Summary of Heat Transfer 19 | Convection Heat Transfer (V) | Mechanical Engineering | GATE Crash Course

Summary of "Heat Transfer 19 | Convection Heat Transfer (V) | Mechanical Engineering | GATE Crash Course"

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Main Ideas and Concepts Covered:

• Recap of Previous Session:
  • Average velocity and its mathematical expression.
  • Concept of temperature in convective heat transfer.
  • Understanding thermally fully developed flow.
  • Introduction to minimum temperature (T_min) or bulk/mixing cup temperature in fluid flow.
• Wall Temperature Cases:
  • Two important boundary conditions in convective heat transfer:
    • Constant Wall Temperature
    • Constant Heat Flux
  • These cases affect how temperature varies along the flow and influence the Nusselt Number (Nu).
• Minimum Temperature (T_min) Concept:
  • T_min varies along the flow direction (x).
  • T_min at inlet and outlet of pipe/duct is discussed.
  • T_min is a function of x; it changes exponentially or linearly depending on the case.
• Nusselt Number (Nu) and Its Importance:
  • Nu relates convective heat transfer coefficient (h) to thermal conductivity (k).
  • Two objectives in Convection Heat Transfer:
    • Finding convective heat transfer coefficient (h).
    • Calculating rate of convective heat transfer.
  • Nu depends on flow conditions and thermal boundary conditions.
  • For internal flows:
    • Nu varies in developing and developed regions.
    • In developed region, Nu is constant and independent of x.
    • In developing region, Nu varies with x.
• Internal Flow and Hydraulic Diameter:
  • For non-circular ducts, Hydraulic Diameter (D_h) is used as characteristic length.
  • Hydraulic Diameter formula: \( D_h = \frac{4 \times \text{flow area}}{\text{wetted perimeter}} \).
• Laminar vs. Turbulent Flow:
  • Flow regime determined by Reynolds Number (Re).
  • Critical Reynolds Number for internal flow ~ 2000.
  • Laminar flow: Nu correlations differ for constant wall temperature and constant heat flux.
  • Turbulent flow: Nu correlations involve empirical relations with Re and Prandtl number (Pr).
• Comparison of Constant Wall Temperature vs. Constant Heat Flux:
  • Nu values are higher in constant heat flux cases than in constant wall temperature cases.
  • Typical values for laminar flow in pipes:
    • Constant wall temperature: Nu ≈ 3.66
    • Constant heat flux: Nu ≈ 4.36
• Energy Balance and Temperature Variation:
  • Energy balance applied to a small fluid element inside the pipe.
  • Heat transferred by convection equals increase in fluid enthalpy.
  • For constant wall temperature:
    • Minimum temperature varies exponentially along the pipe.
  • For constant heat flux:
    • Minimum temperature varies linearly along the pipe.
• Use of Log Mean Temperature Difference (LMTD):
  • LMTD concept is applied to convective heat transfer in pipes.
  • It helps relate heat transfer rate, surface area, and temperature difference.
• Example Problems and Application:
  • Problems involving:
    • Calculation of pipe length required to achieve a certain outlet temperature.
    • Determining exit temperature for given heat flux and flow conditions.
    • Use of Hydraulic Diameter and Reynolds Number for ducts.
    • Application of empirical correlations for Nu in laminar and turbulent flows.
  • Emphasis on understanding problem statements and identifying whether constant wall temperature or constant heat flux applies.
• Important Practical Notes:
  • Heat transfer coefficient (h) and Nu depend on flow regime and thermal boundary conditions.
  • Understanding the physical meaning of T_min and its variation is crucial.
  • Empirical correlations are widely used in engineering problems.
  • Energy balance is the fundamental principle to relate heat transfer and fluid temperature changes.
• Exam Tips and Strategy:
  • Approach problems calmly and carefully analyze given data.
  • Identify flow regime (laminar/turbulent) using Reynolds Number.
  • Determine boundary condition type (constant wall temperature or constant heat flux).
  • Use correct correlations and formulas accordingly.
  • Practice previous year questions for better understanding.

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Detailed Methodology / Instructions Presented:

• Calculating Average Velocity:
  • Use velocity profiles and integrate to find average velocity.
• Determining Minimum Temperature (T_min):
  • Identify inlet and outlet temperatures.
  • Use energy balance to relate heat transfer to fluid temperature changes.
  • For constant wall temperature: T_min varies exponentially with x.
  • For constant heat flux: T_min varies linearly with x.
• Calculating Nusselt Number (Nu):
  • For laminar flow in pipes:
    • Constant wall temperature: Nu = 3.66 (approx.)
    • Constant heat flux: Nu = 4.36

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Educational

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