Estimation of the transient surface temperature and heat flux of a steel slab using an inverse method

In the steel industry it is of great importance to be able to control the surface temperature and heating- or cooling rates during heat treatment processes. An experiment was performed in which a steel slab was heated up to 1250 °C in a fuel fired test furnace. The transient surface temperature and heat flux of a steel slab is calculated using a model for inverse heat conduction. That is, the time dependent local surface temperature and heat flux of a slab is calculated on the basis of temperature measurements in selected points of its interior by using a model of inverse heat conduction. Time- and temperature histories were measured at three points inside a steel slab. Measured temperature histories at the two lower locations of the slab were used as input to calculate the temperature at the position of the third location. A comparison of the experimentally measured and the calculated temperature histories was made to verify the model. The results showed very good agreement and suggest that this model can be applied to similar applications in the Steel industry or in other areas where the target of investigation for some reason is inaccessible to direct measurements.     

Calculating transient wall heat flux from measurements of surface temperature

Wall heat fluxes can be derived from time resolved measurements of the surface temperature. This paper describes an analytical approach to calculate the heat flux from an analytical solution of the one-dimensional transient energy equation with transient boundary conditions using the Laplace transformation. The results are compared to simple test cases for which the heat fluxes are given in literature. The method is used to calculate the heat flux from a fuel spray to a wall at diesel engine conditions.     

Mixed convection from a vertical plate to non-Newtonian fluids with uniform surface heat flux

This paper proposed a mixed-convection parameter ζ to analyze the steady laminar mixed convection heat transfer between non-Newtonian fluids and a vertical plate with constant wall heat flux. The obtained finite-difference solutions are uniformly valid over the entire range of mixed convection from the pure forced convection limit (ζ = 0) to pure free convection limit (ζ = 1). Typical velocity and temperature profiles in the boundary layer are presented. Furthermore, the variations of the local heat transfer rates as well as wall frictions along the plate are shown explicitly.     

Forced convection heat transfer from a heated circular cylinder with arbitrary surface temperature distributions

A Fredholm-type boundary integral expression for evaluation of the forced convection heat transfer from an object with arbitrary surface temperature distributions is proposed. The Fredholm kernel function for a heated circular cylinder was calculated by numerical simulation of the forced convection fields, and then generalized heat transfer coefficients for arbitrary surface temperature distributions were defined. By use of the generalized heat transfer coefficients, it is shown that the difference in local heat transfer characteristics between the case of an isothermal cylinder and that of a uniform heat flux one can be interpreted only as the difference of the surface temperature distributions. Moreover, the mechanism of the effect of the surface temperature distribution on the characteristics of forced convection heat transfer from a cylinder is clarified in detail through the generalized heat transfer coefficients. © 1999 Scripta Technica, Heat Trans Asian Res, 28(6): 484–499, 1999     

The effect of gap distance on the heat transfer between a heated finned surface and a saturated porous plate

Experiments were performed to investigate the effect that the presence of a gap has on the heat transfer between a heated finned surface and a saturated porous plate with an average pore radius of 200 μm. There was evidence that the vapour generated beneath the heated surface can escape to the vapour grooves more easily when a gap distance is introduced. This seemed to decrease the vapour penetration into the porous plate. The heat transfer performance of the heated finned surface initially increased as the gap distance was increased from 0 to 500 μm, but remained relatively unchanged for gap distances of 500–900 μm.     

Estimation of heat flux and temperature distributions in a composite strip and homogeneous foundation

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat flux and temperature distributions for the system composed of a multi-layer composite strip and semi-infinite foundation, from the knowledge of temperature measurements taken within the strip. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. Results show that an excellent estimation on the time-dependent heat flux can be obtained for the test case considered in this study.     

Laminar free convection from a vertical plate with uniform surface heat flux in chemically reacting systems

Two-dimensional steady laminar free convection from a vertical plate with uniform surface heat flux rate is studied in a gas where a reversible very fast reaction of dissociation A↔2B takes place at atmospheric pressure. The effective thermophysical properties of the gas in the interval of dissociation are evaluated and the governing boundary-layer equations are solved numerically by a finite-difference method with control volume formulation for a wide range of values of the independent variables which have a significant influence on the phenomenon. In the case of undisturbed fluid temperature T_∞ smaller than T_0.5, corresponding to a rate of dissociation α=0.5, three different heat transfer regimes, marked by two critical heat fluxes, may be distinguished as the surface heat flux rate increases. The theoretical results obtained for the critical heat fluxes as well as the coefficient of convection are expressed in terms of correlations among dimensionless parameters defined through the mixture effective properties.     

Three-dimensional thermal boundary layer corrections for circular heat flux gauges mounted in a flat plate with a surface temperature discontinuity

Three-dimensional Navier–Stokes computational fluid dynamics (CFD) analysis has been performed in an effort to determine thermal boundary layer correction factors for circular convective heat flux gauges (such as Schmidt–Boelter and plug type) mounted flush in a flat plate subjected to a stepwise surface temperature discontinuity. Turbulent flow solutions with temperature-dependent properties are obtained for a freestream Reynolds number of 1E6, and freestream Mach numbers of 2 and 4. The effect of gauge diameter and the plate surface temperature have been investigated. The 3D CFD results for the heat flux correction factors are compared to quasi-2D results deduced from constant property integral solutions and also 2D CFD analysis with both constant and variable properties. The role of three-dimensionality and of property variations on the heat flux correction factors has been demonstrated.     

Non-invasive blood perfusion measurements using a combined temperature and heat flux surface probe

Non-invasive blood perfusion measurement systems have been developed and tested in a phantom tissue and an animal model. The probes use a small sensor with a laminated flat thermocouple to measure the heat transfer and temperature response to an arbitrary thermal event (convective or conductive) imposed on the tissue surface. Blood perfusion and thermal contact resistance are estimated by comparing heat flux data with a mathematical model of the tissue. The perfusion probes were evaluated for repeatability and sensitivity using both a phantom tissue test stand and exposed rat liver tests. Perfusion in the phantom tissue tests was varied by controlling the flow of water into the phantom tissue test section, and the perfusion in the exposed liver tests was varied by temporarily occluding blood flow through the portal vein. The phantom tissue tests indicated that the probes can be used to detect small changes in perfusion (0.005 ml/ml/s). The probes qualitatively tracked the changes in the perfusion of the liver model due to occlusion of the portal vein.     

Effect of thermocouple sensor dynamics on surface heat flux predictions obtained via inverse heat transfer analysis

A simple thermocouple model is used in this paper to generate data by simulating the imposition of a triangular heat flux history on a one-dimensional domain. A general inverse heat conduction (IHC) analysis computer program is developed and used to estimate the heat flux history based on the generated data. The results show that the effect of the thermocouple's time constant is to diminish the magnitude of the predicted heat flux history and displace its distribution in time.     

Mechanism of convection heat transfer on a heated crystal surface

This paper considers the mechanism of convection heat transfer on a heated crystal surface. An attempt was made to divide the heat transfer process into three links. Phonon theory is used to study and define the "convective power" of a crystal. The results indicate that the convection heat transfer process is discrete. The order of convective power of the crystal is extremely high and is approximately proportional to T ∼︁ T. It can be regarded that the energy exchange is finished in the course of one collision between the heated solid and media particles that is demonstrated by thermal conduction in the gas. The value of the heat transfer coefficient depends on the properties, states, and motion of the media. © 2000 Scripta Technica, Heat Trans Asian Res, 29(7): 573—580, 2000     

Temperature and heat flux estimation from sampled transient sensor measurements

Laplace transform is used to solve the problem of heat conduction over a finite slab. The temperature and heat flux on the two surfaces of a slab are related by the transfer functions. These relationships can be used to calculate the front surface heat input (temperature and heat flux) from the back surface measurements (temperature and/or heat flux) when the front surface measurements are not feasible to obtain. This paper demonstrates that the front surface inputs can be obtained from the sensor data without resorting to inverse Laplace transform. Through Hadamard Factorization Theorem, the transfer functions are represented as infinite products of simple polynomials. Consequently, the relationships between the front and back surfaces are translated to the time-domain without inverse Laplace transforms. These time-domain relationships are used to obtain approximate solutions through iterative procedures. We select a numerical method that can smooth the data to filter out noise and at the same time obtain the time derivatives of the data. The smoothed data and time derivatives are then used to calculate the front surface inputs.     

Asymmetric entrainment effect on the local surface temperature of a flat plate heated by an obliquely impinging two-dimensional jet

The flow and temperature fields caused by a two-dimensional heating air jet obliquely impinging on a flat plate are experimentally characterized. Whilst the jet flow is discharged at Re_Dh = 8.2 × 10³ based on the hydraulic diameter of the orifice, D_h, and the jet exit-to-plate spacing (separation distance) is fixed at 8D_h, the impingement angle (inclination) is systematically decreased from 90° (normal impinging) to 30° (oblique impinging). A separate experiment is carried out for a two-dimensional cooling jet obliquely impinging on a heated plate (constant heat flux). The results demonstrate that the response of local surface temperature to plate inclination behaves in a completely different manner. For impinging jet cooling, the inclination (from normal impinging position) reduces the local effective temperature values at corresponding points about actual stagnation point, inclusive of it. For impinging jet heating, the inclination causes, conversely, an increase in local surface temperature including the stagnation point temperature. However, the shifting of the actual stagnation point towards the uphill side of the plate is consistently observed for both hot and cold jet cases. This newly found feature for an obliquely impinging jet is attributed to the combined effects of asymmetric entrainment and momentum redistribution (i.e., thickening/thinning of hydraulic boundary layers on each side of the plate with respect to the actual stagnation point).     

Free convection along the downward-facing surface of a heated horizontal plate

An experiment has been made on quasi-two-dimensional, free convection heat transfer from a heated horizontal plate of Rayleigh number of the order of 10⁷ in air; the velocity and temperature fields near the downward-facing surface have been measured. The velocity profile was found to be of the dual-flow type, and the possibility of obtaining similarity solutions for the present problem was also experimentally denied. The practically applicable range of boundary-layer approximation is discussed, and the local and average Nusselt numbers are compared with theoretical and experimental results reported by others.     

Enhancement of natural convection heat transfer from a vertical heated plate using inclined fins

An enhancement technique is developed for natural convection heat transfer from a vertical heated plate with inclined fins, attached on the vertical heated plate to isolate a hot air flow from a cold air flow. Experiments are performed in air for inclination angles of the inclined fins in the range of 30° to 90° as measured from a horizontal plane, with a height of 25 to 50 mm, and a fin pitch of 20 to 60 mm. The convective heat transfer rate for the vertical heated plate with inclined fins at an inclination angle of 60° is found to be 19% higher than that for a vertical heated plate with vertical fins. A dimensionless equation on the natural convection heat transfer of a vertical heated plate with inclined fins is presented. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 334–344, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20168     

Estimation of the time-dependent heat flux using the temperature distribution at a point by conjugate gradient method

In this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time-dependent heat flux using the temperature distribution at a point. Also, the effects of noisy data and position of measured temperature on final solution are studied. The numerical solution of the governing equations is obtained by employing a finite-difference technique. For solving this problem the general coordinate method is used. We solve the inverse heat conduction problem of estimating the transient heat flux, applied on part of the boundary of an irregular region. The irregular region in the physical domain (r,z) is transformed into a rectangle in the computational domain (ξ,η). The present formulation is general and can be applied to the solution of boundary inverse heat conduction problems over any region that can be mapped into a rectangle. The obtained results for few selected examples show the good accuracy of the presented method. Also the solutions have good stability even if the input data includes noise and that the results are nearly independent of sensor position.