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Article
Publication date: 2 January 2018

Dawid Taler and Anna Korzen

The paper aims to present the mathematical modeling of plate fin and tube heat exchanger at small Reynolds numbers on the water side. The Reynolds number of the water flowing…

127

Abstract

Purpose

The paper aims to present the mathematical modeling of plate fin and tube heat exchanger at small Reynolds numbers on the water side. The Reynolds number of the water flowing inside the tubes was varied in the range from 4,000 to 12,000.

Design/methodology/approach

A detailed analysis of transient response was modeled for the following changes in the operating parameters of the heat exchanger: a reduction in the water volume flow, an increase in the water volume flow and an increase in the water volume flow with a simultaneous reduction in the air flow velocity.

Findings

The results of the numerical simulation of a heat exchanger by using experimentally determined water-side heat transfer correlation and theoretical correlation derived for the transition tube flow agree very well. The relationship to calculate the air-side Nusselt number was determined experimentally. The correlation for the air-side Nusselt number was the same for the theoretical and experimental water side correlation.

Research limitations/implications

The correlation for the air-side Nusselt number as a function of the Reynolds and Prandtl numbers is based on the experimental data and was determined using the least squares method.

Originality/value

The form of the relationship that was used to approximate experimentally determined water-side Nusselt numbers is identical to the theoretically derived formula for the transition range. The experiments show that the relationship for the water-side Nusselt number in transition and turbulent flow regime that was obtained using theoretical analysis gives quite satisfactory results.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 2 January 2018

Kalidasan K., R. Velkennedy, Jan Taler, Dawid Taler, Pawel Oclon and Rajesh Kanna P.

This study aims to perform a numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature under laminar flow…

152

Abstract

Purpose

This study aims to perform a numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature under laminar flow conditions. The geometry of the enclosure contains two isothermal blocks placed equidistant along the streamwise direction. The top wall is assumed to be cold (low temperature). The bottom wall temperature is either kept as constant or sinusoidally varied with time. The vertical walls are considered as adiabatic. The flow is diagonally upwards and assisted by the buoyancy force. The inlet is positioned at the bottom of the left wall, and the outlet is placed at the top of the right wall. The parameters considered in this paper are Rayleigh number (104-106), Prantdl number (0.71), amplitude of temperature oscillation (0-0.5) and the period (0.2). The effects of these parameters on heat transfer and fluid flow inside the open cavity are studied. The periodic results of fluid flow are illustrated with streamlines and the heat transfer is represented by isotherms and time-averaged Nusselt number. By virtue of increasing buoyancy, the heat transfer accelerates with an increase in the Rayleigh number. Also, the heat transfer is intensive with an increase in the bottom wall temperature.

Design/methodology/approach

The momentum and energy equations are solved simultaneously. The energy equation (3) is initially solved using the alternating direction implicit (ADI) method. The results of the energy equation are updated into the vorticity equation. The unsteady vorticity transport equation is also solved using the ADI method. Dimensionless time step equal to 0.01 is used for high Ra (105 and 106) and 0.001 is used for low Ra (104). Convergence criteria of 10−5 is used during the vorticity, stream function and temperature calculations, as the sum of error should be very small.

Findings

Numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature is performed under laminar flow condition. The effect of the isothermal blocks on the heat transfer is analyzed for different Rayleigh numbers and the following conclusions are arrived. The hydrodynamic blockage effect is subdued by the isothermal heating of square blocks. Based on the streamline diagrams, it is found that the formation of vortices is greatly influenced by the Rayleigh number when all the walls are exposed to a constant wall temperature. The influence of amplitude on the heat transfer is remarkable on the wall exposed to oscillating temperature and is subtle on the opposite static cold wall. The heat transfer increases with an increase in the Rayleigh number and temperature.

Research limitations/implications

Flow is assumed to be two-dimensional and laminar subject to oscillatory boundary condition. The present investigation aims to study natural convection inside the cavity filled with air whose bottom wall is subject to time-variant temperature. The buoyancy is further intensified through two isothermal square blocks placed equidistant along the streamwise direction at mid-height.

Originality/value

The authors have developed a CFD solver to simulate the situation. Effect of Rayleigh number subject to oscillatory thermal boundary condition is simulated. Streamline contour and isotherm contour are presented. Local and average Nusselt numbers are presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 2 January 2018

Dawid Taler

The purpose of this paper is to develop new semi-empirical heat transfer correlations for turbulent flow of liquid metals in the tubes, and then to compare these correlations with…

177

Abstract

Purpose

The purpose of this paper is to develop new semi-empirical heat transfer correlations for turbulent flow of liquid metals in the tubes, and then to compare these correlations with the experimental data. The Prandtl and Reynolds numbers can vary in the ranges: 0.0001 ≤ Pr ≤ 0.1 and 3000 ≤ Re ≤ 106.

Design/methodology/approach

The energy conservation equation averaged by Reynolds was integrated using the universal velocity profile determined experimentally by Reichardt for the turbulent tube flow and four different models for the turbulent Prandtl number. Turbulent heat transfer in the circular tube was analyzed for a constant heat flux at the inner surface. Some constants in different models for the turbulent Prandtl number were adjusted to obtain good agreement between calculated and experimentally obtained Nusselt numbers. Subsequently, new correlations for the Nusselt number as a function of a Peclet number was proposed for different models of the turbulent Prandtl number.

Findings

The inclusion of turbulent Prandtl number greater than one and the experimentally determined velocity profile of the fluid in the tube while solving the energy conservation equation improved the compatibility of calculated Nusselt numbers, with Nusselt numbers determined experimentally. The correlations proposed in the paper have a sound theoretical basis and give Nusselt number values that are in good agreement with the experimental data.

Research limitations/implications

Heat transfer correlations proposed in this paper were derived assuming a constant heat flux at the inner surface of the tube. However, they can also be used for a constant wall temperature, as for the turbulent flow (Re > 3,000), the relative difference between the Nusselt number for uniform wall heat flux and uniform wall temperature is very low.

Originality/value

Unified, systematic approach to derive correlations for the Nusselt number for liquid metals was proposed in the paper. The Nusselt number was obtained from the solution of the energy conservation equation using the universal velocity profile and eddy diffusivity determined experimentally, and various models for the turbulent Prandtl number. Four different relationships for the Nusselt number proposed in the paper were compared with the experimental data.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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