The inaccuracy of heat transfer characteristics of insulated and non-insulated circular duct while neglecting the influence of heat radiation

https://doi.org/10.1016/j.enconman.2009.07.009Get rights and content

Abstract

The non-insulated and insulated ducts are commonly applied in the industries and various buildings, because the heat radiation equation contains the 4th order exponential of temperature which is very complicate in calculations. Most heat transfer experts recognized from their own experiences that the heat radiation effect can be ignored due to the small temperature difference between insulated and non-insulated surface and surroundings. This paper studies in detail to check the inaccuracies of heat transfer characteristics non-insulated and insulated duct by comparing the results between considering and neglecting heat radiation effect. It is found that neglecting the heat radiation effect is likely to produce large errors of non-insulated and thin-insulated ducts in situations of ambient air with low external convection heat coefficients and larger surface emissivity, especially while the ambient air temperature is different from that of surroundings and greater internal fluid convection coefficients. It is also found in this paper that using greater duct surface emissivity can greatly improve the heat exchanger effect and using smaller insulated surface emissivity can obtain better insulation.

Introduction

The insulated and non-insulated cold/hot ducts are commonly applied in the industries and various buildings, because the heat radiation equation contains the 4th order exponential of temperature which is very complicate in calculations. Most heat transfer experts recognized from their own experiences that the heat radiation effect can be ignored due to the small temperature difference between insulated and non-insulated surface and surroundings. From this view point, the demonstrated insulation examples shown in most heat transfer text books (such as [1], [2], [3], [4], [5], [6], [7], [8]), air conditioning and refrigeration text books (such as [9], [10], [11], [12]), most practical commercial designs of insulation, and many research papers commonly ignore the influence of heat radiation even in the situation of very low heat convective coefficient.

Since the insulation of hot and cold ducts and containers has been one of the most important engineering problems. Levinson et al. [13] considered the effects of airflow infiltration on the thermal performance of internally insulated ducts, Wong and Chou [14] studied the heat transfer characteristics of an insulated regular cubic box by using a solid wedge thermal-resistance model, Chou [15] used the optimum interior area thermal-resistance model to analyze the heat transfer characteristics of an insulated pipe with arbitrary shape, Wong and Chou [16] investigated heat transfer characteristics of an insulated regular cubic box by using a regular polygonal top solid wedge thermal-resistance model, Wong et al. [17] figured out the complete heat transfer solutions of an insulated regular polygonal pipe by using a PWTR model, Wong et al. [18] studied the complete heat transfer solutions of an insulated regular cubic tank with a SSWT model, Lee et al. [19] investigated the complete heat transfer solutions of an insulated regular polyhedron by using a RPSWT model, Wong et al. [20] applied the reliable simple one-dimensional 64-CPWTR model to the two-dimensional heat transfer problem of an insulated rectangular duct in an air conditioning or refrigeration system, Wong et al. [21] used a reliable one-dimensional method to solve heat-transfer problems associated with insulated rectangular tanks in refrigeration systems, Wong et al. [22] applied the reliable one-dimensional CPWTR models to two-dimensional insulated polygonal ducts, Chen and Wong [23] applied a reliable analytical method to heat-transfer problems associated with insulated cylindrical tanks. The heat radiation effect was ignored in above papers; it should be acceptable in situations of very thick insulation.

In this present investigation, the influence of heat radiation of insulated and non-insulated ducts is considered and the results of complete heat transfer characteristics are compared with those of neglecting the heat radiation effect. Then the errors of heat transfer characteristics for insulated and non-insulated ducts with neglecting the influence of heat radiation can be found.

Section snippets

Problem formulation

Fig. 1 shows that the non-insulated or insulated circular duct with thickness t1, duct length L, wall conductivity KA, duct surface emissivity ε0; the insulated layer with surface emissivity ε, insulation thickness t and conductivity Ks; internal and external fluids with convection heat transfer coefficients hi and ho as well as temperatures Ti and To, respectively; the duct is exposed to the outside surroundings temperature Tsur, and the duct surface area is very small compared with that of

Numerical heat transfer results

The nature of results of heat equation of non-insulated and insulated circular duct are one-dimensional exact solution. The exact numerical heat transfer results of an insulated circular duct are obtained by one-dimensional LabVIEW programming in this paper. According to the emissivities shown in Table 1, ε = ε0 = 0.8 and ε = ε0 = 0.2 are adopted to represent the high and low surface emissivity cases, respectively. It is shown in Table 2 that most natural convection coefficients of air are below 10 W m−2 K

Results and discussion

In order to increase the generalization of the results, all the results are shown in dimensionless parameters except TD, the surface temperature difference generated by neglecting heat radiation effect for insulated cold duct. An insulated hot duct in situations of Ti = 100 °C, KA = 77 W m−1 K−1, Ks = 0.035 W m−1 K−1, r1 = 195 mm, r2 = 200 mm and ho = 10 W m−2 K−1 and divided into two groups. Group (a): To = Tsur = 30 °C with ε = ε0, and group (b): To = 30°C, Tsur = 32 °C with ε  ε0, are applied as the first case study and the

Conclusion

From the practical numerical results of this study, it demonstrates that one will take a big risk to neglect the influence of heat radiation for the non-insulated and thinner insulated duct in the situations of ambient air with low external convection coefficients and greater surface emissivity, especially while the ambient air temperature is different from that of surroundings and greater internal fluid convection coefficients. Since the emissivity of duct surface should always be different

Acknowledgment

The authors would like to acknowledge the National Science Council of Taiwan, ROC. This investigation is completed under the support of the Project NSC 97-2221-E-168-044-MY2.

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