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To analyze two‐phase flow in micro‐channel heat exchangers used for high flux micro‐electronics cooling and to obtain performance parameters such as thermal resistance, pressure drop, etc. Both uniform and non‐uniform micro‐channel base heat fluxes are considered.

Energy balance equations are developed for two‐phase flow in micro‐channels and are solved using the finite element method (FEM). A unique ten noded element is used for the channel descritization. The formulation also automatically takes care of single‐phase flow in the micro‐channel.

Micro‐channel wall temperature distribution, thermal resistance and the pressure drop for various uniform micro‐channel base heat fluxes are obtained, both for single‐ and two‐phase flows in the micro‐channel. Results are compared against data available in the literature. The wall temperature distribution for a particular case of non‐uniform base heat flux is also obtained.

The analysis is done for a single micro‐channel and the effects of multiple or stacked channels are not considered. The analysis needs to be carried out for higher heat fluxes and the validity of the correlation needs to be ascertained through experimentation. Effects of flow mal‐distribution in multiple channels, etc. need to be considered.

The role of two‐phase flow in micro‐channels for high flux micro‐electronics cooling in reducing the thermal resistance is demonstrated. The formulation is very useful for the thermal design and management of microchannels with both single‐ and two‐phase flows for either uniform or non‐uniform base heat flux.

A simple approach to accurately determine the thermal resistance in micro‐channels with two‐phase flow, for both uniform and non‐uniform base heat fluxes is the originality of the paper.

This is a 3D numerical study of convective heat transfer through a micro concentric annulus governing non-uniform heat flux boundary conditions employing water-Al₂O₃ nanofluid. The nanofluid is modeled using two-phase mixture model, as it has a good agreement to experimental results.

Half of the inner pipe surface area of the annulus section of a double pipe heat exchanger is exposed to a constant heat flux which two models are considered to divide the exposing surface area to smaller ones considering the fact that in all cases half of the inner pipe surface area has to be exposed to the heat flux: in model (A), the exposing surface area is divided radially to two parts (A1), four parts (A2) and eight parts (A3) by covering the whole length of the annulus and in model (B) the exposing surface area is divided axially to two parts (B1), four parts (B2) and eight parts (B3) by covering half of the annulus radially.

The results reveal that model (B) leads to higher Nusselt numbers compared to model (A); however, at Reynolds number 10, model (A3) exceeds model (B3). The average Nusselt number is increased up to 142 and 83 per cent at models (A3) with Reynolds number 10 and model (B3) with Reynolds number 1000, respectively.

This paper is a two-phase investigation of water-Al₂O₃ nanofluid in a micro concentric annulus under non-uniform heat flux boundary conditions.

A finite element method is applied to evaluate the performance of microchannel heat exchangers that are used in electronic packaging. The present approach is validated against the CFD data available in the literature. A comparison of the predicted results with other available results obtained from different concepts shows that the present method is able to predict the surface temperature, the fluid temperature and thus the total thermal resistance of the microchannel heat sink satisfactorily. The present methodology has an added advantage in that non‐uniform surface heat flux distribution over the package base can also be analysed easily. The method used in the present analysis is an alternative to massive CFD calculations.

This study aims to investigate a three-dimensional computational modelling of free convection of Al₂O₃ water-based nanofluid in a cylindrical cavity under heterogeneous heat fluxes that can be used as a thermal storage tank.

Effects of different heat flux boundary conditions on heat transfer and entropy generation were examined and the optimal configuration was identified. The simulation results for nanoparticle (NP) volume fractions up to 4 per cent, and Rayleigh numbers of 10⁴, 10⁵ and 10⁶ were presented.

The results showed that for low Ra (10⁴) the heat transfer and entropy generation patterns were symmetric, whereas with increasing the Rayleigh number these patterns became asymmetric and more complex. Therefore, despite the symmetric boundary conditions imposed on the periphery of the enclosure (uniform in Ɵ), it was necessary to simulate the problem as three-dimensional instead of two-dimensional. The simulation results showed that by selecting the optimal values of heat flux distribution and NP volume fraction for these systems the energy consumption can be reduced, and consequently, the energy efficiency can be ameliorated.

The results of the present study can be used for the design of energy devices such as thermal storage tanks, as both first and second laws of thermodynamics have been considered. Using the optimal design will reduce energy consumption.

One of the most critical gas turbine engine components, the rotor blade tip and casing, is exposed to high thermal load. It becomes a significant design challenge to protect the turbine materials from this severe situation. The purpose of this paper is to study numerically the effect of turbine inlet temperature on the tip leakage flow structure and heat transfer.

In this paper, the effect of turbine inlet temperature on the tip leakage flow structure and heat transfer has been studied numerically. Uniform low (LTIT: 444 K) and high (HTIT: 800 K) turbine inlet temperature, as well as non‐uniform inlet temperature have been considered.

The results showed the higher turbine inlet temperature yields the higher velocity and temperature variations in the leakage flow aerodynamics and heat transfer. For a given turbine geometry and on‐design operating conditions, the turbine power output can be increased by 1.33 times, when the turbine inlet temperature increases 1.80 times. Whereas the averaged heat fluxes on the casing and the blade tip become 2.71 and 2.82 times larger, respectively. Therefore, about 2.8 times larger cooling capacity is required to keep the same turbine material temperature. Furthermore, the maximum heat flux on the blade tip of high turbine inlet temperature case reaches up to 3.348 times larger than that of LTIT case. The effect of the interaction of stator and rotor on heat transfer features is also explored using unsteady simulations. The non‐uniform turbine inlet temperature enhances the heat flux fluctuation on the blade tip and casing.

The increase of turbine inlet temperature is usually proposed to achieve the higher turbine efficiency and the higher turbine power output. However, it has not been reported how much the heat transfer into the blade tip and casing increases with the increased turbine inlet temperature. This paper investigates the heat transfer distributions on the rotor blade tip and casing, associated with the tip leakage flow under high and low turbine inlet temperatures, as well as non‐uniform temperature distribution.

The purpose of this study is to numerically analyze the thermal and entropy generation characteristics on two-dimensional, incompressible, laminar single-phase flow of Al₂O₃-water nanofluid in a micro-channel subjected to asymmetric sinusoidal wall heating with varying amplitude, length of fluctuation period and phase difference of applied heat flux for Reynolds number in the range of 25-1000.

The numerical computation is based on the Finite Element Method and the Lagrange finite element technique is used for approximating the flow variables within the computational domain.

The average Nusselt number increases with increasing Reynolds number (Re) for all the volume fractions of nanofluid. However, the total entropy generation decreases up to a critical value of Re and increases thereafter. Increase in volume fraction shifts the critical Re towards the lower Re regime. The average Nusselt number and total entropy generation increase with amplitude and length of fluctuation period of heat flux. The optimal choice of volume fraction for lesser entropy generation and higher heat transfer is found to be 3 per cent independent of the value of amplitude, length of fluctuation period and phase difference of the heat flux.

To the best of authors’ knowledge, the interplay of various parameters concerning non-uniform heating in achieving the maximum heat transfer with minimum irreversibility has not been investigated. Focusing on this agenda, the results of this study would benefit the industrial sector in achieving the maximum heat transfer at the cost of minimum irreversibilities with an optimal choice of inlet Reynolds number, volume fraction of nanofluid, amplitude, length of the period of fluctuation of heat flux and phase difference of applied heat flux.

The purpose of this paper is to numerically investigate the heat transfer enhancement in a tube filled partially with porous media under non-uniform porosity distribution and thermal dispersion effects. The optimum porous thickness ratio [R_(r,Nu)] for the heat transfer enhancement under these conditions with and without considering required pumping power is evaluated.

The local thermal non-equilibrium and Darcy–Brinkman–Forchheimer models are used to simulated thermal and flow fields in porous region. The tube wall and flow regime are assumed to be isothermal and laminar, respectively. The impacts of Darcy number (Da = 10^-6 - 10^-1) and inertia parameter (F = 0 − 2) on the Nusselt number and friction factor are studied for non-uniform porosity distribution.

First, the effect of Nusselt number indicates that there are two different behaviors with respect to uniform and non-uniform porosity for partially and fully filled porous pipe. Second, variable porosity in porous region has significant influence on the optimum thickness ratio with considering required pumping power. For negligible inertia term, it depends on the Darcy number, whereas it is 0.9 at F > 1. Third, the plug flow assumption cannot be valid even at lower Darcy number under non-uniform porosity, while this assumption is applicable at Da < 10^-3 for constant porosity distribution in porous region.

According to the best knowledge of authors, the optimum porous thickness ratio for the heat transfer enhancement considering the pressure loss effects under variable porosity has not reported up to now. Also the plug flow assumption in such physics is not discussed.

Natural gas leak from underground pipelines could lead to serious damage and global warming, whose spreading in soil should be systematically investigated. This paper aims to propose a three-dimensional numerical model to analyze the methane–air transportation in soil. The results could help understand the diffusion process of natural gas in soil, which is essential for locating leak source and reducing damage after leak accident.

A numerical model using finite element method is proposed to simulate the methane spreading process in porous media after leaking from an underground pipe. Physical models, including fluids transportation in porous media, water evaporation and heat transfer, are taken into account. The numerical results are compared with experimental data to validate the reliability of the simulation model. The effects of methane leaking direction, non-uniform soil porosity, leaking pressure and convective mass transfer coefficient on ground surface are analyzed.

The methane mole fraction distribution in soil is significantly affected by the leaking direction. Horizontally and vertically non-uniform soil porosity has a stronger effect. Increasing leaking pressure causes increasing methane mole flux and flow rate on the ground surface.

Most existing gas diffusion models in porous media are for one- or two-dimensional simulation, which is not enough for predicting three-dimensional diffusion process after natural gas leak in soil. The heat transfer between gas and soil was also neglected by most researchers, which is very important for predicting the gas-spreading process affected by the soil moisture variation because of water evaporation. In this paper, a three-dimensional numerical model is proposed to further analyze the methane–air transportation in soil using finite element method, with the presence of water evaporation and heat transfer in soil.

By modelling the unsteady heat transfer in liquid gas tanks, the temperature distribution in the tank as well as the heat flux reaching the liquid gas can be predicted. Knowledge of the temperature distribution and heat flux can be used to predict evaporation losses from the tank. By minimizing the evaporation losses, the thermal design of a gas tank can be optimized. This paper presents a finite difference simulation of the unsteady three‐dimensional heat transfer in gas tanks and an optimized configuration. The numerical procedure accounts for radiation from the sun as well as radiative and convective heat transfer with the environment. A non‐uniform grid is used because the tank consists of several different materials of varying dimensions and properties. Geometrical effects such as variations in the thickness of the insulation material and the diameter and height of the tanks are also studied in an attempt to optimize the design configuration.

We determine the effects of micro‐inertia density and the vortex viscosity on laminar free convection boundary layer flow of a thermomicropolar fluid past a vertical plate with exponentially varying surface temperature as well as surface heat flux. The governing nonsimilarity boundary layer equations are analyzed using: first, a series solution for small ξ (a scaled streamwise distribution of micro‐inertia density), second, an asymptotic solution for large ξ and, third, a full numerical solution implicit finite difference method together with Keller‐box scheme. Results are expressed in terms of local skin friction and local Nusselt number. The effects of varying the vortex viscosity parameter, Δ, surface temperature and the surface heat flux gradient n and m respectively against ξ for fluids having Prandtl number equals 0.72 and 7.0 are determined.