🔥 Convective Heat Transfer & Boundary Layer Kinematics

Course Project | CHE212 - Heat Transfer | Prof. Anurag Tripathi | IIT Kanpur | Mar – May 2026

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📌 Overview

An experimental and theoretical study of forced and mixed convective heat transfer over a constant-heat-flux heated flat plate inside an enclosed duct. The project captures high-resolution spatial temperature profiles and computes localized thermal boundary layer parameters across different velocities (1.0 m/s, 3.0 m/s) and voltages (100 V, 120 V, 150 V).

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🔬 Key Experiments & Analysis

Analysis	Description
Thermal Boundary Layer	Measured δₜ(x) and compared against theoretical δₜ ∝ √x
Local Nusselt Number	Experimental Nuₓ vs forced/mixed convection correlations
Heat Transfer Coefficient	Local h_x from Fourier's law: q'' = -k(∂T/∂y)
Mixed Convection	Gr/Re² analysis to quantify buoyancy contribution
Temperature Maps	2D contour interpolation of the heated plate surface
Wall Heat Flux	Calculated from measured temperature gradient near wall

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📐 Theory

Boundary Layer Thickness (Laminar Forced Convection)

$$\delta_t(x) = \frac{5x}{\sqrt{Re_x} \cdot Pr^{1/3}}$$

Local Nusselt Number

$$Nu_x = \frac{h_x \cdot x}{k} = 0.332 \cdot Re_x^{1/2} \cdot Pr^{1/3}$$

Wall Heat Flux via Fourier's Law

$$q''_{exp} = -k \left.\frac{\partial T}{\partial y}\right|_{y=0}$$

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🗂️ Files

File	Description
matlabcode.m	Main analysis: boundary layer, Nu, h_x, contour maps, heat flux
yuvi.m	Extended analysis: all velocity/voltage combinations
yuvraj.m	Presentation-quality plots for both velocities

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📊 Generated Plots

1. Thermal boundary layer thickness — experimental vs theoretical (δₜ ∝ √x)
2. Nusselt number comparison — forced vs mixed convection
3. Error analysis — % deviation from theory across voltages
4. Local h_x comparison — experimental vs theoretical
5. Temperature profiles — T(y) at x = 5, 10, 15, 20 cm
6. 2D temperature contour maps — interpolated heat maps
7. Wall heat flux — from Fourier's law

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▶️ How to Run

Open MATLAB and run:

run('matlabcode.m')    % Full integrated analysis
run('yuvi.m')          % Temperature profiles for all conditions
run('yuvraj.m')        % Presentation-quality multi-panel plots

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📋 Experimental Setup

• Duct dimensions: Enclosed horizontal duct
• Plate positions: x = 5, 10, 15, 20 cm from leading edge
• Velocities: u = 1.0 m/s, 3.0 m/s
• Heater voltages: 100 V, 120 V, 150 V
• Fluid: Air (ν = 1.76×10⁻⁵ m²/s, Pr = 0.70, k = 0.0276 W/mK)
• y-probe spacing: 1 mm

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📄 License

MIT License © 2026 Lavanaya Singh, IIT Kanpur