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UPSC ESE Mechanical Engineering Heat Transfer Syllabus

The Heat Transfer syllabus for UPSC ESE Mechanical Engineering in full: 3 chapters and 9 topics, every one listed below, plus 51 Heat Transfer flashcards with answers.

3Chapters
9Topics
51Flashcards

Heat Transfer syllabus: all 3 chapters

Expand any chapter to see its topics and sub-topics.

  1. Conduction

     3 topics
    • Fourier's Law
    • Steady State Conduction
    • Transient Conduction

  2. Convection

     3 topics
    • Newton's Law of Cooling
    • Forced Convection
    • Natural Convection

  3. Radiation

     3 topics
    • Stefan-Boltzmann Law
    • Radiative Heat Exchange
    • View Factors

UPSC ESE Mechanical Engineering Heat Transfer flashcards — 51 questions with answers

  1. State Fourier's law of heat conduction in one dimension and define each term.

    $$Q = -kA\frac{dT}{dx}$$ where $Q$ is the heat conduction rate (W), $k$ is thermal conductivity (W/m·K), $A$ is the cross-sectional area normal to heat flow ($\text{m}^2$), and $\frac{dT}{dx}$ is the temperature gradient. The negative sign indicates heat flows in the direction of decreasing temperature.

  2. What is the physical significance of the negative sign in Fourier's law $Q = -kA\frac{dT}{dx}$?

    It ensures $Q$ is positive in the direction of decreasing temperature, consistent with the second law of thermodynamics — heat flows spontaneously from a hot region to a cold region (down the temperature gradient).

  3. Define thermal conductivity $k$ and give its SI units.

    Thermal conductivity is a material property representing its ability to conduct heat — the rate of heat transfer per unit area per unit temperature gradient. Its SI unit is $\text{W/m·K}$ (or $\text{W/m·°C}$).

  4. What is the general three-dimensional heat conduction equation (Fourier-Biot) with internal heat generation?

    $$\frac{\partial^{2}T}{\partial x^{2}}+\frac{\partial^{2}T}{\partial y^{2}}+\frac{\partial^{2}T}{\partial z^{2}}+\frac{\dot{q}}{k}=\frac{1}{\alpha}\frac{\partial T}{\partial t}$$ where $\dot{q}$ is the volumetric heat generation rate and $\alpha$ is thermal diffusivity.

  5. Define thermal diffusivity $\alpha$ and give its formula and units.

    $$\alpha = \frac{k}{\rho c_{p}}$$ It measures how quickly heat diffuses through a material relative to its heat storage capacity. Units: $\text{m}^2/\text{s}$. A high $\alpha$ means heat propagates rapidly.

  6. For steady-state 1-D conduction with no heat generation through a plane wall, what is the temperature distribution?

    Linear. The governing equation reduces to $\frac{d^{2}T}{dx^{2}}=0$, giving $T(x)=C_{1}x+C_{2}$, a straight-line temperature profile between the two surface temperatures.

  7. Write the conduction thermal resistance for a plane wall of thickness $L$, area $A$, conductivity $k$.

    $$R_{\text{cond}} = \frac{L}{kA}$$ with units $\text{K/W}$. The heat rate is $Q = \frac{\Delta T}{R_{\text{cond}}}$.

  8. Write the conduction thermal resistance for a hollow cylinder (length $L$, inner radius $r_1$, outer radius $r_2$).

    $$R_{\text{cyl}} = \frac{\ln\left(\frac{r_{2}}{r_{1}}\right)}{2\pi k L}$$

  9. Write the conduction thermal resistance for a hollow sphere (inner radius $r_1$, outer radius $r_2$).

    $$R_{\text{sph}} = \frac{r_{2}-r_{1}}{4\pi k\, r_{1} r_{2}}$$

  10. In the thermal resistance (electrical analogy) for heat conduction, what corresponds to voltage and to current?

    Temperature difference $\Delta T$ is analogous to voltage (potential), and heat transfer rate $Q$ is analogous to electric current. Thermal resistance $R$ is analogous to electrical resistance, so $Q=\frac{\Delta T}{R}$.

  11. For composite walls in series, how do the thermal resistances combine?

    They add directly: $R_{\text{total}}=R_{1}+R_{2}+\cdots+R_{n}$, and $Q=\frac{\Delta T_{\text{overall}}}{R_{\text{total}}}$ is the same through each layer.

  12. Define the critical radius of insulation for a cylinder and give its formula.

    The outer insulation radius at which heat loss is maximum (adding insulation up to this radius increases heat loss). For a cylinder: $$r_{c}=\frac{k}{h}$$ where $k$ is insulation conductivity and $h$ is the outer convective coefficient.

  13. What is the critical radius of insulation for a sphere?

    $$r_{c}=\frac{2k}{h}$$ where $k$ is the insulation thermal conductivity and $h$ is the outside convective heat transfer coefficient.

  14. Define the overall heat transfer coefficient $U$ and how it relates to total resistance.

    $U$ combines all conduction and convection resistances into a single coefficient: $$Q = U A\,\Delta T_{\text{overall}}, \qquad \frac{1}{UA}=R_{\text{total}}=\sum R_{i}$$ Units of $U$: $\text{W/m}^2\text{·K}$.

  15. What is a fin (extended surface) and why is it used?

    A fin is an extended surface attached to a body to increase the surface area exposed to a fluid, thereby enhancing convective heat transfer. Used when $h$ is low (e.g., gas-side cooling) to dissipate more heat for a given temperature difference.

  16. Define fin efficiency $\eta_{f}$.

    $$\eta_{f}=\frac{\text{actual heat transferred by fin}}{\text{heat that would transfer if entire fin were at base temperature}}$$ It accounts for the temperature drop along the fin due to its finite conductivity.

  17. For a long (infinitely long) fin of uniform cross-section, what is the temperature distribution and fin parameter $m$?

    $$\frac{\theta}{\theta_{b}}=e^{-mx}, \qquad m=\sqrt{\frac{hP}{kA_{c}}}$$ where $\theta=T-T_{\infty}$, $P$ is perimeter, $A_c$ is cross-sectional area, $\theta_b$ is base excess temperature.

  18. Define the Biot number and its physical meaning.

    $$Bi=\frac{hL_{c}}{k}$$ It is the ratio of internal conduction resistance within a body to the external convective resistance at its surface. Small $Bi$ means uniform internal temperature.

  19. What is the lumped capacitance method and under what condition is it valid?

    It assumes a body has uniform (spatially constant) temperature during transient cooling/heating, treating it as a single 'lump.' Valid when $Bi=\frac{hL_{c}}{k}<0.1$, where $L_{c}=V/A_{s}$.

  20. Give the temperature-time response equation for lumped capacitance transient conduction.

    $$\frac{T-T_{\infty}}{T_{i}-T_{\infty}}=e^{-\frac{hA_{s}}{\rho V c_{p}}t}=e^{-\frac{t}{\tau}}$$ where the time constant $\tau=\frac{\rho V c_{p}}{hA_{s}}$.

Show the other 31 Heat Transfer flashcards

  1. Define the thermal time constant $\tau$ for lumped transient conduction and its significance.

    $$\tau=\frac{\rho V c_{p}}{hA_{s}}=R_{t}C_{t}$$ It is the time for the temperature excess to fall to $\frac{1}{e}$ (about 36.8%) of its initial value. A larger $\tau$ means a slower thermal response.

  2. Define the Fourier number and its physical meaning.

    $$Fo=\frac{\alpha t}{L_{c}^{2}}$$ It is a dimensionless time representing the ratio of the rate of heat conduction to the rate of heat storage in a body. It governs transient conduction problems.

  3. In transient conduction charts (Heisler charts), which two dimensionless numbers are the primary parameters?

    The Biot number $Bi=\frac{hL_{c}}{k}$ and the Fourier number $Fo=\frac{\alpha t}{L_{c}^{2}}$. Heisler charts give the dimensionless center temperature as a function of these for slabs, cylinders, and spheres.

  4. State Newton's law of cooling.

    $$Q = hA_{s}(T_{s}-T_{\infty})$$ The convective heat transfer rate is proportional to the surface area $A_s$ and the temperature difference between the surface $T_s$ and the surrounding fluid $T_{\infty}$, with $h$ the convective heat transfer coefficient (W/m²·K).

  5. What is the convective thermal resistance from a surface to a fluid?

    $$R_{\text{conv}}=\frac{1}{hA_{s}}$$ with units $\text{K/W}$, derived from Newton's law of cooling $Q=\frac{\Delta T}{R_{\text{conv}}}$.

  6. Distinguish between forced convection and natural (free) convection.

    In forced convection, fluid motion is induced by an external agent (pump, fan, wind). In natural convection, fluid motion arises from buoyancy forces caused by density differences from temperature gradients. Forced convection typically gives higher $h$.

  7. Define the Nusselt number and its physical meaning.

    $$Nu=\frac{hL}{k_{\text{fluid}}}$$ It is the ratio of convective to conductive heat transfer across a fluid boundary layer. $Nu=1$ implies pure conduction; larger $Nu$ indicates more effective convection.

  8. Define the Reynolds number and its role in convection.

    $$Re=\frac{\rho V L}{\mu}=\frac{VL}{\nu}$$ It is the ratio of inertial to viscous forces and determines whether flow is laminar or turbulent, governing forced-convection heat transfer correlations.

  9. Define the Prandtl number and its physical meaning.

    $$Pr=\frac{\mu c_{p}}{k}=\frac{\nu}{\alpha}$$ It is the ratio of momentum diffusivity to thermal diffusivity, linking the velocity and thermal boundary layers. For gases $Pr\approx 0.7$; for liquid metals $Pr\ll 1$; for oils $Pr\gg 1$.

  10. For forced convection, the Nusselt number is generally a function of which dimensionless groups?

    $$Nu=f(Re,\ Pr)$$ Typical correlations take the form $Nu=C\,Re^{m}Pr^{n}$, where constants depend on geometry and flow regime.

  11. State the Dittus-Boelter equation for turbulent forced convection in tubes.

    $$Nu=0.023\,Re^{0.8}Pr^{n}$$ where $n=0.4$ for heating ($T_s>T_f$) and $n=0.3$ for cooling. Valid for $Re>10{,}000$, $0.6<Pr<160$, and fully developed turbulent flow.

  12. For fully developed laminar flow in a circular tube with constant wall heat flux, what is the Nusselt number?

    $$Nu=4.36$$ (constant). For constant wall temperature, $Nu=3.66$. These are independent of $Re$ and $Pr$ in the fully developed laminar region.

  13. Define the Grashof number and its physical meaning in natural convection.

    $$Gr=\frac{g\beta(T_{s}-T_{\infty})L^{3}}{\nu^{2}}$$ It is the ratio of buoyancy forces to viscous forces. In natural convection it plays the role $Re$ plays in forced convection. $\beta$ is the coefficient of volumetric thermal expansion.

  14. For natural convection, the Nusselt number is a function of which dimensionless groups?

    $$Nu=f(Gr,\ Pr)=f(Ra)$$ where the Rayleigh number $Ra=Gr\cdot Pr$. Correlations take the form $Nu=C(Gr\,Pr)^{n}=C\,Ra^{n}$.

  15. Define the Rayleigh number and its significance.

    $$Ra=Gr\cdot Pr=\frac{g\beta(T_{s}-T_{\infty})L^{3}}{\nu\alpha}$$ It governs the onset and intensity of natural convection. Above a critical value, buoyancy-driven flow (and transition to turbulence) occurs.

  16. For an ideal gas, what is the coefficient of volumetric thermal expansion $\beta$?

    $$\beta=\frac{1}{T}$$ where $T$ is the absolute temperature in kelvin. This is used in the Grashof and Rayleigh numbers for gases.

  17. What dimensionless number determines whether forced or natural convection dominates in a combined (mixed) convection situation?

    The ratio $\frac{Gr}{Re^{2}}$. If $\frac{Gr}{Re^{2}}\ll 1$, forced convection dominates; if $\frac{Gr}{Re^{2}}\gg 1$, natural convection dominates; if $\approx 1$, both must be considered (mixed convection).

  18. Define the hydrodynamic boundary layer and the thermal boundary layer.

    The hydrodynamic (velocity) boundary layer is the thin region near a surface where velocity changes from zero (no-slip) to the free-stream value. The thermal boundary layer is the region where temperature changes from the surface value to the free-stream value. Their relative thickness is set by $Pr$.

  19. State the Stefan-Boltzmann law for a black body.

    $$E_{b}=\sigma T^{4}$$ The total emissive power of a black body is proportional to the fourth power of its absolute temperature, where $\sigma=5.67\times10^{-8}\ \text{W/m}^2\text{·K}^4$ is the Stefan-Boltzmann constant.

  20. What is the value of the Stefan-Boltzmann constant $\sigma$?

    $$\sigma = 5.67\times10^{-8}\ \text{W/m}^{2}\text{·K}^{4}$$

  21. Define emissivity $\varepsilon$ of a surface.

    $$\varepsilon=\frac{E}{E_{b}}=\frac{\text{emissive power of the surface}}{\text{emissive power of a black body at the same temperature}}$$ It ranges from 0 to 1; $\varepsilon=1$ for a black body. For a gray body, $\varepsilon$ is constant with wavelength.

  22. State Kirchhoff's law of thermal radiation.

    At thermal equilibrium, the emissivity of a surface equals its absorptivity: $$\varepsilon=\alpha$$ A good emitter is also a good absorber at the same temperature and wavelength.

  23. For an opaque surface, what is the relation among absorptivity, reflectivity, and transmissivity?

    $$\alpha+\rho+\tau=1$$ For an opaque body $\tau=0$, so $\alpha+\rho=1$. For a black body $\alpha=1$, $\rho=\tau=0.

  24. State Wien's displacement law.

    $$\lambda_{\max}T = 2898\ \mu\text{m·K}$$ The wavelength at which black-body spectral emissive power peaks is inversely proportional to absolute temperature. Hotter bodies emit at shorter wavelengths.

  25. Write the net radiative heat exchange between two large parallel gray plates (areas equal, infinite extent).

    $$Q_{12}=\frac{\sigma A(T_{1}^{4}-T_{2}^{4})}{\frac{1}{\varepsilon_{1}}+\frac{1}{\varepsilon_{2}}-1}$$

  26. Write the net radiation heat exchange between a small gray body (1) completely enclosed by a large surface (2).

    $$Q_{12}=\varepsilon_{1}\sigma A_{1}(T_{1}^{4}-T_{2}^{4})$$ When $A_1\ll A_2$, the enclosure behaves as a black body and only the small body's emissivity matters.

  27. Define the radiation shape factor (view factor) $F_{12}$.

    $F_{12}$ is the fraction of radiation leaving surface 1 that is directly intercepted by surface 2. It is a purely geometric quantity depending on the size, shape, orientation, and spacing of the surfaces.

  28. State the reciprocity relation for view factors.

    $$A_{1}F_{12}=A_{2}F_{21}$$ This relates the view factors between two surfaces through their areas and is fundamental for radiation network analysis.

  29. State the summation (enclosure) rule for view factors.

    For any surface $i$ in an enclosure of $N$ surfaces: $$\sum_{j=1}^{N}F_{ij}=1$$ All radiation leaving surface $i$ must strike some surface of the enclosure (including itself, $F_{ii}$, if the surface is concave).

  30. What is the view factor $F_{ii}$ of a flat or convex surface with respect to itself, and why?

    $$F_{ii}=0$$ A flat or convex surface cannot 'see' itself — no radiation leaving it strikes itself directly. For a concave surface, $F_{ii}>0$.

  31. In a radiation network, define surface resistance and space (geometric) resistance.

    Surface resistance accounts for a surface's non-black emissivity: $$R_{\text{surface}}=\frac{1-\varepsilon}{\varepsilon A}$$ Space (geometric) resistance accounts for the view factor between surfaces: $$R_{\text{space}}=\frac{1}{A_{1}F_{12}}$$ Heat flows between black-body emissive powers $E_b=\sigma T^4$ through these resistances.

UPSC ESE Mechanical Engineering Heat Transfer FAQ

What is in the UPSC ESE Mechanical Engineering Heat Transfer syllabus?

UPSC ESE Mechanical Engineering Heat Transfer is split into 3 chapters: Conduction, Convection and Radiation. Together they contain 9 topics.

How many chapters are in UPSC ESE Mechanical Engineering Heat Transfer?

3 chapters, containing 9 topics. The largest chapter is Conduction, with 3 topics.

Are there flashcards for UPSC ESE Mechanical Engineering Heat Transfer?

Yes — a 51-card Heat Transfer deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.