Heat Transfer Experiments

Heat transfer is a fundamental concept in physics and engineering, concerned with the movement of thermal energy from one body or system to another. Studying heat transfer through experiments helps understand conduction, convection, radiation, and the laws governing these processes.

This post provides a detailed guide to heat transfer experiments, including theoretical background, experimental setups, calculations, error analysis, and practical applications.

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1. Introduction

Heat is a form of energy that flows due to a temperature difference. Heat transfer studies the mechanisms through which energy moves between bodies or within a system. Experiments in heat transfer aim to:

• Verify laws of conduction, convection, and radiation
• Measure thermal conductivity, emissivity, and specific heat capacity
• Understand real-world applications in engineering and daily life

Heat transfer occurs via:

1. Conduction: Transfer through a solid or stationary fluid
2. Convection: Transfer via bulk motion of fluid
3. Radiation: Transfer through electromagnetic waves

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2. Modes of Heat Transfer

2.1 Conduction

• Heat transfer through direct molecular contact
• Occurs mainly in solids
• Governed by Fourier’s law:

Q=−kAdTdxQ = -k A \frac{dT}{dx}Q=−kAdxdT​

Where:

• QQQ = heat transfer per unit time (W)
• kkk = thermal conductivity (W/m·K)
• AAA = cross-sectional area (m²)
• dT/dxdT/dxdT/dx = temperature gradient

Experimental goal: Measure thermal conductivity kkk of a material.

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2.2 Convection

• Heat transfer due to fluid motion
• Two types:
  1. Natural convection: Caused by density differences due to temperature
  2. Forced convection: Caused by external means like a fan or pump

Newton’s law of cooling: Q=hA(Ts−T∞)Q = h A (T_s – T_\infty)Q=hA(Ts​−T∞​)

Where:

• hhh = convective heat transfer coefficient
• TsT_sTs​ = surface temperature
• T∞T_\inftyT∞​ = fluid temperature far from surface

Experimental goal: Measure convective heat transfer coefficient.

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2.3 Radiation

• Heat transfer via electromagnetic waves without a medium
• Governed by Stefan-Boltzmann law:

Q=ϵσA(T4−Tsur4)Q = \epsilon \sigma A (T^4 – T_\text{sur}^4)Q=ϵσA(T4−Tsur4​)

Where:

• ϵ\epsilonϵ = emissivity of surface
• σ\sigmaσ = Stefan-Boltzmann constant (5.67×10−85.67 \times 10^{-8}5.67×10−8 W/m²K⁴)
• TTT = temperature of surface
• TsurT_\text{sur}Tsur​ = surrounding temperature

Experimental goal: Determine emissivity of surfaces.

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3. Common Heat Transfer Experiments

3.1 Measurement of Thermal Conductivity (Conduction)

Objective: Determine thermal conductivity kkk of a metal rod

Apparatus:

• Metal rod with known length LLL and cross-sectional area AAA
• Heater or steam source
• Thermocouples or thermometers at regular intervals
• Insulating material to minimize heat loss

Procedure:

1. Heat one end of the rod steadily
2. Record steady-state temperatures at different points along the rod
3. Calculate temperature gradient dT/dxdT/dxdT/dx
4. Apply Fourier’s law:

k=QLAΔTk = \frac{Q L}{A \Delta T}k=AΔTQL​

Where ΔT\Delta TΔT = temperature difference over distance LLL

Observations:

• Heat flow is linear with temperature gradient
• Compare kkk with standard values for metal

Applications:

• Material selection in heat exchangers and insulation

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3.2 Measurement of Convective Heat Transfer Coefficient

Objective: Determine hhh for fluid flow over a heated surface

Apparatus:

• Flat plate or heated cylinder
• Hot water or air stream
• Thermocouples
• Flow meter for fluid velocity

Procedure:

1. Heat surface to known temperature
2. Measure fluid temperature far from surface
3. Record heat supplied to maintain surface temperature
4. Calculate:

h=QA(Ts−T∞)h = \frac{Q}{A(T_s – T_\infty)}h=A(Ts​−T∞​)Q​

Observations:

• Forced convection has higher hhh than natural convection
• Flow velocity, surface orientation, and fluid type affect hhh

Applications:

• Design of heaters, radiators, and cooling fins

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3.3 Stefan-Boltzmann Experiment (Radiation)

Objective: Measure emissivity ϵ\epsilonϵ of different surfaces

Apparatus:

• Black body source or heated surface
• Radiometer or thermal detector
• Thermometers for surface and surroundings

Procedure:

1. Heat surface to steady temperature
2. Measure heat radiated QQQ
3. Apply:

ϵ=QσA(T4−Tsur4)\epsilon = \frac{Q}{\sigma A (T^4 – T_\text{sur}^4)}ϵ=σA(T4−Tsur4​)Q​

Observations:

• Black surfaces have ϵ≈1\epsilon \approx 1ϵ≈1
• Shiny surfaces have lower emissivity

Applications:

• Solar panels, radiative cooling, thermal coatings

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3.4 Cooling Curve Experiment

Objective: Study Newton’s law of cooling

Apparatus:

• Heated liquid or object
• Thermometer or thermocouple
• Stopwatch

Procedure:

1. Heat liquid or object to known temperature
2. Record temperature vs time as it cools in air
3. Plot ln(T – T_env) vs time

Theory: Newton’s law: dTdt=−k(T−T∞)\frac{dT}{dt} = – k (T – T_\infty)dtdT​=−k(T−T∞​)

• Slope of linear plot gives cooling constant

Applications:

• Food cooling, chemical reactions, environmental studies

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3.5 Insulation Experiment

Objective: Compare effectiveness of different insulating materials

Apparatus:

• Hot plate or steam source
• Cylindrical container
• Thermocouples
• Materials: wool, glass wool, foam

Procedure:

1. Wrap cylinder with insulating material
2. Measure heat loss over time
3. Compare temperature decay for different materials

Observations:

• Materials with lower thermal conductivity reduce heat loss
• Graph temperature vs time for each material

Applications:

• Refrigeration, building insulation, thermal blankets

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3.6 Thermal Conductivity of Liquids (Lee’s Disc Method)

Objective: Measure thermal conductivity of liquids

Apparatus:

• Liquid container with heater
• Thermometers or thermocouples
• Stopwatch

Procedure:

1. Heat liquid uniformly
2. Measure temperature difference across known distance
3. Calculate heat transfer using conduction formula adapted for liquids

Observations:

• Compare thermal conductivity of water, oil, and alcohol
• Liquids generally have lower thermal conductivity than metals

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4. Data Analysis

• Calculate mean values of measured quantities
• Determine errors using standard deviation

Example formulas:

1. Percentage error:

%Error=∣Experimental – Theoretical∣Theoretical×100\% \text{Error} = \frac{|\text{Experimental – Theoretical}|}{\text{Theoretical}} \times 100%Error=Theoretical∣Experimental – Theoretical∣​×100

2. Propagation of errors for derived quantities:

Δkk=ΔQQ+ΔLL+ΔAA+Δ(ΔT)ΔT\frac{\Delta k}{k} = \frac{\Delta Q}{Q} + \frac{\Delta L}{L} + \frac{\Delta A}{A} + \frac{\Delta (\Delta T)}{\Delta T}kΔk​=QΔQ​+LΔL​+AΔA​+ΔTΔ(ΔT)​

3. Graphical methods:

• Plot temperature gradient vs heat flux for conduction
• Plot temperature vs time for cooling experiments

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5. Sources of Experimental Error

• Heat loss to surroundings
• Inaccurate temperature measurement
• Uneven heating or contact resistance
• Air currents affecting convection
• Instrument calibration errors

Reducing errors:

• Use insulation
• Maintain steady-state conditions
• Repeat experiments and average results
• Calibrate thermometers and sensors

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6. Graphical Representation

• Conduction: Plot QQQ vs dT/dxdT/dxdT/dx → linear relation
• Convection: Plot QQQ vs Ts−T∞T_s – T_\inftyTs​−T∞​ → slope = hAh AhA
• Radiation: Plot QQQ vs T4−Tsur4T^4 – T_\text{sur}^4T4−Tsur4​ → slope = ϵσA\epsilon \sigma AϵσA
• Cooling curve: Plot ln(T−T∞)ln(T – T_\infty)ln(T−T∞​) vs time → slope = -k

Graphs help verify theoretical laws and extract parameters like k,h,ϵk, h, \epsilonk,h,ϵ.