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The Fay and Riddell (F–R) formula is an empirical equation for estimating the stagnation-point heat flux on noncatalytic and fully catalytic surfaces, based on an assumption of equilibrium. Because of its simplicity, the F–R has been used extensively for reentry flight design as well as ground test facility applications. This study aims to investigate the uncertainties of the F-R formula by considering velocity gradient, chemical species at the boundary layer edge, and the thermochemical nonequilibrium (NEQ) behind the shock layer under various hypersonic NEQ flow environments.

The stagnation-point heat flux calculated with the F–R formula was evaluated by comparison with thermochemical NEQ calculations and existing flight experimental values.

The comparisons showed that the F–R underestimated the noncatalytic heat flux, because of the chemical composition at the surface. However, for fully catalytic heat flux, the F–R results were similar to values of surface heat flux from thermochemical NEQ calculations, because the F–R formula overestimates the diffusive heat flux. When compared with the surface heat flux results obtained from flight experimental data, the F–R overestimated the fully catalytic heat flux. The error was 50% at most.

The results provided guidelines for the F–R calculations under hypersonic flight conditions and for determining the approximate error range for noncatalytic and fully catalytic surfaces.

The transient temperature distribution in a rotating cylindrical shell which is heated by an incident time varying heat flux (nuclear pulse) as well as a constant heat flux, is determined numerically by a finite difference method. The shell is cooled by combined convection and thermal radiation. The effects of cooling and rotation on the temperature distribution as well as the time‐ and space‐dependence are shown. Rotation provides a sinusoidal temperature variation in time for a fixed surface and circumferential position. Increased rotation reduces the maximum temperature in the shell and also provides a more uniform temperature distribution in the circumferential direction.

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.

To develop an effective and reliable procedure for the calculation of heat fluxes from the measured temperatures in experimental tests of impingement water cooling.

An inverse heat transfer analysis procedure is developed and implemented into a 2D finite element program. In this method, the least‐squares technique, sequential function specification and regularization are used. Simplifications in the sensitivity matrix calculation and iterative procedures are introduced. The triangular and impulse‐like profiles of heat fluxes simulating practical conditions of impingement water cooling are used to investigate the accuracy and stability of the proposed inverse procedure. The developed program is then used to determine the heat flux during impingement water cooling.

A hybrid procedure is developed in which inverse calculations are conducted with a computation window. This procedure may be used as a whole time domain method or become a periodically sequential or real sequential method by adjusting the sequential steps.

Parametric study and application show that the developed method is effective and reliable and that inverse analysis may obtain the heat flux with an acceptable level of accuracy.

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.

Many a times, the information about the boundary heat flux is obtained only through inverse approach by locating the thermocouple or temperature sensor in accessible boundary. Most of the work reported in literature for the estimation of unknown parameters is based on heat conduction model. Inverse approach using conjugate heat transfer is found inadequate in literature. Therefore, the purpose of the paper is to develop a 3D conjugate heat transfer model without model reduction for the estimation of heat flux and heat transfer coefficient from the measured temperatures.

A 3 D conjugate fin heat transfer model is solved using commercial software for the known boundary conditions. Navier–Stokes equation is solved to obtain the necessary temperature distribution of the fin. Later, the complete model is replaced with neural network to expedite the computations of the forward problem. For the inverse approach, genetic algorithm (GA) and particle swarm optimization (PSO) are applied to estimate the unknown parameters. Eventually, a hybrid algorithm is proposed by combining PSO with Broyden–Fletcher–Goldfarb–Shanno (BFGS) method that outperforms GA and PSO.

The authors demonstrate that the evolutionary algorithms can be used to obtain accurate results from simulated measurements. Efficacy of the hybrid algorithm is established using real time measurements. The hybrid algorithm (PSO-BFGS) is more efficient in the estimation of unknown parameters for experimentally measured temperature data compared to GA and PSO algorithms.

Surrogate model using ANN based on computational fluid dynamics simulations and in-house steady state fin experiments to estimate the heat flux and heat transfer coefficient separately using GA, PSO and PSO-BFGS.

This work is devoted to the numerical analysis of laminar natural convection in two-dimensional vertical cavities, filled with air and of high aspect ratios. One of the sidewalls is cooled isothermally while the other is heated by a uniform or linear heat flux whose average is located at mid-height of the wall. The paper aims to discuss these issues.

The governing equations are discretized by the finite volume method and solved, in transient regime, by using the SIMPLE algorithm.

The flow structure, air temperature field, local convective heat flux on the cold wall, variation of the temperature along the heated wall as well as its average and its maximum are analyzed for various combinations of the controlling parameters. These parameters are the linear heat flux slope γ (γ=0, 1 and −1, for a uniform, increasing and decreasing heat flux, respectively), the average Rayleigh number Ra _m (103Ra _m 3×104) and the aspect ratio A (10A80). It was found that for a given A and Ra _m , the highest (lowest) mean temperature of the hot wall is obtained when the linear heating is descending (ascending). While the maximum temperature increases with the three controlling parameters.

Accurate correlations which allow calculating the average and maximum temperatures of the heated wall are developed for each type of heating. Also, an empirical relationship for the position of the maximum temperature is provided for γ=−1.

Despite its fundamental and practical interest, natural convection in cavities with 10A80 and submitted to non-uniform heat flux was not examined before. Development of original correlations.

The measurement of heat flux is of importance to the development of aerospace engine as basic physical quantities in extreme environment. Heat radiation is one of the basic forms of heat transfer phenomenon. The structure optimizing can improve the performance and infrared absorptivity of the thin film sensor.

This paper designed one kind of thin film heat flux sensor (HFS) with antireflective coating based on transparent conductive oxide thermopile. The introduced membrane structure is so thin that it has little impact on sensor performance. Fabrication of thin film sensors were fabricated by physical vapor deposition (PVD) process.

The steady-state and dynamic response characteristics of the HFS were investigated by calibration platform. The experimental results shown that the absorptivity of the membrane structure (for1070nm) improved compared with that before optimization. The sensitivity of heat flux gauge was 48.56 µV/ (kW/m2) and its frequency response was determined to be about 1980 Hz.

The thin film HFS uses thermopile based on Indium Tin Oxid and In2O3. The antireflective coating is introduced to hot endpoint of HFS to improve sensitivity on laser thermal source. The infrared optical properties of membrane layer structure were investigated. The steady-state and the transient response characteristics of the heat flux sensor were also investigated.

This paper describes a one dimensional moving grid model for the pyrolysis of charring materials. In the model, the solid is divided by a pyrolysis front into a char and a virgin layer. Only when the virgin material reaches a critical temperature it starts to pyrolyse. The progress of the front determines the release of combustible volatiles by the surface. The volatiles, which are produced at the pyrolysis front, flow immediately out of the solid. Heat exchange between those volatiles and the char layer is taken into account. Since the model is used here as a stand‐alone model, the external heat flux that heats up the solid, is assumed to be known. In the future, this model will be coupled with a CFD code in order to simulate fire spread. The char and virgin grid move along with the pyrolysis front. Calculations are done on uniform and on non‐uniform grids for the virgin layer. In the char layer only a uniform grid is used. Calculations done with a non‐uniform grid are about 3 times faster than with a uniform gird. The moving grid model is compared with a faster but approximate integral model for several cases. For sudden changes in the boundary conditions, the approximate integral model gives significant errors.

The purpose of this paper is to consider the conjugate heat transfer from a flat plate involving a turbulent plane wall jet. The bottom wall of the solid block is heated by a constant heat flux.

High Reynolds number two‐equation model (κ‐ϵ) has been used for turbulence modeling. The parameters considered are the conductivity ratio of solid and fluid, the solid slab thickness and the Prandtl number. The Reynolds number considered is 15,000 because the flow becomes fully turbulent and then is independent of the Reynolds number. The range of parameters considered are: conductivity ratio = 1‐1,000, solid slab thickness = 1‐10 and Prandtl number = 0.01‐100.

The non‐dimensional bottom surface temperature is high for high‐Prandtl number fluid and vice versa. As conductivity ratio increases, it decreases whereas it increases with the increase in slab thickness. Similar trend is observed for the distribution of the interface temperature. The Nusselt number computed based on the interface temperature increases with Prandtl number. It is observed that for the range of parameters considered, local Nusselt number distribution superimposes with each other. The average heat flux at the interface has been computed and found to be equal with average heat flux at the bottom which ensures the overall heat balance.

The study of conjugate heat transfer with a turbulent wall jet will be useful for cooling of heated body.