HEAT AND MASS TRANSFER (RME-502)
B.Tech (SEM-V) – AKTU
Time: 3 Hours Total Marks: 70
SECTION A
(Attempt all questions in brief – 2 × 7 = 14 marks)
Q1 (a) Define three different modes of heat transfer. Give a practical example where all three modes occur simultaneously.
The three modes of heat transfer are conduction, convection, and radiation.
Conduction is heat transfer through a solid due to temperature gradient.
Convection is heat transfer between a solid surface and a moving fluid.
Radiation is heat transfer in the form of electromagnetic waves.
A practical example is heating of water in a metal vessel on a gas stove, where heat is conducted through the vessel, convected within the water, and radiated from the flame.
Q1 (b) What do you mean by thermal conductivity? Why are good electrical conductors also good heat conductors?
Thermal conductivity is the ability of a material to conduct heat.
Good electrical conductors are also good heat conductors because both heat and electrical conduction in metals occur due to free electrons.
Q1 (c) What do you understand by overall heat transfer coefficient?
Overall heat transfer coefficient represents the combined effect of conduction, convection, and fouling resistances on heat transfer across a composite system. It is used in heat exchanger analysis.
Q1 (d) Write down the significance of critical radius of insulation.
Critical radius of insulation is the radius at which heat loss from a cylindrical or spherical body is maximum. Beyond this radius, adding insulation reduces heat loss. It is significant in pipes and electrical cables.
Q1 (e) Write the significance of the following:
(i) Temperature at the edge of the space
(ii) Heat dissipation
Temperature at the edge of the space helps determine boundary conditions in heat transfer analysis.
Heat dissipation indicates the rate at which heat is removed from a system to maintain safe operating conditions.
Q1 (f) Define heat dissipation.
Heat dissipation is the process of removing heat from a system to prevent overheating. It occurs through conduction, convection, and radiation.
Q1 (g) What is Biot number? State its significance.
Biot number is the ratio of internal thermal resistance to external convective resistance.
If Bi < 0.1, lumped system analysis is applicable.
SECTION B
(Attempt any three – 7 × 3 = 21 marks)
Q2 (a) Derive the general heat conduction equation in Cartesian coordinates.
The general heat conduction equation is derived by applying energy balance to a differential control volume considering heat conduction in x, y, and z directions, internal heat generation, and transient effects. The final equation relates temperature variation with space and time.
Q2 (b) Explain the significance of critical radius of insulation with suitable sketch.
Critical radius explains why adding insulation initially increases heat loss due to increased surface area. After reaching critical radius, further insulation reduces heat loss. This concept is important in steam pipes and electric cables.
Q2 (c) Explain Newton’s law of cooling.
Newton’s law of cooling states that the rate of heat loss of a body is proportional to the temperature difference between the body and surroundings, provided the temperature difference is small.
Q2 (d) Explain the concept of lumped heat capacity system.
In a lumped system, temperature within the body is assumed uniform. This assumption is valid when Biot number is less than 0.1, simplifying transient heat transfer analysis.
SECTION C
Q4 (a) A steel ball of 12 mm diameter is annealed by heating to 800°C and then slowly cooled to 127°C in air at 50°C.
Given: h = 20 W/m²°C, k = 45 W/m°C, ρ = 7830 kg/m³, c = 600 J/kg·K.
Calculate the time required for cooling.**
(7 marks)
This problem is solved using lumped heat capacity method since Biot number is less than 0.1.
Using Newton’s law of cooling, the time required for cooling is calculated by substituting given values into the transient heat transfer equation.
Q5 (a) Air at atmospheric pressure and 300°C flows over a flat plate with velocity 5 m/s.
The plate is 15 mm wide and maintained at 120°C.
Calculate the thickness of hydrodynamic and thermal boundary layers and local heat transfer coefficient at a distance of 0.5 m from leading edge.**
(7 marks)
The problem is solved using boundary layer theory for laminar flow over a flat plate.
Reynolds number is calculated first to confirm flow regime.
Hydrodynamic and thermal boundary layer thicknesses are obtained using standard correlations, followed by calculation of local heat transfer coefficient.
