Questions
6 questions in major PSU papers
Difficulty
Medium-Hard
Importance
High yield for HPCL/NTPC
Overview
Heat Transfer is a fundamental pillar of Thermal Engineering that governs energy exchange mechanisms in industrial systems like boilers, heat exchangers, and power plants. Mastering this topic is essential for PSU exams as it involves complex numerical problem-solving related to temperature gradients and heat dissipation rates. Aspirants must grasp the distinct physical laws governing conduction, convection, and radiation to solve analytical questions quickly.
Conduction and Fourier Law
Conduction is the transfer of heat through stationary media by atomic or molecular interaction. Fourier Law of Heat Conduction provides the linear relationship between the heat transfer rate and temperature gradient, which is the cornerstone for solving 1D steady-state heat conduction problems.
- Fourier Law: Q = -k*A*(dT/dx)
- Thermal resistance for slab: Rth = L/(k*A)
- Thermal resistance for cylinder: Rth = ln(r2/r1) / (2*pi*L*k)
- Critical thickness of insulation: r_crit = k/h
- Variable thermal conductivity: Q = k_avg * A * (T1-T2)/L
Convection and Newton Law
Convection involves heat transfer between a surface and a moving fluid, governed primarily by Newton's Law of Cooling. Exams focus heavily on dimensionless numbers like Nusselt, Reynolds, Prandtl, and Grashof, which define the relationship between conductive and convective resistance.
- Newton Law of Cooling: Q = h*A*(Ts-Tf)
- Nusselt Number: Nu = h*L/k
- Reynolds Number: Re = rho*v*D/mu
- Prandtl Number: Pr = mu*Cp/k
- Grashof Number (Natural Convection): Gr = g*beta*(Ts-Tf)*L^3/nu^2
Radiation and Stefan-Boltzmann
Radiation is the transfer of thermal energy via electromagnetic waves without requiring a medium. PSU exams frequently test the Stefan-Boltzmann Law and the concepts of view factors and emissivity for grey and black bodies.
- Stefan-Boltzmann Law: E = sigma * T^4
- Wien's Displacement Law: lambda_max * T = 2898 micron-K
- Kirchhoff's Law: Emissivity = Absorptivity for grey bodies
- Radiosity: J = epsilon*Eb + (1-epsilon)*G
- View factor summation rule: Sum of Fij = 1
Heat Exchangers and Fins
Heat exchangers are tested through Log Mean Temperature Difference (LMTD) and Effectiveness-NTU methods. Fins are analyzed based on their efficiency and effectiveness, often appearing as tricky conceptual questions regarding their impact on total heat transfer.
- LMTD formula: (deltaT1 - deltaT2) / ln(deltaT1/deltaT2)
- Effectiveness: epsilon = Q_actual / Q_max
- Number of Transfer Units: NTU = UA/C_min
- Fin Efficiency: eta = Q_fin / Q_max_possible
- Fin Effectiveness: epsilon_fin = sqrt(k*P / h*A_c)
Formula Sheet
Q = -k*A*(dT/dx)
Q = h*A*(Ts-Tf)
Q = sigma*A*epsilon*(T1^4 - T2^4)
LMTD = (deltaT1 - deltaT2) / ln(deltaT1/deltaT2)
r_crit = k/h
Nu = h*L/k
NTU = UA/C_min
Re = rho*v*D/mu
epsilon_fin = sqrt(k*P / h*A_c)
lambda_max * T = 2898
Exam Tip
Always identify the thermal resistance network first; if you can draw the circuit, the solution for steady-state conduction is almost always a simple voltage-divider-style algebraic equation.
Common Mistakes
- Confusing the thermal resistance formulas for plane walls versus cylindrical geometries, leading to incorrect calculations.
- Neglecting the impact of units (e.g., using Celsius instead of Kelvin) in radiation problems involving the Stefan-Boltzmann law.
- Failing to identify whether the flow is laminar or turbulent when choosing the correct Nusselt number correlation.
More Revision Notes
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