Solving Inverse Heat Transfer Problems When Using CFD Modeling

The chapter presents solving steady-state inverse heat transfer problems using Computational Fluid Dynamics (CFD) software. Two examples illustrate the application of the proposed method. As the first inverse problem determining the absorbed heat flux to water walls in furnaces of steam boilers is presented in detail. Three different measurement devices (flux tubes) were designed to identify steady-state boundary conditions in water wall tubes of combustion chambers. The first meter is made of a short eccentric tube in which four thermocouples on the fire side below the inner and outer tube surfaces are installed. The fifth thermocouple is situated at the rear of the tube on the housing side of the water wall tube. The second meter has two longitudinal fins that are welded to the bare eccentric tube. In the third option of the instrument, the fins are attached to the water wall tubes but not to the flux tubes as in the second version of the flux tubes. The first instrument is used to measure the heat flux to water walls made from bare tubes, while another two heat flux tubes are designated for measuring the heat flux to membrane walls. Unlike the existing devices, the flux tube is not attached to neighboring water-wall tubes. The absorbed heat flux on the outer surface and the heat transfer coefficient at the inner surface of the flux tube are determined from temperature measurements at internal points. The thermal conductivity of the flux-tube material is a function of temperature. The nonlinear inverse problem of heat conduction (IHCP) is solved using the least-squares method. Three unknown parameters are determined using the Levenberg–Marquardt method. In each iteration, the temperature distribution in the cross section of the heat flux instrument is determined using the ANSYS/CFX software

The CFD Based Method for Determining Heat Transfer Correlations on Individual Rows of Plate-Fin and Tube Heat Exchangers

The chapter provides an analytical mathematical model of a car radiator, which includes different heat transfer coefficients (HTCs) on the first and second row of pipes. The air-side HTCs in the first and second row of pipes in the first and second pass were calculated using the correlations for the Nusselt number, which were determined by CFD simulation using the ANSYS software. Mathematical models of two radiators were built, one of which was manufactured of round tubes and the other of oval tubes. The model permits the determination of thermal output of the first and second row of tubes in the first and second pass. The small relative differences between the thermal capacities of the heat exchanger occur for different and uniform HTCs. However, the heat flow rate in the first row is much greater than the heat flow in the second row if the air-side HTCs are different on the first and second tube row compared to a case where the HTC is uniform in the whole heat exchanger. The heat transfer rates in both radiators calculated using the developed mathematical model were compared with those determined experimentally. The method for modeling of plate-fin and tube heat exchanger (PFTHE) proposed in the paper does not require empirical correlations to calculate HTCs both on the air side and on the inner surfaces of pipes. The presented method of calculating PFTHEs, considering different air-side HTCs evaluated using CFD modeling, may considerably reduce the cost of experimental research concerning new design heat exchangers implemented in manufacturing

Numerical investigation of heat transfer enhancement in solar air heaters using polygonal-shaped ribs and grooves

Solar air heating thermal systems have found extensive utilization in a broad array of industrial and residential settings, playing a pivotal role in the conversion and reclamation of solar energy. Implementing repeated artificial roughness in the surfaces has the potential to augment thermal performance in solar air heaters (SAHs). This study presents a numerical investigation of SAHs with artificial rough surfaces, consisting of polygonal-shaped ribs and grooves located at different places inside the rectangular duct, that improve thermal efficiency. ANSYS Fluent software was employed to simulate the SAH with different relative pitch distances of p = 10 mm and 20 mm and relative rib heights e/d = 0.09–0.045. The working fluid air flows at different Reynolds numbers (Re), ranging from 3,800 to 18,000. Nusselt number (Nu), friction factor (f), and Thermal Hydraulic Performance (THP) are parameters to evaluate the performance of the SAH. The renormalized group (RNG) k-ϵ turbulent model was implemented in this simulation. The study outcomes indicate that increasing the rib height improves the heat transfer rate and nonetheless increases pressure drop while increasing the pitch distance. The higher Nusselt number (Nu) is 3.762 attained at p = 10 mm and 3.420 at p = 20 mm in the center-positioned rib at Re 3,800. The lower friction factor (ƒ) obtained in p = 20 mm is 1.681 and 0.785 in p = 10 mm in the staggered positioned rib at higher Re 15,000. The optimal THP was achieved at 2.813 at a staggered rib height at a pitch distance of p = 10 mm at Re 8,000. The study’s findings suggest that the incorporation of artificial rough surfaces has the potential to enhance the THP of an SAH

Simple heat transfer correlations for turbulent tube flow

The paper presents three power-type correlations of a simple form, which are valid for Reynolds numbers range from 3·103 ≤ Re ≤ 106, and for three different ranges of Prandtl number: 0.1 ≤ Pr ≤ 1.0, 1.0 < Pr ≤ 3.0, and 3.0 < Pr ≤ 103. Heat transfer correlations developed in the paper were compared with experimental results available in the literature. The comparisons performed in the paper confirm the good accuracy of the proposed correlations. They are also much simpler compared with the relationship of Gnielinski, which is also widely used in the heat transfer calculations

Steady-state and transient heat transfer through fins of complex geometry

Various methods for steady-state and transient analysis of temperature distribution and efficiency of continuous-plate fins are presented. For a constant heat transfer coefficient over the fin surface, the plate fin can be divided into imaginary rectangular or hexangular fins. At first approximate methods for determining the steady-state fin efficiency like the method of equivalent circular fin and the sector method are discussed. When the fin geometry is complex, thus transient temperature distribution and fin efficiency can be determined using numerical methods. A numerical method for transient analysis of fins with complex geometry is developed. Transient temperature distributions in continuous fins attached to oval tubes is computed using the finite volume - finite element methods. The developed method can be used in the transient analysis of compact heat exchangers to calculate correctly the heat flow rate transferred from the finned tubes to the fluid