Embedded Files
Heating System Schematic
Objectives
Objectives
To model and optimize a steady-state water heating system using cross-flow hot gas over a thin-walled copper tube. The objective was to generate parametric design plots that visualize acceptable combinations of tube diameter (D), length (L), gas velocity (V), and gas temperature (T∞) required to meet a water heating target of 10°C to 40°C. This project was completed as part of MAE 3314: Heat Transfer at the University of Texas at Arlington.
Quick Summary
Quick Summary
Project Type: Individual
Duration: ~2–3 weeks
Tools: MATLAB, heat transfer formulas, air property tables
Focus: Cross-flow heat exchanger sizing, parametric modeling, effects of gas velocity and temperature
Outcome: Generated design plots for velocity and temperature across three tube diameters; validated tube sizing and thermal performance within industrial constraints (L ≤ 14 m)
Technical Details & Skills
Technical Details & Skills
Applied convective heat transfer equations and log-mean temperature difference (LMTD) method
Used MATLAB to compute Reynolds number, Nusselt number, and convection coefficients
Modeled heat transfer for three tube diameters (20, 30, 40 mm) across velocities of 20–40 m/s
Built parametric plots of required tube length vs. gas velocity at T∞ = 250°C, 375°C, and 500°C
Interpolated air property data to estimate film temperature-dependent parameters
Developed iterative MATLAB scripts to automate multi-case heat exchanger calculations
Design Limit Check
Design Overview & Features
Design Overview & Features
Heating Mechanism: Copper tube with internal water flow and external cross-flow hot air
Thermal Input: Hot gas temperatures (T∞) of 250°C, 375°C, and 500°C
Boundary Conditions:
Water mass flow rate: 0.2 kg/s
Inlet/outlet water temperatures: 10°C to 40°C
Tube wall assumed thermally thin
Heat transfer area defined by varying tube diameter and length
Key Design Limit: Tube length must not exceed 14 meters (L ≤ 14 m)
Simulation & Engineering Decision
Simulation & Engineering Decision
Calculated Reynolds numbers for internal (water) and external (air) flow conditions
Applied empirical correlations:
Dittus-Boelter equation for internal Nusselt number (turbulent pipe flow)
Churchill–Bernstein correlation for external cross-flow over tube
Computed convection coefficients and applied log-mean temperature difference (LMTD) for heat transfer evaluation
Solved for required tube length using the steady-state energy balance equation
Modeled three gas temperature cases:
T∞ = 250°C
T∞ = 375°C
T∞ = 500°C
Key Findings:
Higher gas velocity leads to longer required tube (due to reduced residence time)
Higher gas temperature leads toshorter required tube (greater heat transfer potential)
Simulation Plots & Analysis
Simulation Plots & Analysis
Length as a function of Velocity 250C
Length as a function of Velocity 375C
Length as a function of Velocity 500C
Formulas Used:
Reynolds number, Nusselt number (via Dittus–Boelter and Churchill–Bernstein correlations), and log-mean temperature difference (LMTD)-based energy balance for steady-state heat exchanger sizing.
Insights from Simulation Results:
All plots confirm that tube length increases with gas velocity due to reduced residence time.
Higher gas temperatures significantly reduce the required tube length due to greater heat transfer potential.
At fixed diameter and velocity, increasing T∞ from 250°C to 500°C leads to over 60% reduction in required tube length.
Trends are consistent across all three diameters (20, 30, and 40 mm), showing scalable design behavior.
These results are applicable for preliminary sizing in systems where space, heat load, and flow rate are critical constraints (e.g., industrial water heating, thermal process control, or power generation subsystems).
*Note: MATLAB code with parametric sweep logic is included in the report appendix. All plots were auto-generated from iterative simulation loops*
Challenges & Iteration
Challenges & Iteration
Estimated surface temperature through trial-and-error to ensure energy balance consistency between water and gas sides
Performed property interpolation from air tables with 50 K spacing to obtain accurate film temperature values
Verified flow regime validity (turbulent, fully developed) before applying Nusselt number correlations
Iteratively adjusted gas-side heat transfer assumptions, including film temperature and wall interaction, to ensure physically realistic results across all diameter and velocity cases
Outcomes & Contributions
Outcomes & Contributions
Developed parametric MATLAB scripts to automate heat exchanger sizing across multiple tube diameters and hot gas conditions
Generated clear, actionable design plots showing velocity–length relationships, aiding future system-level decision making
Confirmed system feasibility within the design constraint of maximum tube length ≤ 14 m
Demonstrated strong grasp of external forced convection over cylindrical surfaces, integrating empirical correlations and energy balance logic
Skills Applied
Skills Applied
Heat Transfer Analysis · Log-Mean Temperature Difference (LMTD) · Parametric Design Modeling · MATLAB Plotting & Scripting · Reynolds & Nusselt Number Calculations · External/Internal Convection Coefficients · Technical Engineering Documentation
Reflection
Reflection
This project reinforced my understanding of convection heat transfer and system-level thermal modeling. By developing automated MATLAB scripts and exploring tradeoffs in gas velocity and temperature, I gained confidence applying Nusselt number correlations and LMTD concepts to real-world design sizing problems. These skills directly support engineering tasks in HVAC, energy systems, and electronics cooling.
*Note: Full MATLAB code is available in the attached project report (PDF)*
Download Project PDF
View or Download Project Report (PDF)
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