Heat Transfer Coefficient (HTC)

Heat Transfer Coefficient (HTC) is a measure of heat transfer across a solid-fluid interface. HTC was conceived as a model reduction approach to calculate heat flux or temperature on solid surfaces for predefined flow geometries via empirical formulas based on dimensional and dimensionless parameters of the case without solving for the fluid flow. Currently, HTC is predominantly employed as a means of offline coupling between a fluid and solid solver. Most empirical HTC formulas assume constant temperature or constant heat flux and feature several dimensional and dimensionless variables that allow for active modification of the HTC values by the solid solver during calculations. In contrast, most HTC coefficients extracted from CFD simulations are constant and only apply to the specific scenario solved to obtain them. In this respect, HTC coefficients extracted by CFD solvers are more akin to plain heat flux rather than the form represented by empirical HTC formulas.

To obtain the most accurate form of HTC representing heat flux for a simple heat transfer case through numerical simulation, you must solve the coupled solid and fluid problems by conducting a full scale simulation, considering temperature dependent fluid and solid properties.

All boundary conditions and source terms must be fully defined and the simulation must reach a steady state for both thermal and flow fields. The heat fluxes and temperature values obtained from this simulation are then used to calculate HTC values on the solid surfaces. Naturally there are drawbacks to this approach. Not all problems reach a steady state and the ones with a transient nature should either rely on a snapshot of HTC per output or use a time averaging method which may reduce the accuracy of the obtained HTC. Furthermore, even for inherently steady cases, the difference in thermal and flow timescales bind the simulation time of the coupled flow and thermal problem to the longer of the two timescales. Satisfying the spatial and temporal resolution requirements of the coupled problem might put further strain on the computational resources. In some cases, the thermal domain may extend further beyond the flow domain, putting additional strain on the coupled solver. In short, solving the full problem is the most accurate method for obtaining HTC representing heat flux for steady state flows. However, it may not be feasible for most practical cases.

Calculating HTC is a part of the extractor feature. Extractors offer two forms of output for HTC values. The first output option is the regular VTK polydata format shared with other extractor outputs. To facilitate using the HTC values in other solvers, extractors offer a space delimited text file output option separately.

The text files are placed in extractor_name_txt under EXTRACT directory with a file generated for each output time named surfext_timestepnumber.txt, similar to vtp output format. Each text output contains coordinates of the extractor surface centers as well as instantaneous (i) and periodically time averaged (pta) output. A separate text file containing header information is also generated to help in identifying column content. The header file is not regenerated when a recon run is carried out in the same directory as the clean run, that is the header file will not be updated even if the number of columns in the text outputs change after the recon run.

Note that even if all vtp outputs are turned off, vtp, vtm (in case of sync output), and pvd files will still be generated. The vtp files in this case will only contain coordinates, but no other data. pvd files can be used to associate file names with physical simulation times for both vtp and txt files. An easy way to see these values is to open the pvd file in a text editor or in ParaView.

Non-reset Partial Energy Equation (NRPEE)

HTC based on solving non-reset partial energy equation, non-reset partial energy equation HTC (NRPEE HTC), uses the temperature field obtained from the simulation to calculate the HTC based on the following formulas:

$\mathrm{q"}=\mathrm{-\kappa }\left(\frac{\partial T}{\partial n}\right)$

Where, $h$ is HTC, $\mathrm{q"}$ is heat flux, $\kappa$ is thermal conductivity, $n$ is wall normal direction and $T$ is temperature while subscripts $w$ and $\inf$ denotes wall and bulk, respectively. In essence, this form of HTC represents a heat flux divided by a set of temperature difference.

Flat Plate Based Empirical Approach (EMP)

Nusselt number ( $\mathrm{Nu}$ ) of an isothermal flat plate subject to uniform parallel flow where the fluid is heated as it passes over the solid has a well known empirical relation in literature of the form.

$\mathrm{Nu}=\mathrm{0.644}{\mathrm{Re}}^{\mathrm{0.5}}{\mathrm{Pr}}^{\mathrm{0.33}}$

There is no way to know where the actual modeled plate starts and ends which translates into an issue of specifying the exact value of $L$ . We, therefore, relegate to assuming the extractor surface is made of a collection of free floating dx long platelets, for the lack of a better term. One of the consequences of this approximation is that the expected fall in heat transfer coefficient for longer plates may not be captured. Another side effect of this approximation is that changing resolution for the same problem affects the calculated EMP HTC directly.