Forced Convection Heat Transfer Quiz
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Questions and Answers

What does Newton's law of cooling express about convection heat transfer?

  • It is only applicable to gases.
  • It is independent of temperature difference.
  • It increases with the surface area only.
  • It is proportional to the temperature difference. (correct)

Which type of convection typically has the highest convection heat transfer coefficient?

  • Free convection of gases
  • Forced convection of liquids
  • Free convection of liquids
  • Boiling and condensation (correct)

What is a key factor in determining the heat transfer characteristics of cross flow configurations?

  • The conductivity of the material
  • Type of fluid in the tubes
  • The size of the tubes used
  • Thermal boundary layer development (correct)

Which number relates the Nusselt number to Reynolds number and Prandtl number?

<p>Reynolds number (B)</p> Signup and view all the answers

What factor is practically constant for gases under a wide range of conditions?

<p>Prandtl number (B)</p> Signup and view all the answers

What is the purpose of the Perspex rods in the experimental setup?

<p>To simulate a cross flow heat exchanger (D)</p> Signup and view all the answers

What is a limitation in calculating average heat transfer coefficients in cross flow?

<p>3-D and time dependent flow instabilities (B)</p> Signup and view all the answers

What is the preferred method to indicate air velocity past the tube bank?

<p>Observing pressure drop (D)</p> Signup and view all the answers

What is the maximum pressure difference and velocity head achievable in the apparatus?

<p>75 mm water gauge (B)</p> Signup and view all the answers

Which of the following best describes the convection heat transfer coefficient for forced convection of gases?

<p>25-250 W/m² °C (A)</p> Signup and view all the answers

What is the temperature characteristic of the thermocouples within the specified range?

<p>Approximately linear (D)</p> Signup and view all the answers

What is the specific heat of the copper element used in the apparatus?

<p>380 J/kg.K (A)</p> Signup and view all the answers

Which dimension corresponds to the diameter of the tube elements?

<p>12.5 mm (B)</p> Signup and view all the answers

What is the formula for calculating the Reynolds number?

<p>$Re = \frac{ρVd}{μ}$ (D)</p> Signup and view all the answers

What type of manometer can be used for greater precision in measuring pressure drop?

<p>Electronic micro manometer (B)</p> Signup and view all the answers

Which dimension represents the surface area of the element?

<p>$A = \frac{d^2}{4} \times \pi$ (C)</p> Signup and view all the answers

What is the maximum temperature that the copper element reaches when heated?

<p>80 °C (B)</p> Signup and view all the answers

Which instrument measures the temperature difference within the copper element?

<p>Thermocouple potentiometer (C)</p> Signup and view all the answers

What purpose does the honeycomb flow straightener serve in the apparatus?

<p>To prevent swirl from the fan (D)</p> Signup and view all the answers

How is the velocity through the apparatus regulated?

<p>By using a manual throttle valve (D)</p> Signup and view all the answers

What feature allows for the exploration of the flow pattern upstream of the tube bank?

<p>Total head tube (B)</p> Signup and view all the answers

What is the purpose of the static tapings associated with the apparatus?

<p>To record the velocity head (C)</p> Signup and view all the answers

What initial measurement is indicated at the inlet of the air stream?

<p>Initial air temperature (D)</p> Signup and view all the answers

What is a function of the centrifugal fan in the apparatus?

<p>To regulate air velocity through the working section (D)</p> Signup and view all the answers

What happens to the Nusselt number as the Reynolds number increases in forced convection scenarios?

<p>It increases, indicating improved heat transfer. (C)</p> Signup and view all the answers

Which measurement is required for calculating the velocity head upstream of the element?

<p>Upstream water height in cm H<sub>2</sub>O (B)</p> Signup and view all the answers

When the radiator in a car shows a dangerous temperature after stopping, what could be a potential explanation?

<p>Insufficient airflow over the radiator during idling. (D)</p> Signup and view all the answers

In the context of heat transfer, what does the relationship TA refer to?

<p>Ambient temperature of the surrounding environment. (B)</p> Signup and view all the answers

What is one way to characterize forced convection in a system?

<p>Movement of the fluid is created by external means like fans or pumps. (D)</p> Signup and view all the answers

What assumption is made about the temperature gradients within the cylindrical copper element?

<p>They are negligible, allowing accurate temperature measurement. (C)</p> Signup and view all the answers

What correction is applied to the true length of the copper element?

<p>8.4 mm (B)</p> Signup and view all the answers

Which variable in the equation for heat transfer rate ($q=hA(T-T_A)$) represents the temperature difference?

<p>$(T-T_A)$ (D)</p> Signup and view all the answers

How is the heat transfer coefficient ($h$) ultimately determined?

<p>By measuring the slope of a plot of log data against time. (D)</p> Signup and view all the answers

Which equation indicates the relationship between temperature change and time?

<p>$ rac{dT}{dt} = rac{hA_1}{m.c}(T-T_A)$ (A)</p> Signup and view all the answers

What is plotted on a semi-log paper to estimate the heat transfer coefficient?

<p>$ rac{T-T_A}{T_o-T_A}$ vs $t$ (D)</p> Signup and view all the answers

When integrating the temperature change equations, what form does the equation take?

<p>$log_e rac{T-T_A}{T_o-T_A} = - rac{hA_1t}{m.c}$ (C)</p> Signup and view all the answers

In the context of heat transfer, what does the variable $(T_o)$ represent?

<p>The element temperature at time $t=0$. (D)</p> Signup and view all the answers

How is the heat transfer coefficient (h) related to the slope (M) of the line on semi-log paper?

<p>$h = -2.3026\frac{m.c}{A_1}M$ (B)</p> Signup and view all the answers

What is the equation for dynamic pressure measured by a Pitot tube?

<p>$\Delta P = \frac{\rho V_1^2}{2}$ (D)</p> Signup and view all the answers

What is the value of the gas constant R for the density equation?

<p>287 J/kg.K (B)</p> Signup and view all the answers

According to the equations, what is the effective velocity (V) based on the condition of studying a single element in isolation?

<p>$V = \frac{10}{9}V_1$ (B)</p> Signup and view all the answers

Under what condition is the Prandtl (Pr) number considered constant?

<p>For gases under a wide range of conditions (A)</p> Signup and view all the answers

What does the relationship $\frac{hd}{k} = f( \frac{pVd}{\mu},\frac{\mu C_p}{k})$ signify in dimensional analysis?

<p>A variable heat transfer coefficient based on velocity (A)</p> Signup and view all the answers

What does equation $Nu = f(Re.Pr)$ suggest about the heat transfer?

<p>It is influenced by both Reynolds and Prandtl numbers (B)</p> Signup and view all the answers

What is the corresponding dynamic pressure formula in relation to head difference (ΔH) measured by a manometer?

<p>ΔP = ρgΔH (D)</p> Signup and view all the answers

Flashcards

Convection Heat Transfer

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

Newton's Law of Cooling

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

Convection Heat Transfer Coefficient (h)

A proportionality constant that determines the rate of convective heat transfer.

Free Convection

Convection driven by density differences in the fluid, often due to temperature variations.

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Forced Convection

Convection resulting from the external force like a fan or pump pushing the fluid.

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Nusselt Number

A dimensionless number used in convective heat transfer correlations to relate heat transfer.

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Reynolds Number

A dimensionless number that indicates the ratio of inertial forces to viscous forces in a fluid flow.

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Prandtl Number

A dimensionless number that describes the relative thickness of momentum and thermal boundary layers.

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Pressure drop in tube banks

The pressure difference across a tube bank is proportional to the air flow velocity. Specifically, the pressure drop is about four times the velocity head.

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Velocity head

A measure of kinetic energy per unit volume of a fluid, expressed as the height of a column of fluid that would have the same energy as the moving fluid.

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Static pressure

The pressure at a point in a fluid at rest, relative to a reference pressure.

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Thermocouple

A device composed of two different metals joined together, which produces a voltage proportional to the temperature difference between the junction points.

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Transverse pitch

The distance between adjacent tubes in a tube bank, measured perpendicular to the direction of flow.

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Longitudinal pitch

The distance between adjacent tubes in a tube bank, measured parallel to the direction of flow.

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Nusselt number (Nu)

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

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Reynolds number (Re)

A dimensionless number indicating the ratio of inertial forces to viscous forces in a fluid flow.

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Heat Transfer Coefficient

A measure of how effectively heat is transferred between a surface and a fluid flowing past it.

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Semi-Logarithmic Plot

A graph where one axis has a logarithmic scale, allowing for a clearer view of exponential changes in data.

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What is the purpose of the honeycomb flow straightener?

To prevent swirl in the airflow from the fan from interfering with the measurements in the working section.

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What is the purpose of the total head tube?

To measure the total pressure (static pressure + velocity pressure) of the airflow.

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What is the purpose of the traversing stations?

To measure the velocity distribution across the airflow, providing a detailed view of the flow pattern.

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What is the purpose of the bell-mouth?

To create a smooth, uniform airflow into the working section, minimizing any distortions.

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How is the element heated?

The element is heated by placing it in a cylindrical electric heater, which raises its temperature to about 80°C.

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Heat Loss Assumption

In this experiment, it's assumed that all heat lost from the copper element is transferred to the air flowing past it.

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Negligible Temperature Gradients

The assumption that temperature differences within the copper element are negligible, meaning the thermocouple accurately measures the entire element's surface temperature.

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Plastic Extension Effect

Heat loss through the plastic extensions is accounted for by adding an equivalent length to the copper element, resulting in an 'effective length' used in calculations.

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Heat Transfer Coefficient (h)

A measure of how effectively heat is transferred from a surface to a fluid. It is defined by the rate of heat transfer per unit area and temperature difference.

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Equation 1: Heat Transfer Rate

The equation (q = h * A *(T-T_A)) describes the rate of heat transfer (q) based on the heat transfer coefficient (h), surface area (A), and temperature difference between the element (T) and the air (T_A).

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Equation 2: Heat Loss and Temperature Change

This equation, (-q.dt = m.c.dT), relates the heat loss (q) in a time period (dt) to the mass (m), specific heat (c), and temperature change (dT) of the element.

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Equation 3: Combining Equations 1 & 2

This equation, ( rac{dT}{dt} = rac{hA_1}{m.c}(T-T_A)), combines the equations for heat transfer rate and temperature change to express how the element's temperature changes over time.

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Equation 4: Integrating to Find h

This equation, (log_e rac{T-T_A}{T_o-T_A} = - rac{hA_1t}{m.c} ), results from integrating Equation 3 and allows us to calculate the heat transfer coefficient (h) using the measured temperature data.

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How does a radiator in a car work?

The radiator uses forced convection to remove heat from the engine coolant. As the hot coolant flows through the radiator, air forced through it by the fan cools the coolant down.

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Semi-log Paper

Graph paper with one axis having a logarithmic scale and the other a linear scale. It is useful for plotting data that spans a wide range, especially when exponential relationships are involved.

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Velocity Head (ΔH)

The height of a fluid column representing the kinetic energy per unit volume of a moving fluid. It's a way to express the fluid's motion in terms of a static pressure equivalent.

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Dynamic Pressure (ΔP)

The pressure created by the motion of a fluid. It's directly related to the fluid's density and velocity squared.

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Effective Velocity (V)

The average velocity of a fluid passing through a tube bank, considering the minimum flow area available. It's used to account for the constricted flow paths between tubes.

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Prandtl Number (Pr)

A dimensionless number comparing the relative thicknesses of momentum and thermal boundary layers within a fluid. It indicates how well heat and momentum transfer are coupled.

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Study Notes

Forced Convection Heat Transfer

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

Background

  • Convection: Energy transfer between a solid surface and a moving fluid (liquid or gas). This involves combined conduction and fluid motion.
    • Faster fluid motion leads to greater heat transfer by convection.
    • In the absence of bulk fluid movement, heat transfer is purely by conduction.
    • Fluid motion enhances heat transfer with a solid surface but also makes determining rates more complex.
  • Forced Convection: Fluid movement is forced by external means (e.g., fan, pump, wind).
  • Natural (Free) Convection: Fluid movement is caused by buoyancy forces due to density differences from temperature variations within fluid.

Experimental Setup

  • Apparatus: Perspex working section with air flow by a centrifugal fan.
    • Perspex rods can be inserted to simulate cross-flow heat exchangers.
    • A copper element is used for heat transfer studies within working section.
  • Instrumentation:
    • Thermocouples: Measures the element and air inlet temperatures.
    • Manometer/Micro-manometer: Measures pressure difference & velocity head.
    • Potentiometer: Records temperature difference for calculations.

Theoretical Background

  • Newton's Law of Cooling: The rate of convection heat transfer is proportional to the temperature difference.
  • Heat Transfer Coefficient: Rate of transmission of heat from the element to air (h).
  • Equation for Heat Transfer Coefficient: An equation relating temperature change over time to heat transfer coefficient (using log).
  • Calculating Velocity: The velocity of air is measured using a pitot tube, dynamic pressure (AP), and a manometer
  • Minimum Flow Area: Critical flow area consideration when calculating velocities through a tube bank.

Experimental Procedure

  • Detailed steps for setting up the apparatus and conducting the convection experiments.
    • Setup procedures include manometer connections, element placement, and flow rate control.
    • Specific procedures for recording measurements, plotting cooling curves and using heat transfer coefficient calculations.

Results and Analysis

  • Data: Collected data on temperature, time, flow rate...
  • Calculations: Calculate heat transfer coefficients using the obtained data.
  • Comparison: Comparison of calculated heat transfer coefficients with existing correlations / established theoretical models.

Additional Information

  • (Specimen data, tables)

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Description

Test your understanding of forced convection heat transfer, its differences from natural convection, and how to measure the heat transfer coefficient in tube systems. This quiz will also cover the presentation of experimental measurements and comparisons with existing correlations.

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