[Paper Review] Sensitivity studies of heat transfer: forced convection across a cylindrical pipe and duct flow

Andrea Ferrantelli, Paul Melóis+1 more|arXiv (Cornell University)|Aug 13, 2013

Wind and Air Flow Studies6 references3 citations

TL;DR

This paper presents a sensitivity analysis of forced convection heat transfer in cylindrical pipes and ducts, using analytical derivations of the heat transfer coefficient $ h $ as a function of velocity, temperature, and pipe diameter. By applying the Churchill-Bernstein correlation and thermophysical property models, it quantifies how $ h $, Reynolds number, and Nusselt number vary with temperature and flow conditions, offering a didactic and practical reference for engineering education and simulation validation with explicit formulas and interpolation curves for air and oil.

ABSTRACT

We consider two common heat transfer processes and perform a through sensitivity study of the variables involved. We derive and discuss analytical formulas for the heat transfer coefficient in function of film velocity, air temperature and pipe diameter. The according plots relate to a qualitative analysis of the multi-variable function $h$, according to functional optimization. For each process, we provide with graphs and tables of the parameters of interest, such as the Reynolds number. This method of study and the specific values can constitute a useful reference for didactic purposes.

Motivation & Objective

• To provide a didactic framework for understanding heat transfer phenomena in engineering education through analytical sensitivity studies.
• To quantify the dependence of the heat transfer coefficient $ h $, Reynolds number, and Nusselt number on fluid temperature, velocity, and pipe diameter in cylindrical flows.
• To offer accurate interpolation curves for thermophysical properties of air and oil using the least squares method, enabling predictive modeling.
• To support numerical simulations by enabling theoretical pre-validation of results through analytical insight into parameter dependencies.
• To bridge the gap between theoretical physics and engineering practice by emphasizing functional optimization in heat transfer analysis.

Proposed method

• Derives analytical expressions for the heat transfer coefficient $ h $ using the Churchill-Bernstein correlation, which relates $ h $ to Reynolds and Prandtl numbers.
• Uses temperature-dependent models for kinematic viscosity $ u(T) $, thermal conductivity $ k(T) $, and Prandtl number $ \mathrm{Pr}(T) $, with empirical fits for air and oil.
• Applies the least squares method to fit polynomial functions to experimental data for $ u(T) $, achieving average errors of 0.09% for air and 0.98% for oil.
• Plots and tabulates $ h $, $ \mathrm{Re}_D $, and critical length $ L_{\mathrm{cr}} $ as functions of temperature, velocity, and diameter for air and oil.
• Uses film temperature concept to evaluate properties at the mean of wall and bulk fluid temperatures in convection calculations.
• Validates analytical curves against empirical data points for critical length in laminar-to-turbulent transition over flat plates.

Experimental results

Research questions

• RQ1 How does the heat transfer coefficient $ h $ vary with fluid temperature, velocity, and pipe diameter in external flow over a cylinder?
• RQ2 What is the functional dependence of the Reynolds number $ \mathrm{Re}_D $ on temperature for air and oil, and how does it affect flow regime transitions?
• RQ3 How accurately can the critical length for boundary layer transition be predicted using polynomial fits to kinematic viscosity data?
• RQ4 To what extent do analytical models of $ h $, based on the Churchill-Bernstein correlation, align with empirical data for air and oil?
• RQ5 Can interpolation curves derived via least squares method reliably represent thermophysical properties for use in heat transfer calculations?

Key findings

• For air, the kinematic viscosity $ \nu(T) $ is modeled as a third-degree polynomial with an average error of 0.09%, yielding highly accurate predictions of $ \mathrm{Re}_D $ and $ h $.
• The convection coefficient $ h $ for air at $ D = 5\,\mathrm{cm} $, $ V = 5\,\mathrm{m/s} $, and $ T = 15^\circ\mathrm{C} $ is quantified and plotted, showing strong dependence on velocity and temperature.
• The critical length $ L_{\mathrm{cr}} $ for laminar-to-turbulent transition in air is predicted with high accuracy using a third-degree polynomial fit to $ \nu(T) $, with no visible deviation from empirical data in plots.
• For oil, the critical length $ L_{\mathrm{cr}} $ is modeled using a second-degree polynomial with a 0.98% average error, showing good agreement with experimental points.
• The heat transfer coefficient $ h $ increases with velocity and decreases with increasing pipe diameter, as shown in plots for both air and water under varying conditions.
• The study demonstrates that analytical sensitivity analysis provides a priori insight into parameter behavior, enabling efficient and validated numerical simulations in heat transfer.