Heater Shape Research Articles

Bayesian Inference for Estimating Heat Sources Through Temperature Assimilation

Abstract This paper utilizes a Bayesian inference framework to address the two-dimensional (2D) steady-state heat conduction problem, focusing on the estimation of unknown distributed heat sources in a thermally conducting medium with uniform conductivity. The goal is to infer the locations, strength, and shape of heaters by assimilating temperature data in Euclidean space, employing a Fourier series to represent each heater's shape. The Markov Chain Monte Carlo (MCMC) method, incorporating the random-walk Metropolis–Hasting (MH) algorithm and parallel tempering, is utilized for posterior distribution exploration in both unbounded and wall-bounded domains. It is found that multiple solutions arise in cases where the number of temperature sensors is less than the number of unknown states. Moreover, smaller heaters introduce greater uncertainty in estimated strength. To address the challenge of estimating the heater's strength and shape simultaneously due to their strong correlation, our method incorporates sharp priors on one to ensure accurate and feasible solutions of the other. The diffusive nature of heat conduction smooths out any deformations in the temperature contours, especially in the presence of multiple heaters positioned near each other, impacting convergence. In wall-bounded domains with Neumann boundary conditions, the inference of heater parameters tends to be more accurate than in unbounded domains.

Comparative analysis of the lattice Boltzmann method and the finite difference technique of thermal convection in closed domains with heaters

PurposeThe purpose of this paper is to investigate numerically thermal convection heat transfer in closed square and cubical cavities with local energy sources of various geometric shapes.Design/methodology/approachThe analyzed regions are square and cubical cavities with two isothermally cold opposite vertical walls, whereas other walls are adiabatic. A local energy element of rectangular, trapezoidal or triangular shape is placed on the lower surface of the cabinet. The lattice Boltzmann technique has been used as the main method for the problem solution in two-dimensional (2D) and three-dimensional (3D) formulations, whereas the finite difference technique with non-primitive parameters such as stream function and vorticity has been also used.FindingsThe velocity and temperature fields for a huge range of Rayleigh number 104–106, as well as for various geometry shapes of the heater have been studied. A comparative analysis of the results obtained on the basis of two numerical techniques for 2D and 3D formulations has been performed. The dependences of the energy transfer strength in the region on the shape of energy source and Rayleigh number have been established. It has been revealed that the triangular shape of the energy source corresponds to the maximum values of the velocity vector and temperature within the cavity, and the rectangular shape corresponds to the minimum values of these mentioned variables. With the growth of the Rayleigh number, the difference in the values of these mentioned variables for rectangular and triangular shapes of heaters also increases.Originality/valueThe originality of this work is to scrutinize the lattice Boltzmann method and finite difference method for the problem of natural convection in 2D and 3D closed chambers with a local heated element.

Heater shape effects on thermal plume formation

This paper presents the results of numerical modeling of the evolution of thermal plumes in a fluid layer heated locally from below. Special attention is paid to the development of a boundary layer that precedes thermal plume generation. Equations for natural convection are solved using the ANSYS Fluent software package. The calculated temperature fields are compared with the results of a full-scale experiment. The variation of parameters of the numerical model gives two mechanisms of heat transfer from a local heat source – conductive and convective. In the first case, uniform heating of fluid above the heater surface leads to the formation of a single plume. In the second case, the boundary layer near the heater edges experiences deformation that causes a convective jet to bifurcate. The purpose of the present work is to study the effect of heat source shapes (triangular, square, pentagonal and circular) on the boundary layer structure. For each heater shape, the critical value of the Rayleigh number determined. It is shown that bifurcation of a thermal plume is initiated when the Rayleigh number exceeds a critical value.

Homogeneous heating of a sample space by a modified heating assembly in a belt-type high-pressure apparatus.

To create homogeneous heating in the sample space in a belt-type high-pressure apparatus, modified heating assemblies under pressure of 2.5 GPa and temperature up to 1700 °C were examined. Counterbores (with several diameters) were made at both ends of a cylindrical graphite heater to suppress the temperature gradient along the cylindrical axis of the heater. Temperature distributions within the heaters were measured by thermocouples and geothermometers. Both sets of measurements revealed that the temperature distribution in the sample space (6.9 mm outside diameter/12 mm length) was homogenized (i.e., variation of less than 10 °C under heating at 1700 °C) by optimizing the heater shape.

Effect of Storage Heater Shape on Performance of Built -In –Storage Solar Collector Suitable for IRAQ Environment

Effect of Storage Heater Shape on Performance of Built -In –Storage Solar Collector Suitable for IRAQ Environment

Performance Comparison of Square and Split Heaters

We investigated performance of square and split heaters experimentally. Four micro heaters were prepared. They included two square heaters, S20 (20μm×20μm) and S24 (24μm×24μm), and two split heaters, D22 (22μm×10μm×2) and D26 (26μm×12μm×2). Square and split heaters showed similar characteristics in electrical strengths irrespective of size and electric resistance. Heater shape seemed to have little influence on the actuating performance. Temperature on the heater surface was measured using an infrared (IR) microscope. Larger thermal spreading was observed on the split heater. The split heater is expected to manage relatively higher energy compared to the square heater of similar size.

Study of Stirling Engine Having Heat Exchangers Consisting of Pin-Fin Arrays

The structure and numerically predicted results of a new Stirling engine with a circular disk heat exchanger consisting of pin-fin arrays are presented. Pin-fin arrays are carved into the circular heat exchanger disk's face. An annular cover plate is attached to these tips. A cooler of similar shape is located. So-called “α”, “β” and “γ” configurations are capable in present engine. Numerical prediction of power employing second-order approximation method is carried out in so-called “β” configuration engine case. The fluid resistances of many parts are regarded and some mechanical friction losses are regarded. The predicted engine output becomes 1 kW with the temperature of 773 and 298 [K] on the heating side and cooling side, respectively. In conclusion, the Stirling engine described here is suitable for biomass and solar use because its heater shape is circular and has unique feature that it doesn't need any heat exchanger pipe.

Origin and effect of thermocapillary convection in subcooled boiling: observations and conclusions from experiments performed at microgravity.

During the past two decades we have performed pool boiling experiments under microgravity conditions with saturated and subcooled liquids using various fluids, mostly fluorinated hydrocarbons, and various shapes of heaters. The common observation at subcooled boiling is the development of thermocapillary convection around bubbles. This convection forms jet streams above the head of the bubbles that carry the heat from the bubbles into the ambient liquid. Heat transfer measurements demonstrate that this flow does not directly contribute to the overall heat transfer itself, but that it is an important transport mechanism in subcooled boiling, not only at microgravity, but also under terrestrial conditions. The development of a thermocapillary flow is surprising, because it is well known that for this convection a temperature gradient along the interface of a bubble is necessary. However, it is also well known that the interfacial kinetics of evaporation and condensation is very strong. Thus, small temperature differences generate strong mass flow rates across the interface, coupled with high heat transfer rates that immediately equalize even moderate temperature gradients appearing along the bubble interface. This is confirmed by the observation that, during boiling in saturated liquids under microgravity conditions, thermocapillary convection was never observed, thus indicating uniformity of the temperature along the interface. From this we must conclude that the temperature difference of wall superheat, which generates boiling, cannot be the driving force for the observed thermocapillary flow even in subcooled liquids. Therefore, the question about the origin of this flow arises and is discussed in this paper.

Optimization of pulsating heaters in forced convection

This is a theoretical, numerical and experimental study that shows how to optimize the performance of on and off pulsating heaters in forced convection. Scale analysis shows that there exists an optimal heat pulse interval or frequency that maximizes the overall thermal conductance between the heater and the free stream U ∝. Numerical results for a flat plate heater and experimental results for a cylinder in cross-flow validate the theory. Numerically it is shown that the optimal pulsating regime can be identified accurately by using a complete simulation of the flow and temperature field around the heater. Boundary layer simplified numerical methods fail to simulate the short-times (high frequency) range of the process. The maximized overall conductance of a pulsating heater does not exceed the conductance associated with a steady (continuous) heater. The experimental and numerical results are nondimensionalized and correlated by using the scales recommended by theory. When the ‘on’ and ‘of’ intervals are comparable, the optimal heat pulse interval is approximately 0.1 L U ∝ , where L is the scale of the swept length of the heater shape. This conclusion also applies to a pulsating heater embedded in a porous medium with uniform flow.

A generalized correction factor for the Knudsen radiometer gauge with arbitrary vane and heater shape

A general expression involving the transverse radiometer effect for the response of a Knudsen gauge, valid for any vane and heater shape, is derived. In principle, the formula is also valid for all distances and dimensions. The calculation in the case of circular discs is presented in detail and the results for spherical and rectangular vanes and heaters are discussed. A simple configuration representing a very good approximation to Knudsen's original formula is proposed.

Rating of heating elements for electric furnaces: Test data and integration of interference between resistors

A study of the practical considerations involved in assigning kilowatt ratings to radiant heating elements in furnace chambers. Constants for radiation and absorption are given. Consideration is given to shape and spacing of elements with respect to shielding due to adjacent elements. A method of determining the equivalent unshielded element is worked out to provide a basis for comparing dissimilar shapes of heaters.

Rating of Heating Elements for Electric Furnaces Test Data and Integration of Interference Between Resistors

A study of the practical considerations involved in assigning kilowatt ratings to radiant heating elements in furnace chambers. Constants for radiation and absorption are given. Consideration is given to shape and spacing of elements with respect to shielding due to adjacent elements. A method of determining the equivalent unshielded element is worked out to provide a basis for comparing dissimilar shapes of heaters.