Heat Transfer Coefficient - A248

Heat Transfer Coefficient
Foundational knowledge article
Document Type	Article
Document Identifier	248
Themes	Thermal management
Relevant Class	Equipment
Prerequisites	Heat transfer Convection

Introduction

The heat transfer coefficient (HTC), h is used to characterize the heat flux across an interface. It is defined as the proportionality constant that determines the amount of heat flux across an interface for a given temperature difference across the interface.

Scope

This page defines the heat transfer coefficient, explains its significance in composites processing, and provides some typical values. Typical methods for measurement and use in process modelling are also briefly discussed.

Significance

The accuracy and usefulness of a process simulation framework depends on the sufficient knowledge of the initial and boundary conditions. In the context of thermal management models, the HTCs are used to characterize convective boundary conditions. These thermal models are useful in designing appropriate cure cycles, tool and part thermal profiling as well as evaluating mitigation strategies for large exotherms in parts during a manufacturing process.

Prerequisites

Recommended documents to review before, or in parallel with this document:

• Heat transfer
• Convection
• Thermal management

Level I

Level II

Definition

The convective heat transfer coefficient \(h\) is the proportionality constant between the heat flux and the temperature difference between a fluid and solid surface. It can be expressed by Newton’s law of cooling (the same expression applies for heating):

\(q = h\, \Delta T\) Newton’s law of cooling, where:<br />\(q\) = Heat flux [W/m²],<br />\(h\) = Convective heat transfer coefficient (HTC) [W/m²·K], and<br />\(\Delta T\) = Temperature difference between fluid and solid surface [K],<br />

Terminology and Symbol Notation

Convective heat transfer coefficient vs overall heat transfer coefficient
The convection heat transfer coefficient is used to characterize the heat flow across a fluid-solid interface. The overall heat transfer coefficient is used to represent the effective heat transfer coefficient of a composite system that involves heat exchange between multiple fluid and solid bodies.

In composites process simulation, the overall heat transfer coefficient is used to lump the effects of various consumables (like vacuum bags, breathers etc.) while modelling the heat exchange between tool-part configurations and the surroundings. Henceforth, in the remainder of this article and the other articles in the KPC, the terms "heat transfer coefficient" or "HTC" or \(h\) have been used interchangeably to represent the overall heat transfer coefficient.

Units

The general units of the heat transfer coefficient can be represented as

\(h=\frac{Power\, unit}{Area\, unit \cdot Temperature\, unit}\)

The following are common International System of Units (SI) and US Customary Units found in the literature for specific heat capacity:

	SI Units	US Customary Units
Base units	W/m2·K	BTU/s.ft2·°F

Typical Values

Typical HTC values for different equipment setups^#

Stagnant air	Outdoors with wind or indoors with airflow	Oven	Autoclave
2-10 W/m\(^2\)K	>15 W/m\(^2\)K depending on airflow velocity	15-50 W/m\(^2\)K	60-200 W/m\(^2\)K

^#Note: These values depend on the conditions in which they were measured according to the factors described on the Level II. It's possible that values outside these ranges exist under different system conditions.

Factors influencing HTCs

HTCs are mainly affected by the following factors:

Fluid flow

The velocity and direction of the fluid flow around the interface has a significant effect on the HTC. The higher the velocity of the fluid, the higher would be the HTC. In general, more turbulent flow patterns lead to higher HTCs. The HTC within a system such as an autoclave may vary drastically from location to location (ie. top of tool vs bottom of tool). In composites manufacturing, the shape of the tool and substructure as well as the shape and size of the equipment affect the air flow pattern which ultimately influences the HTCs. Thus, tooling and equipment design are important factors that can determine the HTCs during process cycles. Additionally, the HTCs can be used to quantify the tool-equipment interactions of different tooling and equipment configurations.

To learn more about how the tool design influences the HTCs, refer to the following links: effect of tooling in a thermal management system - substructure and HTC effects.

Pressure and Temperature

The fluid pressure and temperature are key parameters affecting the heat transfer coefficient. Their effects are commonly represented by expressing the HTC as a direct function of these variables. In the context of autoclave processes, a simple relationship was observed for turbulent gas flow by Johnston et al. .

\(h \varpropto \left ( \frac{P}{T} \right )^{\frac{4}{5}}\) Relationship between pressure, temperature and convective heat transfer coefficient for turbulent flow:<br />\(h\) = Convective heat transfer coefficient (HTC),<br />\(P\) = Pressure, and<br />\(T\) = Temperature

Estimating HTCs

HTCs can be estimated by a number of ways that involve different levels of complexities and experimental effort, which are useful at different phases of the design to manufacturing path. The methods to determine the HTCs can be broadly classified into two types:

• Simulation methods: Simulating the airflow using tools like Computational Fluid Dynamics (CFD) is one of the popular ways to estimate HTCs for a given tool-equipment configuration. These methods are specifically beneficial in the preliminary design stages of initial tooling and equipment design.

Learn more about estimating HTCs by simulating the airflow: How to simulate airflow in a thermal system

• Experimental methods: Experimental methods used to estimate HTCs involve measuring the temperatures of a tool-part configuration (and in some cases, the local air temperature) using temperature sensors. The temperature data can be analyzed using several methods of different complexities ranging from lumped mass analysis to Bayesian inference.

Learn more about estimating HTCs by experimental methods: How to experimentally determine the HTC

Usage of HTCs

HTCs are used as boundary conditions in process simulation models for thermal management practices. In composites manufacturing, autoclave processes rely on convective heat transfer from the pressurized gas to the tool-part configuration. Even in out-of-autoclave processes like room temperature curing, managing the exotherm of resins depends on the surrounding air conditions. For such processes, using HTCs to understand the potential temperature distributions in the part is important to prevent thermal degradation of resins during cure.

References

About	Help

The use of multiphysics models to predict the outcome of real-world scenarios. May be analytical (closed form, "hand calculations") or computational (implementation on computers is required due to the large number of calculations involved. e.g. finite element method, finite difference method)

Most often in composite materials engineering, modelling refers to either:

• Process modelling (predicting manufacturing outcomes, or the inverse problem of predicting manufacturing parameters to achieve a desired outcome), or
• Performance modelling (predicting the stiffness/strength/suitability of a structure, or the inverse problem of the material properties and dimensional requirements to achieve a desired stiffness/strength/suitability of a structure)

(same as "Simulation")

A central processing theme in the manufacturing cycle. This theme is concerned with managing the thermal response of materials during storage and handling or parts/tools when they are subsequently heated.

Experimental thermal profiling is a typical practice where part/tool temperatures and temperature rates are empirically measured using temperature measurement devices (typically thermocouples). This activity is performed to ensure that representative locations in the part of interest satisfy the cure window with respect to minimum/maximum heat up and cool down rates and length (duration) of temperature holds.

The heat transfer coefficient applied to surface boundaries that include lumped bagside and/or toolside effects. These effects include bagging and consumables, tool size effects, tool substructure and heat transfer due to convection (e.g. airflow) and radiation (e.g. wall, rack effects).

Engineered materials (designed to have specific properties) made from two or more constituent materials with different physical or chemical properties. The constituents remain separate and distinct on a macroscopic level within the finished structure.

The use of multiphysics models to predict the outcome of real-world scenarios. May be analytical (closed form, "hand calculations") or computational (implementation on computers is required due to the large number of calculations involved. e.g. finite element method, finite difference method)

Most often in composite materials engineering, simulation refers to either:

• Process simulation (predicting manufacturing outcomes, or the inverse problem of predicting manufacturing parameters to achieve a desired outcome), or
• Performance simulation (predicting the stiffness/strength/suitability of a structure, or the inverse problem of the material properties and dimensional requirements to achieve a desired stiffness/strength/suitability of a structure)

(same as "Modelling")