Theory of Heat Transfer — Summer 2025

What are three modes of heat transfer? Explain their differences briefly with example.

Write Fourier rate equation of heat transfer by conduction. Give units of each parameter appearing in this equation.

Using dimensional analysis, obtain a general form of equation for force convective heat transfer.

Compare free convection and force convection.

Derive an expression of critical radius of insulation for the cylinders.

Derive equations of temperature distribution and heat dissipation for infinite fin.

Asteel pipe 3 cm in diameter has its outer surface at 210°C, is placed in air at 35°Cwith heat transfer coefficient of 8.5 W/m2K. It is proposed to add insulation (k = 0.07 W/mK) on its outer surface to reduce the heat loss by 40%. Estimate the thickness of insulation required, if pipe temperature and heat transfer coefficient remain unchanged.

Define: Biot number and Fourier number.

Enlist assumptions need to be considered for the analysis of heat flow through the fin.

Alarge vertical flat plate 3 m high and 2 m wide is maintained at 75°Cand is exposed to atmosphere at 25°C. Calculate the rate of heat transfer. The thermophysical properties of air are evaluated at the mean temperature and are as follow:  = 1.088 kg/m3, Cp = 1.00 kJ/kg.K,  = 1.96 × 10-5 Pa-s, k = 0.028 W/mK, Pr = 0.7. Use the following correlation for convective heat transfer coefficient Nu = 0.1 (Gr.Pr)1/3.

Explain the following terms: (a) Thermal diffusivity (b) Thermal Conductivity (c) Thermal contact resistance

Explain mean film temperature and bulk mean temperature.

Asolid copper sphere of 10 cm diameter [ρ = 8954 kg/m3, c = 383 J/kg K, p k = 386 W/mK] initially at a uniform temperature t = 250 °C, is suddenly i immersed in a well-stirred fluid which is maintained at a uniform temperature t = 50 °C. The heat transfer coefficient between the sphere and a the fluid is h = 200 W/m2K. Determined the temperature of the copper block at τ = 5 min after immersion.

Define: Thermal boundary layer, Hydrodynamic boundary layer, Laminar sub layer.

Differentiate parallel flow and counter flow heat exchanger.

Discuss the concept of thermal boundary layer in case of flow over the plates. How it differ from velocity boundary?1

State & explain Lambert’s cosine law.

Explain the following terms in heat exchanger: (1) Effectiveness (2) NTU

Derive the Stefan-Boltzmann law from the Plank’s law of thermal radiation. What is the value of Stefan-Boltzmann constant?

Justify that a good absorber is also a good emitter for radiation heat transfer.

List the factors on which the rate of emission of radiation by a body depends.

With a neat sketch explain filmwise and dropwise condensation.

What do you understand by fouling factor in case of heat exchanger? List the causes of fouling.

Differentiate between boiling and condensation.

Derive equation of effectiveness of parallel flow heat exchanger.