract

The effect of conjugation on the enhancement of heat transfer in a liquid metal flow past a thermally conducting and sinusoidally oscillating infinite flat plate, when a constant temperature gradient is superimposed on the fluid, is investigated. The plate is made up of the materials compatible with the liquid metals used and is considered to be of finite thickness. Analytical solutions for the velocity and the temperature of the fluid and the solid are obtained. The effects of thermal conductivity and the thickness of the plate on the total time averaged heat flux transported and the thermal boundary layer thickness are investigated in detail. It is found that the effects of wall thickness and wall thermal conductivity on the heat flux transported depend on their effects on the transverse temperature gradient at any frequency. The optimum value of wall thickness at which the net heat flux transported attains the maximum value, for each fluid and for each wall material under consideration, is reported. A maximum increase of 46.14 % in the heat flux transported can be achieved by optimizing the wall thickness. A maximum convective heat flux of 1.87 × 10 8 W /m 2 is achieved using Na with AISI 316 wall. All the results obtained have been compared with the experimental and analytical results reported in the literature and are found to be in good agreement. It is believed that the new insights gained will be of significant use while designing liquid metal heat transfer systems.

Enhancement of Heat Transfer in a Laminar Hydromagnetic Flow of a Liquid Metal Past a Thermally Conducting and Oscillating Infinite Flat Plate

“…For all the fluids and wall materials when increases, Q 1 decreases at whatever may be the value of ε. This result has already been observed in the nonmagnetic case as well . Similar observations are made for every M varying from 0 to 1.6.…”

“…Indeed, Kurzweg and Kaviany have not assumed the above approximation in their problems and their time‐averaged results are not significantly different from the results reported in the literature with the above approximation. Hence, the temperature distribution, for both the fluid and the solid, is assumed to have the form proposed by Chatwin and used by Kurzweg , Kurzweg and Zhao , Puvaneswari and Shailendhra , Kaviany , Inaba and colleagues , and Shailendhra and Anjali Devi which is given as follows: …”

“…Hence, all the analytical and experimental works carried out so far in the literature, with this regard, for the past three decades are all one‐dimensional problems. In particular, in the literature, there are three articles in which enhancement of heat transfer in the flow past an oscillating flat plate is investigated and in all three of these problems the flow is considered to be one‐dimensional. Therefore, following the footprints of the earlier authors, we too have considered the flow to be one‐dimensional.…”

“…The various applications and the advantages of dream pipes over the conventional heat pipes are explained clearly in and . Heat transfer using oscillatory flow of liquid metals is effectively used to enhance heat transfer in many engineering applications such as cooling of high power electronics and electrical equipment, Sterling and Brayton engines , many high‐temperature and high‐power density space, and terrestrial power and energy systems to remove thermal energy .…”

“…They have stated in their concluding remarks that the plates of finite thickness with heat storage capability should receive future consideration as they expected significant changes in the results, particularly when dealing with low Prandtl number fluids like liquid metals, due to the change in the boundary conditions reflecting the effect of conjugation. Hence, Puvaneswari and Shailendhra have extended the same problem by considering the wall to be thermally conducting and analyzed the effects of conjugation on the net heat flux transported and the thermal boundary layer thickness. Further, Shailendhra and Anjali Devi extended the problem by applying a transverse magnetic field and analyzed its effect on the net heat flux transported and the thermal boundary layer thickness.…”