What are the three types of heat transfer and how do they differ?

The three types of heat transfer are conduction, convection, and radiation.

Conduction is the transfer of heat through a solid or stationary medium via molecular vibration, like heat moving through a metal rod.

Convection involves heat transfer by the movement of a fluid, such as air over a hot surface.

Radiation is the transfer of energy via electromagnetic waves, requiring no medium, like heat from the sun.

Can you explain Fourier’s law of conduction?
Fourier’s Law states that the heat flux (q) is proportional to the temperature gradient: q = -k * A * (dT/dx).

Here, q is the heat transfer rate (W), k is the thermal conductivity (W/m·K) measuring a material’s ability to conduct heat, A is the cross-sectional area (m²) perpendicular to heat flow, and dT/dx is the temperature gradient (K/m) driving the heat transfer.

The negative sign indicates heat flows from high to low temperature.

What is the difference between heat transfer coefficient and thermal conductivity?
Thermal conductivity (k) is a material property that quantifies how well a material conducts heat, measured in W/m·K.

The heat transfer coefficient (h), measured in W/m²·K, describes the rate of heat transfer between a surface and a fluid, influenced by fluid properties, flow type (laminar/turbulent), and geometry—not just the material.

For example, k is fixed for copper, but h varies with airspeed over a copper surface.

How would you calculate the overall heat transfer coefficient for a composite wall?
The overall heat transfer coefficient (U) is found using the total thermal resistance: 1/U = ΣR, where R is the resistance of each layer.

For a wall with conduction through layers and convection on both sides, R_total = (1/h₁) + (L₁/k₁) + (L₂/k₂) + … + (1/h₂).

Here, h₁ and h₂ are convective coefficients, L is thickness, and k is thermal conductivity of each layer.

Then, U = 1/(R_total * A), where A is the area. This accounts for all resistances in series.

What is the significance of the Nusselt number in convective heat transfer?
The Nusselt number (Nu = hL/k) is a dimensionless parameter that measures the enhancement of heat transfer due to convection compared to conduction alone. A Nu of 1 means pure conduction; higher values indicate convection dominates. It depends on flow conditions (e.g., Reynolds and Prandtl numbers) and geometry, helping engineers predict convective heat transfer rates.

Physically, Nu represents the ratio of convective heat transfer to conductive heat transfer over the length L. A higher Nu means convection is more dominant, while a lower Nu suggests conduction plays a larger role.

The Physical Interpretation of Nusselt Number

Nu = 1: Heat transfer is purely conductive, as if the fluid were stagnant. For example, in a still fluid layer, heat moves only by molecular diffusion, and hL equals k.
Nu > 1: Convection enhances heat transfer beyond conduction, due to fluid motion mixing warmer and cooler regions. This is common in engineering applications.
Nu < 1: Rare, but possible in highly viscous or thin layers where convection is suppressed below conduction levels.
For instance, in turbulent pipe flow, Nu might be 100, meaning convection transfers heat 100 times more effectively than conduction alone across the pipe diameter.

Why is Nusselt Number so important?
The Nusselt number bridges theory and application. Since h is hard to measure directly, engineers use Nu correlations (derived from experiments or theory) to estimate h based on flow conditions and geometry. It’s critical for:

Sizing equipment: A higher Nu means a smaller surface area (A) is needed for the same heat transfer rate (q = hAΔT).
Optimizing designs: Adjusting flow (e.g., speed, turbulence) or geometry to increase Nu improves efficiency.
How Nu is Determined:

Nu depends on the flow regime, fluid properties, and geometry, often expressed via dimensionless groups:

Reynolds Number (Re = ρvL/μ): Indicates laminar (smooth) vs. turbulent (chaotic) flow. Higher Re increases Nu due to better mixing.
Prandtl Number (Pr = μc_p/k): Ratio of momentum diffusivity to thermal diffusivity, showing how fluid properties affect heat transfer. High Pr (e.g., oils) increases Nu in some cases.
Geometry: Nu varies—e.g., Nu for a pipe differs from a flat plate.

What are some practical applications of Nusselt Number?
In a heat exchanger, a high Nu means efficient heat transfer, reducing size or cost. For a CPU heat sink, increasing Nu (via fans or fin design) keeps temperatures low. Conversely, in insulation design, a low Nu (still air) is desirable to minimize heat loss.

In summary, the Nusselt number is a subset of convective heat transfer analysis, taking into account fluid dynamics and thermal properties. It’s both a diagnostic tool and a design parameter, widely used across mechanical, chemical, and aerospace engineering.

What is Prandtl Number?
The Prandtl number (Pr) is a dimensionless parameter in heat transfer and fluid dynamics that characterizes the relative thickness of the momentum boundary layer to the thermal boundary layer in a fluid. It’s a fundamental property that helps engineers understand how momentum (velocity) and heat diffuse through a fluid under convective conditions

The Prandtl number is defined as:

Pr = ν/α

Where:

ν (nu) is the kinematic viscosity of the fluid (m²/s), which measures how momentum diffuses due to viscosity. It’s given by ν = μ/ρ, where μ is dynamic viscosity (Pa·s) and ρ is density (kg/m³).
α (alpha) is the thermal diffusivity (m²/s), which measures how heat diffuses through the fluid. It’s given by α = k/(ρcp), where k is thermal conductivity (W/m·K), ρ is density, and cp is specific heat capacity (J/kg·K).
Simply put, Pr = momentum diffusivity/thermal diffusivity

or if we substitute some of the variables above, we get

Pr = μcp/k

Physical Interpretation of Prandtl Number

The Prandtl number tells us how fast momentum spreads compared to heat in a fluid:

Pr < 1: Heat diffuses faster than momentum (α > ν). The thermal boundary layer is thicker than the velocity boundary layer. Common in liquid metals like mercury (Pr ≈ 0.01–0.03)
Pr = 1: Momentum and heat diffuse at the same rate (ν = α). The thermal and velocity boundary layers are roughly equal in thickness. This occurs approximately in gases like air (Pr ≈ 0.7–0.71)
Pr > 1: Momentum diffuses faster than heat (ν > α). The velocity boundary layer is thicker than the thermal boundary layer. Typical for viscous fluids like water (Pr ≈ 7 at 20°C) or oils (Pr ≈ 100–1000)
This ratio influences how heat transfer behaves in convection—whether the fluid’s motion or its thermal properties dominate the process.

What is the relationship between Prandtl number and Nusslet Number?
The Prandtl number is critical in convective heat transfer because it affects the Nusselt number (Nu = hL/k), which quantifies convection efficiency. Nu correlations often include Pr to account for fluid properties:

In laminar flow (e.g., over a flat plate), Nu ∝ Pr^(1/3). A higher Pr increases Nu, enhancing convective heat transfer because the thinner thermal boundary layer steepens the temperature gradient.
In turbulent flow (e.g., Dittus-Boelter correlation, Nu = 0.023Re^0.8Pr^n), Pr^n (n = 0.4 for heating, 0.3 for cooling) reflects its role in turbulent mixing of heat and momentum.
As an example, oils with high Pr need more vigorous flow (higher Re) to achieve the same Nu as water, due to slower heat diffusion.

Calculate Prandtl Number for the following fluids:
Water at 20 deg C
Water at 20 deg Celsius will yield the following:

μ = 0.001 Pa·s (dynamic viscosity)
cp = 4180 J/kg·K (specific heat)
k = 0.6 W/m·K (thermal conductivity)
As a result,

Pr = μcp/k

Pr = (.001) x (4180) / (0.6)

Pr = ~6.97

Air at 20 deg C
Air at 20 deg Celsius will yield the following:

μ = 1.81×10⁻⁵ Pa·s
cp = 1005 J/kg·K
k = 0.026 W/m·K
As a result,

Pr = μcp/k

Pr = (1.81×10⁻⁵) x (1005) / (.026)

Pr = ~0.7

Water’s higher Pr reflects its greater viscosity and heat capacity relative to conductivity, while air’s near-unity Pr shows balanced diffusion.

How would you design a heat exchanger to maximize heat transfer efficiency?
I’d maximize surface area with fins or tubes, use a counterflow arrangement for a higher temperature gradient, select materials with high thermal conductivity (e.g., copper), and increase fluid velocity to boost the convective coefficient.

What is more efficient, parallel flow or counter flow in a heat exchanger, and why?
In a heat exchanger, counterflow (also called countercurrent flow) is generally more efficient than parallel flow(or cocurrent flow) for transferring heat between two fluids. This efficiency stems from the temperature distribution and the resulting driving force for heat transfer.

The key difference lies in the temperature gradient along the heat exchanger, which drives heat transfer (q = UAΔTm, where ΔTm is the mean temperature difference). Counterflow maintains a more consistent and favorable ΔTm, leading to better performance.

Counterflow is more efficient because it maintains a higher, more uniform temperature difference, leading to greater heat transfer and effectiveness. Its superiority is rooted in thermodynamics and is quantifiable via LMTD or ε-NTU methods. However, design trade-offs (cost, complexity, stress) might occasionally favor parallel flow.

How would you experimentally measure the thermal conductivity of a material?

I’d use the guarded hot plate method. Place the sample between a heated plate (controlled temperature) and a cold plate, with guard heaters to minimize edge losses. Measure the heat flux (q) and temperature difference (ΔT) across the sample thickness (L). Then, k = qL/(AΔT). I’d ensure steady-state conditions and calibrate instruments for accuracy.