Heat and Mass Transfer (ME-701) - Important Questions

What is the critical thickness / critical radius of insulation and what is its significance / application?

Steady one-dimensional heat conduction through a single homogeneous solid (plane wall / rod) to find rate of heat transfer or total heat loss using Fourier's law

Explain the three modes/mechanisms of heat transfer: conduction, convection and radiation, including governing laws and distinguishing features.

Derive the expression for the critical thickness of insulation for a cylinder and explain its importance / variation of heat transfer with radius.

Numerical problems on critical thickness of cylindrical insulation and effect of adding insulation on heat loss / current-carrying capacity.

Steady heat transfer through a composite multi-layer plane wall with convection on surfaces to find rate of heat transfer and surface/interface temperature

A domestic oven has a composite wall formed by $0.5$ cm thick chrome-nickel ($k = 19\, W/mk$) sheet supported by $1$ cm thick asbestos ($k = 0.1105\, W/mk$) sheet. In steady state operation the hot gases inside the oven are at $350^{\circ}C$ while atmospheric air in at $30^{\circ}C$. The convective heat transfer coefficient at inside and outside surface of the oven are $100\, W/m^2k$ and $15\, W/m^2k$ respectively. Determine the rate of heat losses per unit area through the oven wall.

Calculate temperature drop across a layer in a composite wall with convection using overall heat transfer coefficient.

Compare and distinguish heat conduction from convection.

Derive expression for temperature distribution under one-dimensional steady-state heat conduction for a plane wall

Derive an expression of general heat conduction equation in rectangular coordinates.

Write down the expressions for the physical laws that govern each mode of heat transfer, and identify the variables involved in each relation.

Check validity of lumped system analysis via Biot number for a solid suddenly exposed to convection.

Using lumped capacitance method, calculate time required for the solid to cool to a specified temperature.

Derive the governing differential equation for one-dimensional heat transfer in a longitudinal fin of uniform cross-section (including infinitely long fin case).

Write short notes on selected heat and mass transfer topics including fin effectiveness, gray body, Fick's law, LMTD, thermocouple, and parallel flow heat exchanger.

Derive the lumped capacitance (infinite thermal conductivity) transient conduction temperature-time relation and sketch temperature vs time.

Calculate heat loss from a straight rectangular fin of given dimensions and thermal conditions.

Calculate fin efficiency and tip temperature for a rod fin with insulated tip.

Define the parameters used to measure fin performance (fin effectiveness and fin efficiency).

Explain the reason for the widespread use of fins on heat transfer surfaces.

Differentiate between fin effectiveness and fin efficiency.

Derive the expression for fin efficiency for a constant cross-section fin with tip condition, and simplify for circular and rectangular fins.

Define the types of fins used in various automotive applications.

Explain laminar vs turbulent flow regimes in convection heat transfer and compare their heat transfer coefficients, with diagram.

Explain the definition of the Nusselt number and its physical significance, including significance of Reynolds number for convection.

Derive the momentum equation for hydrodynamic boundary layer over a flat plate.

State the Buckingham pi-theorem and use it to derive the forced-convection correlation between Nusselt, Reynolds and Prandtl numbers.

Numerical on forced cross-flow over a cylinder: calculate heat loss per unit length.

What is forced convection and how does external forced convection differ from internal forced convection?

State the Buckingham Pi theorem.

How does the Rayleigh number differ from the Grashof number?

Use the Buckingham Pi theorem to determine the dimensionless Pi groups governing heat transfer from fins.

Numerical on natural convection over a vertical plate: calculate average heat transfer coefficient and boundary layer thickness.

Explain the advantages and limitations of dimensional analysis.

A horizontal heated plate at $200^\circ C$ and facing upwards has been placed in still air at $20^\circ C$. If the plate measures $1.25m \times 1m$. Calculate the heat loss by natural convection. The convective film coefficient for free convection is given by the following empirical relation: $h = 0.32\,(\theta)^{0.25} W/m^2$-k. Where $\theta$ is mean film temperature in degree Kelvin.

Explain the classification / types of heat exchangers with diagrams and characteristics.

Derive the expression for logarithmic mean temperature difference (LMTD) for a parallel-flow heat exchanger.

In a cross-flow heat exchanger with air heated by water, given inlet temperatures, mass flow rates, overall heat transfer coefficient and area, find the exit temperatures of both fluids.

Numerical application of LMTD to determine mean temperature difference and required heat exchanger size (area / tube length) for parallel-flow and counter-flow arrangements.

Write short notes on selected topics including LMTD for parallel flow, mass diffusion equation, and Wien's displacement law.

For a binary gas mixture at given temperature, total pressure and partial pressures, determine molar concentration, mass densities, mass fractions and mole fractions.

Classify heat exchangers according to flow type and explain the characteristics of each type.

Derive the expression for logarithmic mean temperature difference (LMTD) for a counter-flow heat exchanger.

Explain the various modes of mass transfer and their applications.

Explain mass average velocity.

What is fouling in a heat exchanger and what are its effects on performance?

Give the answer in brief with neat sketch (within 100 words) c) Define about diffusion and explain Fick's law of diffusion. Explain the term mass diffusivity.

Derive the general expression for radiation shape factor and the reciprocity theorem $A_1F_{12}=A_2F_{21}$ for black surfaces separated by a non-absorbing medium, including the equal-area case.

Explain what a radiation shield is and why it is used.

Distinguish between filmwise and dropwise condensation and identify which gives higher heat transfer.

Distinguish between evaporation and boiling.

Calculate the rate of radiant heat transfer from a hemispherical cavity of given diameter, surface temperature and emissivity.

Determine radiative heat loss from a small gray surface to a large isothermal room.

Explain the Planck's distribution law?

Write short notes on any four of: shape factor, black body, Planck's law of distribution, regimes of boiling, radiation shield, nucleate boiling.

Calculate net radiant heat exchange between two long concentric black cylindrical surfaces at different temperatures.

State and prove Kirchhoff's law of radiation.

Write a short note comparing black body and gray body.

Describe the distinct regimes observed in film boiling and nucleate boiling, emphasizing the differences in heat transfer mechanisms and surface conditions that define each regime.

How are heat, internal energy, and thermal energy related to each other?