heat transfer formula sheet

Guri Bee

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16-10-2024

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Heat Transfer Formula Sheet: Your Guide to Understanding Heat Flow

Understanding heat transfer is crucial in various fields, from engineering and physics to everyday applications like cooking and building design. This article provides a concise formula sheet for heat transfer, summarizing essential equations and offering practical insights. We'll explore conduction, convection, and radiation, the three primary modes of heat transfer.

Conduction:

1. Fourier's Law of Conduction

This law describes the rate of heat transfer through a solid material due to a temperature difference.

Q = -kA(dT/dx)

• Q: Heat transfer rate (W)
• k: Thermal conductivity of the material (W/mK)
• A: Area of heat transfer (m²)
• dT/dx: Temperature gradient (K/m)

Example: Imagine a metal rod heated at one end. The heat will flow from the hotter end to the colder end, following Fourier's Law. The rate of heat transfer depends on the material's conductivity, the rod's cross-sectional area, and the temperature difference between the ends.

2. Thermal Resistance

For a solid material, thermal resistance is defined as the ratio of temperature difference to the heat transfer rate.

R = (dT/Q)

• R: Thermal resistance (K/W)
• dT: Temperature difference (K)
• Q: Heat transfer rate (W)

3. Combined Thermal Resistance

When multiple materials are involved in heat transfer, we can combine their thermal resistances. For resistances in series, we simply add them. For resistances in parallel, we use the reciprocal rule.

Convection:

1. Newton's Law of Cooling

This law describes the heat transfer rate between a surface and a moving fluid.

Q = hA(Ts - T∞)

• Q: Heat transfer rate (W)
• h: Convection heat transfer coefficient (W/m²K)
• A: Surface area (m²)
• Ts: Surface temperature (K)
• T∞: Fluid temperature (K)

Example: Think of a hot cup of coffee. Heat is lost to the surrounding air through convection. The rate of heat transfer depends on the air's convection heat transfer coefficient, the cup's surface area, and the temperature difference between the coffee and the air.

2. Nusselt Number (Nu)

The Nusselt number represents the ratio of convective heat transfer to conductive heat transfer.

Nu = hL/k

• Nu: Nusselt number (dimensionless)
• h: Convection heat transfer coefficient (W/m²K)
• L: Characteristic length (m)
• k: Thermal conductivity of the fluid (W/mK)

Radiation:

1. Stefan-Boltzmann Law

This law describes the total energy radiated per unit area by a blackbody at a given temperature.

Q = σA(T⁴)

• Q: Heat transfer rate (W)
• σ: Stefan-Boltzmann constant (5.67 x 10⁻⁸ W/m²K⁴)
• A: Surface area (m²)
• T: Absolute temperature (K)

2. View Factor

The view factor represents the fraction of radiation leaving one surface that reaches another surface.

Fij = Qij / (σA1T1⁴)

• Fij: View factor from surface i to surface j (dimensionless)
• Qij: Rate of radiation exchange between surface i and j (W)
• A1: Area of surface i (m²)
• T1: Temperature of surface i (K)

Example: Consider a campfire. The flames radiate heat towards you. The amount of heat you receive depends on the view factor between the flames and your body.

Important Notes:

• These equations are simplified representations of complex phenomena.
• Factors like surface properties, fluid flow patterns, and environmental conditions can significantly impact heat transfer.
• The use of appropriate units is crucial for accurate calculations.

Beyond Formulas:

This formula sheet provides a foundation for understanding heat transfer. However, real-world applications often require more advanced knowledge, including:

• Heat exchanger design: Understanding heat transfer in devices like radiators and condensers is essential for efficient energy utilization.
• Thermal analysis: Analyzing the distribution of heat within complex systems is crucial in areas like electronics cooling and building design.
• Computational fluid dynamics (CFD): Simulating heat transfer using computer models provides insights into complex flow patterns and heat distribution.

References:

• Fundamentals of Heat and Mass Transfer by Incropera, DeWitt, Bergman, Lavine
• Heat Transfer by Holman
• Introduction to Heat Transfer by Cengel and Ghajar

This article aims to provide a valuable starting point for understanding heat transfer concepts. The provided formulas and examples offer a foundation for further exploration and practical application. Remember, the understanding of heat transfer is essential for addressing various engineering and scientific challenges, leading to efficient solutions in diverse fields.