How is the Biot number used in heat transfer analysis?

The Biot number in heat transfer analysis is used to determine the relative significance of internal versus external thermal resistance of a solid object. It helps assess whether the lumped capacitance method can be applied, indicating that if the Biot number is less than 0.1, the object can be assumed to have a uniform temperature.

What is the significance of the Biot number in thermal conductivity measurements?

The Biot number indicates the relative resistance to heat conduction within a body compared to its resistance to heat transfer across the surface. In thermal conductivity measurements, a low Biot number implies uniform temperature distribution, while a high Biot number suggests significant temperature gradients within the material.

How do you calculate the Biot number for a given system?

The Biot number (Bi) is calculated using the formula: Bi = hL_c/k, where h is the convective heat transfer coefficient, L_c is the characteristic length (typically the volume of the body divided by its surface area), and k is the thermal conductivity of the material.

What is the physical meaning of the Biot number in the context of heat conduction?

The Biot number is a dimensionless parameter that compares the internal thermal resistance within a body to the thermal resistance across the convective boundary layer at its surface. A low Biot number indicates uniform temperature distribution inside the body, suggesting that conduction is much faster than convection. Conversely, a high Biot number implies significant temperature gradients within the object, highlighting conduction constraints.

What are the typical applications where the Biot number plays a crucial role?

The Biot number is crucial in applications involving heat transfer analysis, such as determining the temperature distribution in solid bodies, evaluating whether a lumped capacitance model is applicable in thermal systems, and designing thermal insulation for materials used in engineering processes.

What does a low Biot number imply?

External convection is significantly weaker than internal conduction.

How is the Biot number calculated?

\[ Bi = \frac{h}{L_c k} \], dividing by length and thermal conductivity.

What does a Biot number less than 0.1 imply?

It indicates a significant temperature gradient, requiring detailed analysis.

What does the Biot number indicate?

The interaction between pressure and temperature changes in polymers.

Biot Number: Definition & Formula

Biot number

The Biot number (Bi) is a dimensionless constant used in heat transfer calculations to compare the conduction resistance within a body to the convection resistance across its boundary. It is defined as the ratio of the thermal resistance inside a solid to the thermal resistance at the surface, calculated using the formula \\( Bi = \\frac{hL_c}{k} \\), where \\( h \\) is the convective heat transfer coefficient, \\( L_c \\) is the characteristic length, and \\( k \\) is the thermal conductivity of the material. Understanding the Biot number helps in determining whether lumped capacitance models can be applied, with \\( Bi < 0.1 \\) suggesting that temperature gradients within the body are negligible.

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Biot Number Definition

The Biot number is a crucial dimensionless parameter in heat transfer that represents the ratio of conductive heat resistance within a body to the convective heat transfer across its boundary. This parameter helps you understand whether the assumption of a uniform temperature within a solid is valid.

Understanding the concept of the Biot number is fundamental in applied thermodynamics and engineering, particularly when analyzing the efficiency of heat exchangers and modeling the thermal characteristics of materials.

Expression and Calculation

The Biot number is calculated using the formula:

\[ Bi = \frac{hL_c}{k} \]

Where,

h is the convective heat transfer coefficient (W/m²K)
L_c is the characteristic length (m), which is typically the volume to surface area ratio of the body
k is the thermal conductivity of the material (W/mK)

The Biot number characterizes the conduction-convection ratio within a system, indicating whether the body can be treated as thermally thin or thick. A Biot number much less than 1 implies uniform temperature distribution.

Example: Consider a metal sphere with a characteristic length of 0.05 m, a thermal conductivity of 385 W/mK, and subjected to convective heat transfer with a coefficient of 25 W/m²K. To find the Biot number, use the formula:\[ Bi = \frac{25 \times 0.05}{385} \]The calculated Biot number determines the temperature profile inside the sphere.

A Biot number less than 0.1 typically means the body reaches thermal equilibrium quickly, ideal for lumped system analysis.

In detailed heat transfer analysis, a low Biot number indicates small internal thermal resistance compared to external resistance. This is common in thin surfaces like films or sheets, where thermal gradients are minimal. In contrast, a high Biot number signifies significant internal resistance, possible in thicker bodies like bricks or metals, warranting a distributed analysis to factor in temperature differences across the body. This impacts engineering decisions such as insulation design and material selection when considering efficiency versus economy in constructing thermal equipment.

Biot Number Formula

The Biot number is a key dimensionless parameter used in thermal and fluid engineering to evaluate the relative strength of internal resistance to heat conduction against external resistance to heat convection.

This concept plays a crucial role in assessing whether we can assume a uniform temperature distribution within a material.

Calculating the Biot Number

The Biot number is calculated from the following equation:

\[ Bi = \frac{hL_c}{k} \]

Where:

h: Convective heat transfer coefficient \((\text{W/m}^2\text{K})\)
L_c: Characteristic length \((\text{m})\)
k: Thermal conductivity of the material \((\text{W/mK})\)

Characteristic length \(L_c\) usually equals the ratio of volume to surface area of the body.

The Biot number \((Bi)\) is a dimensionless parameter that indicates the balance between heat conduction within a solid and heat convection at its surface.

Example: Suppose a cylindrical rod with a characteristic length of 0.02 m has a thermal conductivity of 400 W/mK and is exposed to an environment with a convective heat transfer coefficient of 10 W/m²K. To find the Biot number, apply the formula:

\[ Bi = \frac{10 \times 0.02}{400} \]

This calculation helps determine if temperature within the rod can be considered uniform.

When the Biot number is less than 0.1, the object generally has a uniform temperature, simplifying calculations.

Exploring the extremes of the Biot number reveals its importance in practical engineering scenarios. A low Biot number, typically below 0.1, prevalently occurs in bodies where internal resistance to heat conduction is negligible compared to external convective resistance. Such conditions often justify the use of the lumped capacitance model in analysis. In contrast, a high Biot number suggests substantial internal thermal resistance, necessitating more complex methods, such as finite difference or finite element analysis, to ensure precise temperature distribution modeling within the material.

Remember, for most engineering applications, a Biot number below 1 is often preferred for efficient thermal management.

Biot Number in Heat Transfer

Understanding the Biot number is essential when dealing with problems in heat transfer. It is a crucial dimensionless parameter that helps you determine the significance of conduction heat transfer relative to convection heat transfer, particularly in problems involving solids exposed to fluid flow.

In practical scenarios, knowing the Biot number guides you in choosing the right heat transfer model to apply, whether it involves lumped system analysis or requiring detailed finite element methods for non-uniform temperature distributions.

Expression and Calculation of Biot Number

The formula for calculating the Biot number is as follows:

\[ Bi = \frac{hL_c}{k} \]

Here, the symbols denote:

h: Convective heat transfer coefficient (W/m²K)
L_c: Characteristic length (m), often defined as the volume to surface area ratio
k: Thermal conductivity of the solid (W/mK)

This calculation becomes instrumental in identifying whether a solid object has an approximately uniform temperature distribution internally.

The Biot number \((Bi)\) is a dimensionless parameter used in heat transfer problems to compare the thermal resistance within an object to the heat transfer resistance at the object's surface.

Example: Consider a flat plate with a thickness of 0.1 m and thermal conductivity of 20 W/mK surrounded by a fluid with a heat transfer coefficient of 5 W/m²K. To calculate the Biot number, use:

\[ Bi = \frac{5 \times 0.1}{20} \]

By evaluating the Biot number, you can assess how effective the heat transfer from the surface to the center of the plate is.

A Biot number less than 0.1 often indicates that temperature gradients inside a material are negligible, simplifying the analysis.

Diving deeper into the concept, a Biot number significantly greater than 1 suggests notable internal thermal resistance. This means that heat conduction within the object is dominant, requiring an analysis of the full temperature profile rather than assuming a uniform temperature distribution. High Biot numbers are typical in larger or thicker objects, such as thick walls or large cylindrical objects, where even slight variations in thermal properties or external conditions can have substantial impacts on the overall heat transfer process.

Biot Number Characteristic Length

In the realm of heat transfer analysis, the concept of characteristic length emerges as a key factor when calculating the Biot number. This length correlates with how heat transfer affects different geometries of bodies.

It's crucial to calculate it accurately as it impacts the Biot number's value, which in turn determines whether you can assume a uniform temperature distribution within an object.

Biot Number Explained with Examples

The Biot number \((Bi)\) plays a pivotal role in determining the internal temperature distribution of a solid body subjected to convection. It is calculated using:

\[ Bi = \frac{hL_c}{k} \]

Where,

h: Convective heat transfer coefficient \((\text{W/m}^2\text{K})\)
L_c: Characteristic length defined as the volume-to-surface-area ratio of a body \((\text{m})\)
k: Thermal conductivity of the material \((\text{W/mK})\)

The Biot number is a dimensionless quantity used in heat transfer to compare conductive heat transport within an object to convective heat transfer across its boundary.

Example: Imagine a cylindrical pipe with a diameter of 0.5 m, a thermal conductivity of 15 W/mK, and exposed to a fluid with a convective heat transfer coefficient of 30 W/m²K.

To calculate the Biot number, find the characteristic length \(L_c\) as:

\[ L_c = \frac{V}{A} = \frac{\frac{\pi d^2 h}{4}}{\pi d h} = \frac{d}{4} \]

Thus, for an example length of 1 m, calculate Biot:

\[ Bi = \frac{30 \times 0.125}{15} \]

This calculation helps in assessing whether a lumped system assumption is valid.

Consider a Biot number less than 0.1 for systems where lumped capacitance assumptions simplify thermal analysis greatly.

Beyond straightforward applications, the Biot number is vital in determining how different materials respond to thermal stress. For instance, a high Biot number indicates substantial internal resistance to heat flow, implying the need for complex thermal modeling to accurately predict temperature gradients and associated stresses within the material. This understanding is key in industries where thermal stability is vital, such as aerospace and automotive engineering, where materials are subjected to extreme temperatures and rapid thermal cycles.

Biot number - Key takeaways

Biot number definition: It is a dimensionless parameter in heat transfer, representing the ratio of conductive heat resistance within a body to the convective heat transfer across its boundary.
Biot number formula: Bi = \( \frac{hL_c}{k} \), where h is the convective heat transfer coefficient, \( L_c \) is the characteristic length, and k is the thermal conductivity of the material.
Characteristic length: Typically the volume-to-surface-area ratio, crucial for calculating the Biot number and assessing temperature distribution within an object.
Biot number in heat transfer: Determines the significance of conduction relative to convection, affecting the choice of heat transfer models like lumped system analysis.
Biot number explained: A Biot number less than 0.1 indicates uniform temperature distribution; above this suggests notable internal resistance, affecting engineering analyses.
Examples of Biot number calculation: Calculating Biot number for various geometries, such as spheres and cylinders, helps determine temperature profiles and the validity of uniform temperature assumptions.

Biot number

StudySmarter Editorial Team