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title: Newton's law of cooling
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# Newton's law of cooling
Unit 2, Lecture 16

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## Newton's law of cooling

- Course: Heat and Mass Transfer (DI05019071)
- Unit 2: Convection
- Lecture 16: Newton's Law of Cooling

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Welcome to Unit 2. Today we begin our study of Convection. We will start with the fundamental principle governing convective heat transfer, which is Newton's Law of Cooling.
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## Lecture Agenda

- 1. Introduction to Convection
- 2. Mechanism of Convective Heat Transfer
- 3. Types of Convection
- 4. Newton's Law of Cooling
- 5. Convection Heat Transfer Coefficient
- 6. Factors Affecting the Heat Transfer Coefficient

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Here is our roadmap for today. We will define convection, understand how it works, and formally state Newton's Law of Cooling before diving into the details of the heat transfer coefficient.
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## Introduction to Convection

- Convection is the mode of heat transfer between a solid surface and the adjacent liquid or gas that is in motion.
- It involves the combined effects of:
- 1. Conduction (at the surface)
- 2. Fluid motion (macroscopic movement of fluid parcels)
- Without fluid motion, heat transfer between a solid surface and an adjacent fluid is purely by conduction.

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Convection is unique because it requires a fluid in motion. If the fluid is perfectly still, the heat transfer from the surface to the fluid is just conduction. Fluid motion enhances heat transfer.
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## Mechanism of Convection

- Near the solid surface, fluid velocity is zero (no-slip condition).
- Heat is first transferred to this stationary fluid layer by conduction.
- This heat is then carried away by the macroscopic motion of the fluid away from the surface.
- Therefore, convection is essentially conduction combined with fluid advection.

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The no-slip condition means the fluid particles directly touching the surface are stationary. So, the very first step of convection is actually conduction through this stationary layer!
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## Types of Convection

- Convection is broadly classified based on how the fluid motion is initiated:
- 1. Forced Convection: Fluid is forced to flow over the surface by external means (pump, fan, wind).
- 2. Free (Natural) Convection: Fluid motion is caused by buoyancy forces due to density differences induced by temperature gradients.

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We will explore forced and free convection in much more detail in the next lecture, but it is important to know these two main categories right now.
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## Newton's Law of Cooling

- Governs the rate of convection heat transfer.
- Statement: The rate of heat transfer is directly proportional to the surface area and the temperature difference between the surface and the fluid.
- Equation: q = h * A * (T_s - T_\infty)
- Where:
- - q: Rate of heat transfer (W)
- - h: Convection heat transfer coefficient (W/m²K)
- - A: Surface area (m²)

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This is the fundamental equation for convection. Unlike Fourier's law for conduction which involves thermal conductivity, this law introduces the convection heat transfer coefficient, denoted by 'h'.
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## Understanding the Equation

- Equation details: q = h * A * (T_s - T_\infty)
- T_s: Temperature of the surface.
- T_\infty: Temperature of the fluid sufficiently far from the surface (free-stream temperature).
- The direction of heat transfer depends on which temperature is higher. If T_s > T_\infty, heat flows from the surface to the fluid.

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The temperature difference is the driving force. Note that T_infinity is the bulk fluid temperature, measured far enough away from the surface that it's unaffected by the surface temperature.
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## Convection Heat Transfer Coefficient (h)

- It is not a property of the fluid.
- It is an experimentally determined parameter whose value depends on all the variables influencing convection.
- Units: Watts per square meter Kelvin (W/m²·K) or W/m²·°C.
- It characterizes how effectively heat is transferred by convection.

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This is crucial: unlike thermal conductivity 'k', 'h' is not a fundamental property of a fluid like water or air. It depends on how the fluid is moving, the surface geometry, and more.
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## Factors Affecting 'h'

- The convection heat transfer coefficient depends heavily on:
- 1. Fluid properties (dynamic viscosity, thermal conductivity, density, specific heat).
- 2. Surface geometry (flat plate, cylinder, sphere).
- 3. Surface roughness.
- 4. Fluid velocity (flow type: laminar vs. turbulent).

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Because 'h' depends on so many variables, finding its value is often the most difficult part of convection heat transfer problems. We will use dimensionless numbers later to help us find 'h'.
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## Typical Values of 'h'

- Free Convection (Gases): 2 - 25 W/m²·K
- Free Convection (Liquids): 50 - 1,000 W/m²·K
- Forced Convection (Gases): 25 - 250 W/m²·K
- Forced Convection (Liquids): 50 - 20,000 W/m²·K
- Boiling and Condensation: 2,500 - 100,000 W/m²·K

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As you can see, liquids generally have much higher 'h' values than gases, and forced convection has higher values than free convection. Phase change processes like boiling have the highest 'h' values.
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## Comparison: Conduction vs. Convection

- Conduction:
- - Mechanism: Molecular vibration/electron drift.
- - Medium: Solid (mostly), stationary fluid.
- - Law: Fourier's Law (q = -kA(dT/dx)).
- Convection:
- - Mechanism: Macroscopic fluid motion + conduction.
- - Medium: Moving fluid.
- - Law: Newton's Law of Cooling (q = hA(ΔT)).

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To wrap up our introduction, let's contrast convection with what we learned in Unit 1 about conduction. The key difference is macroscopic fluid motion.
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## Summary

- Convection combines conduction with fluid motion.
- Newton's Law of Cooling is q = h * A * (T_s - T_\infty).
- The convection heat transfer coefficient 'h' is an empirical parameter, not a material property.
- 'h' depends on fluid properties, flow conditions, and surface geometry.

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These are the core takeaways. Remember the equation and understand that determining 'h' is the central challenge in convection problems.
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## Next Lecture Preview

- Topic: Concept of forced and free convection
- Key questions:
- - How do buoyancy forces create fluid motion in free convection?
- - When does forced convection transition from laminar to turbulent flow?

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In the next lecture, we will dive deeper into the two primary types of convection: forced and free convection. We will look at their distinct mechanisms.
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