Forced Convection Heat Transfer Concepts
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Questions and Answers

What is Newton's law of cooling, and what does it express in terms of heat transfer?

Newton's law of cooling expresses the rate of convection heat transfer as $Q_{conv} = hA(T_s - T_A)$, indicating it is proportional to the temperature difference.

Describe the typical range of convection heat transfer coefficients for forced convection of gases.

The typical range of convection heat transfer coefficients for forced convection of gases is between 25 and 250 W/m² °C.

Why is it difficult to calculate average heat transfer coefficients for cross flow configurations analytically?

It is difficult due to boundary layer separation and time-dependent flow instabilities that occur, making analytical calculations complex.

What are the primary factors influencing heat transfer rate for gases according to the document?

<p>The heat transfer rate for gases is primarily influenced by the Reynolds number since the Prandtl number remains practically constant under many conditions.</p> Signup and view all the answers

Explain the significance of the thermal boundary layer development in heat exchangers.

<p>Thermal boundary layer development is significant as it affects the heat transfer characteristics in configurations like cylinders and tube bundles.</p> Signup and view all the answers

What kind of experimental setup is used to study heat transfer phenomena associated with flow past cylindrical tubes?

<p>The experimental setup consists of a Perspex working section where air flows past cylindrical elements, simulating cross flow conditions.</p> Signup and view all the answers

What role do correlations of experimental data play in heat transfer calculations for arbitrary Reynolds numbers?

<p>Correlations of experimental data are used to relate the Nusselt number to Reynolds number and Prandtl number due to the difficulty in making direct calculations.</p> Signup and view all the answers

What is the material composition of the rod used in the experimental setup mentioned?

<p>The rod used in the setup is made of pure copper, approximately 10 cm in length, attached to extension rods of a fabric-based plastic compound.</p> Signup and view all the answers

What is the primary difference between natural convection and forced convection?

<p>Natural convection occurs due to buoyancy forces from temperature differences, while forced convection involves external means, such as fans or pumps, to circulate the fluid.</p> Signup and view all the answers

How does flow velocity affect the heat transfer coefficient in forced convection?

<p>As flow velocity increases, the heat transfer coefficient also increases due to enhanced fluid motion and reduced thermal resistance.</p> Signup and view all the answers

What dimensionless numbers are used to present the relationship between heat transfer and fluid flow in this experiment?

<p>The Nusselt number (Nu) represents heat transfer, and the Reynolds number (Re) characterizes fluid flow.</p> Signup and view all the answers

In the context of heat transfer, what role does conduction play in the process of convection?

<p>Conduction transfers energy from the solid surface to the adjacent fluid, while convection carries that energy away through fluid motion.</p> Signup and view all the answers

What happens to heat transfer when the temperature difference between the solid surface and the fluid is minimal?

<p>When the temperature difference is minimal, heat transfer is primarily by conduction rather than convection.</p> Signup and view all the answers

Why is it significant to compare experimental Nusselt number and Reynolds number relationships to correlations in textbooks?

<p>Comparing these relationships allows for validation of experimental methods and can help improve understanding of heat transfer phenomena.</p> Signup and view all the answers

What is the effect of bulk fluid motion on heat transfer at a solid surface?

<p>Bulk fluid motion enhances heat transfer by removing heated fluid near the surface and replacing it with cooler fluid.</p> Signup and view all the answers

What is a tube bundle, and why might it be significant to measure heat transfer in such configurations?

<p>A tube bundle consists of multiple tubes arranged to enhance fluid flow around them, and measuring heat transfer in these configurations is significant for improving efficiency in heat exchangers.</p> Signup and view all the answers

What is the relationship between pressure drop and velocity head in the experimental setup?

<p>The static pressure drop across the tube banks is about four times the velocity head.</p> Signup and view all the answers

What is the range of the inclined manometer provided in the apparatus?

<p>The inclined manometer has a range of approximately 75 mm water gauge.</p> Signup and view all the answers

Which materials are used for the thermocouples in the experimental setup?

<p>The thermocouples are made from copper and constantan.</p> Signup and view all the answers

What is the specific heat of the copper element as mentioned in the specifications?

<p>The specific heat of the copper element is 380 J/kg.K.</p> Signup and view all the answers

What is the value of the diameter of the elements used in the tube banks?

<p>The diameter of the elements is 12.5 mm.</p> Signup and view all the answers

How is the temperature characteristic of the thermocouple described within the range of 0-50°C?

<p>The temperature characteristic is approximately linear, where 1 °C corresponds to 0.041 mV.</p> Signup and view all the answers

What is the formula for the Nusselt number as a dimensionless group?

<p>The Nusselt number is given by the formula $Nu = \frac{hd}{k}$.</p> Signup and view all the answers

What is the longitudinal pitch of the elements in the experimental setup?

<p>The longitudinal pitch of the elements is 18.75 mm.</p> Signup and view all the answers

What is the purpose of connecting the manometer to the total head tube?

<p>The manometer measures the pressure drop between the atmosphere and the upstream static pressure to calculate velocity head.</p> Signup and view all the answers

Why is it important to standardize the thermocouple potentiometer before starting the experiment?

<p>Standardizing ensures accurate temperature readings of the heated element during the experiment.</p> Signup and view all the answers

What should be monitored when the throttling valve is opened to achieve the desired flow rate?

<p>The air inlet temperature and total head tube reading need to be recorded.</p> Signup and view all the answers

How does replacing the heated element affect the measurement process during the experiment?

<p>Reinstalling the heated element allows for continuous measurement of cooling curves at varying temperatures.</p> Signup and view all the answers

What role does the stopwatch play in the experimentation process mentioned?

<p>The stopwatch is used to time how long it takes for the galvanometer needle to pass through the zero position.</p> Signup and view all the answers

Why is it beneficial to plot cooling curves for different air velocities?

<p>It provides insight into how airflow affects the cooling rate of the heated element.</p> Signup and view all the answers

What preliminary information can be obtained from the pressure drop across the tube bank?

<p>The pressure drop can be correlated to upstream velocity head, providing a more accurate measure of flow velocity.</p> Signup and view all the answers

In what contexts would measuring velocity distribution upstream and within the wake be useful?

<p>Measuring velocity distribution helps analyze flow characteristics and assesses the performance of the working section.</p> Signup and view all the answers

What is the significance of the effective length correction of 8.4 mm in heat transfer calculations?

<p>The effective length correction of 8.4 mm accounts for the additional surface area contributed by the plastic extensions, ensuring accurate heat transfer calculations.</p> Signup and view all the answers

How is the heat transfer coefficient (h) estimated from the cooling of the element?

<p>The heat transfer coefficient (h) is estimated by plotting the logarithmic relationship of temperature drop against time and calculating the slope of the resulting straight line.</p> Signup and view all the answers

What does the variable (T_o) represent in the heat transfer equations?

<p>(T_o) represents the initial temperature of the element at time (t = 0).</p> Signup and view all the answers

Explain how the fall in temperature (dT) relates to the heat transfer rate (q) over time (dt).

<p>The fall in temperature (dT) is proportional to the heat transfer rate (q) and is given by the equation -q.dt = m.c.dT, indicating energy transfer across mass and specific heat.</p> Signup and view all the answers

In the context of the derived equations, what effect does a higher heat transfer coefficient (h) have on temperature change over time?

<p>A higher heat transfer coefficient (h) results in a faster rate of temperature change, meaning the element cools more quickly.</p> Signup and view all the answers

What is the purpose of integrating equation (3) in the heat transfer analysis?

<p>Integrating equation (3) helps derive a relationship that can be analyzed to understand temperature decay over time and estimate the heat transfer coefficient.</p> Signup and view all the answers

Discuss the difference between using log_e and log_10 in plotting the temperature data.

<p>Log_e is used in the original equations for accurate relationship modeling, while log_10 is applied on semi-log paper, which affects the interpretation of the plotted data.</p> Signup and view all the answers

How does the concept of negligible temperature gradients apply to the analysis of the copper element's heat transfer?

<p>Negligible temperature gradients imply that the temperature measured at the center accurately reflects the effective surface temperature, simplifying the analysis.</p> Signup and view all the answers

How is the heat transfer coefficient (h) related to the slope (M) in the semi-log paper representation?

<p>The heat transfer coefficient is related by the expression $h = -2.3026\frac{m.c}{A_1}M$.</p> Signup and view all the answers

What does the dynamic pressure (ΔP) represent in the context of measuring the velocity (V₁) of air?

<p>The dynamic pressure (ΔP) represents the pressure difference related to the velocity of the air, given by $ΔP = \frac{ρV_1^2}{2}$.</p> Signup and view all the answers

What is the relationship between $H$ and the dynamic pressure ΔP as expressed in equation (6a)?

<p>The relationship is $ρV_1^2 = 98.1 H$, where ΔP is measured in terms of head difference.</p> Signup and view all the answers

How is the effective velocity (V) of air in a tube bank determined when all tubes are present?

<p>When all tubes are present, the effective velocity is given by $V = 2V_1$.</p> Signup and view all the answers

Explain the significance of the Prandtl (Pr) number in heat transfer analysis for gases.

<p>The Prandtl number is significant as it remains constant for gases under a wide range of conditions, affecting heat transfer rates.</p> Signup and view all the answers

What expression relates the Reynolds number (Re) and the Nusselt number (Nu) in convection heat transfer?

<p>The expression is $Nu = f(Re)$.</p> Signup and view all the answers

What is the formula for calculating the velocity (V₁) of air given the head (H) and temperature (Tₐ)?

<p>The formula is $V_1 = 237.3\sqrt{\frac{H.T_A}{p_A}}$.</p> Signup and view all the answers

Describe how the minimum flow area is determined when studying a single element in isolation.

<p>The minimum flow area is (9/10) of the full working section area, leading to the expression $V = \frac{10}{9}V_1$.</p> Signup and view all the answers

Flashcards

Forced Convection

Heat transfer where fluid motion is caused by external forces like fans or pumps.

Natural Convection

Heat transfer where fluid motion is caused by temperature differences and density variations (buoyancy).

Heat Transfer Coefficient

A measure of how effectively heat transfers between a surface and a fluid.

Conduction

Heat transfer through a material without bulk motion of the material.

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Nusselt Number (Nu)

A dimensionless number representing the ratio of convective to conductive heat transfer.

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Reynolds Number (Re)

A dimensionless number representing the ratio of inertial forces to viscous forces.

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Cross Flow

Fluid flow perpendicular to a surface.

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Heat Transfer Laboratory

A setting for studying and measuring heat transfer.

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Convection Heat Transfer

Heat transfer through the movement of fluids (liquids or gases).

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Newton's Law of Cooling

The rate of convective heat transfer is proportional to the temperature difference between a surface and surroundings.

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Convection Heat Transfer Coefficient (h)

Measures how efficiently heat is transferred by convection.

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Cross Flow Heat Exchanger

Heat exchangers where the flow is perpendicular to the tubes (or other heat transfer surfaces).

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Nusselt Number

A dimensionless number correlating heat transfer characteristics in convective flow.

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Reynolds Number

A dimensionless number that measures the ratio of inertial forces to viscous forces within a fluid.

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Static Pressure Drop

The difference in pressure between two points in a fluid flow, excluding the pressure due to fluid velocity.

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Velocity Head

The pressure equivalent of the kinetic energy of a fluid due to its velocity.

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Thermocouple

A sensor consisting of two dissimilar metals that produce a voltage proportional to temperature difference.

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Effective Length

The actual length of a tube that contributes to heat transfer, considering the end effects.

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Effective Surface Area

The surface area of a tube that is actually in contact with the fluid transferring heat.

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Prandtl Number (Pr)

A dimensionless number representing the ratio of momentum diffusivity to thermal diffusivity in a fluid.

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Heat Transfer Coefficient (h)

A measure of how efficiently heat is transferred between the copper element and the surrounding air.

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What is the formula for heat transfer rate?

q = h * A * (T - T_A), where q is the heat transfer rate, h is the heat transfer coefficient, A is the surface area, T is the element temperature, and TA is the air temperature.

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How is the temperature change over time (dT/dt) related to heat transfer?

dT/dt = (h * A) / (m * c) * (T - T_A), where m is the mass of the element, and c is its specific heat capacity.

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What does the slope of the log(T-T_A)/(T_o-T_A) vs. t graph represent?

The slope of the graph is equal to -hA1/(m*c), allowing us to calculate the heat transfer coefficient (h) since other factors are known.

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How can we measure the heat transfer coefficient (h) from the experiment?

By plotting log_e[(T-TA)/(To-TA)] against time (t) and determining the slope of the resulting straight line.

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What are the two ways to plot the data?

  1. Plot log_e(T-T_A)/(T_o-T_A) on a linear y-axis and t on a linear x-axis. 2. Plot (T-TA)/(To-TA) on a semi-log paper, linear on the x-axis (t) and log_10 on the y-axis.
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Why is a correction factor applied to the length of the copper element?

Because the plastic extension pieces also conduct heat, we need to account for this additional heat transfer by adding a correction factor to the actual length of the element.

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Upstream Velocity Head

The dynamic pressure of the air flow before the working section, representing the air's kinetic energy.

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Static Pressure Tapping

A small hole in the apparatus where static pressure is measured, representing the pressure of the air at rest.

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Total Head Tube

A device to measure the total pressure (static + dynamic) of the air flow.

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Throttle Valve

A mechanism to control the flow rate of air by adjusting the opening.

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Thermocouple Potentiometer

An instrument that measures the temperature of the heated element by converting electrical signals.

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Galvanometer Needle

A pointer in the potentiometer that indicates the temperature of the element by responding to electrical signals.

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Cooling Curve

A graph that shows the temperature of the heated element decreasing over time.

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Tube Bank

A group of tubes arranged in rows and columns forming a heat exchanger.

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Semi-log paper

A type of graph paper where one axis is logarithmic, and the other is linear. It's used to visualize exponential relationships, like the relationship between heat transfer coefficient and temperature difference.

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Slope (M) on a Semi-log Plot

On semi-log paper, the slope of the line represents the change in the logarithmic value of the dependent variable (usually temperature) with respect to the linear value of the independent variable (usually time).

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Pitot Tube

A device used to measure the velocity of a fluid by converting the kinetic energy of the fluid into static pressure.

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Dynamic Pressure (ΔP)

The pressure a fluid possesses due to its motion. It's related to the fluid's velocity and density.

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Minimum Flow Area

The smallest cross-sectional area through which a fluid flows in a system. This is often used to calculate the effective velocity of the fluid.

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Study Notes

Forced Convection Heat Transfer to a Tube in Cross Flow

  • Objectives:
    • Understand the difference between natural and forced convection.
    • Measure heat transfer coefficient (on a tube in cross flow) as a function of flow velocity.
    • Present experimental measurements in dimensionless form (Nusselt number (Nu) versus Reynolds number (Re)).
    • Compare measured Nu-Re relation with existing correlations.
    • Repeat measurements, correlation, and comparison for a tube bundle.

Background

  • Convection: The mode of energy transfer between a solid surface and adjacent fluid (liquid or gas) in motion. It combines conduction and fluid motion. Faster fluid motion = greater heat transfer via convection. Without bulk fluid motion, heat transfer is purely conductive.
  • Forced Convection: Fluid flow is forced (e.g., by a fan, pump, or wind).
  • Natural (Free) Convection: Fluid motion due to buoyancy forces (caused by density differences from temperature variations).

Experimental Setup

  • Apparatus: Perspex working section with air drawn by a centrifugal fan.
  • Rods: Copper rods in the working section simulate a heat exchanger.
  • Thermocouples: Measure temperature, with a junction embedded in the element and a reference junction in the air stream.
  • Manometer: Measures pressure difference and velocity head.
  • Air Velocity Measurement: Using Pitot tube (dynamic pressure measurements).

Theoretical Background

  • Heat Transfer Rate: Dependent on convection heat transfer coefficient, area, and temperature difference (Newton's Law of Cooling).

  • Convection Equations:

    • Heat Transfer Rate (q)= h * A * (T - Ta), where h = convective heat transfer coefficient, A = surface area, T = element temperature, Ta = air temperature.

  • Heat Transfer Coefficient Calculation: Using logarithmic cooling curve. Obtaining slope of curve will yield h.

Summary Table

  • Materials: Copper (element diameter, length, weight).
  • Nomenclature: Defining key variables, with units (e.g., diameter, length of element, velocity).

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Description

This quiz focuses on the principles of forced convection heat transfer, specifically related to tubes in cross flow. It covers how to measure the heat transfer coefficient and the importance of dimensionless form in experimental measurements. Additionally, it includes comparisons with existing correlations, enhancing understanding of convection phenomena.

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