GATE Chemical Engineering Heat Transfer Syllabus

Heat Transfer syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Heat Transfer in GATE Chemical Engineering, not a summary of it.

1. 1

   Equation of Energy and Heat Transfer

   4 topics

   • Steady Heat Conduction
   • Unsteady Heat Conduction
   • Convection
     • Thermal Boundary Layer
     • Heat Transfer Coefficients
   • Radiation
2. 2

   Boiling, Condensation, and Evaporation

   3 topics

   • Types of Heat Exchangers
   • Types of Evaporators
   • Process Calculations
3. 3

   Design of Heat Exchangers and Evaporators

   4 topics

   • Double Pipe Heat Exchangers
   • Shell and Tube Heat Exchangers
   • Single Effect Evaporators
   • Multiple Effect Evaporators

Heat Transfer flashcards for GATE Chemical Engineering

19 of 51 cards from the Heat Transfer deck — real questions with worked answers.

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

   $$q = -k\,A\,\frac{dT}{dx}$$ where $q$ is heat flow rate (W), $k$ is thermal conductivity ($\mathrm{W/m\cdot K}$), $A$ is cross-sectional area, and $\frac{dT}{dx}$ is the temperature gradient. The minus sign shows heat flows from high to low temperature.

2. Write the heat-conduction resistance for a plane wall and the resulting steady heat flux expression.

   Thermal resistance $R = \frac{L}{kA}$, so $$q = \frac{\Delta T}{R} = \frac{kA(T_1 - T_2)}{L}$$ analogous to Ohm's law with $\Delta T$ as the driving potential.

3. Give the conduction resistance of a hollow cylinder of length $L$, inner radius $r_1$, outer radius $r_2$.

   $$R = \frac{\ln(r_2/r_1)}{2\pi k L}$$ Heat flow $q = \dfrac{2\pi k L (T_1 - T_2)}{\ln(r_2/r_1)}$.

4. Give the conduction resistance of a hollow sphere of inner radius $r_1$ and outer radius $r_2$.

   $$R = \frac{r_2 - r_1}{4\pi k\, r_1 r_2}$$ so $q = \dfrac{4\pi k\, r_1 r_2 (T_1 - T_2)}{r_2 - r_1}$.

5. What is the critical radius of insulation for a cylinder, and why does it matter?

   $$r_c = \frac{k}{h}$$ Below $r_c$, adding insulation actually increases heat loss (because added surface area lowers convective resistance faster than conduction resistance rises). For a sphere $r_c = \frac{2k}{h}$.

6. Write the general 3-D unsteady heat conduction (heat diffusion) equation with internal generation.

   $$\nabla^2 T + \frac{\dot{q}}{k} = \frac{1}{\alpha}\frac{\partial T}{\partial t}$$ where $\alpha = \frac{k}{\rho c_p}$ is the thermal diffusivity ($\mathrm{m^2/s}$).

7. Define thermal diffusivity and state its physical meaning.

   $$\alpha = \frac{k}{\rho c_p}$$ It measures how fast a temperature disturbance propagates through a material — the ratio of heat conducted to heat stored. Higher $\alpha$ means faster thermal response.

8. What is the lumped capacitance method and what condition validates its use?

   It assumes a body has uniform (spatially negligible) temperature gradients during transient cooling/heating. Valid when the Biot number $Bi = \frac{h L_c}{k} < 0.1$, where $L_c = V/A_s$.

9. Write the temperature–time response for lumped-capacitance transient cooling.

   $$\frac{T - T_\infty}{T_i - T_\infty} = \exp\!\left(-\frac{h A_s}{\rho V c_p}\, t\right)$$ The time constant is $\tau = \frac{\rho V c_p}{h A_s}$.

10. Define the Biot number and the Fourier number and give what each compares.

    Biot: $Bi = \frac{hL_c}{k}$ — ratio of internal conduction resistance to surface convection resistance. Fourier: $Fo = \frac{\alpha t}{L_c^{2}}$ — dimensionless time governing transient penetration.

11. State Newton's law of cooling for convection.

    $$q = h\,A\,(T_s - T_\infty)$$ where $h$ is the convective heat transfer coefficient ($\mathrm{W/m^2\cdot K}$), $T_s$ is the surface temperature and $T_\infty$ the bulk fluid temperature.

12. Distinguish free (natural) convection from forced convection.

    Forced convection: fluid motion is driven by an external means (pump, fan). Natural/free convection: fluid motion arises from buoyancy due to density differences from temperature gradients, characterized by the Grashof number.

13. Define the Nusselt number and state what it physically represents.

    $$Nu = \frac{h L}{k_f}$$ It is the ratio of convective to conductive heat transfer across a fluid layer. $Nu = 1$ corresponds to pure conduction.

14. Define the Prandtl number and give 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.

15. Define the Reynolds, Grashof and Stanton numbers used in convection.

    Reynolds $Re = \frac{\rho u L}{\mu}$ (inertial/viscous). Grashof $Gr = \frac{g\beta\,\Delta T\, L^3}{\nu^2}$ (buoyancy/viscous). Stanton $St = \frac{h}{\rho u c_p} = \frac{Nu}{Re\,Pr}$.

16. Write the Dittus–Boelter correlation for turbulent flow in tubes and its validity.

    $$Nu = 0.023\,Re^{0.8}\,Pr^{n}$$ with $n = 0.4$ for heating and $n = 0.3$ for cooling of the fluid. Valid for $Re > 10^4$, $0.7 < Pr < 160$, fully developed turbulent flow.

17. What is the Nusselt number for fully developed laminar flow in a circular tube with constant wall temperature vs. constant heat flux?

    Constant wall temperature: $Nu = 3.66$. Constant wall heat flux: $Nu = 4.36$. Both are constants (independent of $Re$ and $Pr$) for fully developed laminar flow.

18. Define the velocity (hydrodynamic) and thermal boundary layers.

    Velocity boundary layer: thin region near a surface where fluid velocity rises from zero (no-slip) to ~99% of free-stream velocity. Thermal boundary layer: region where fluid temperature changes from the wall value to ~99% of the free-stream temperature.

19. How are the thicknesses of the thermal ($\delta_t$) and velocity ($\delta$) boundary layers related to Prandtl number?

    $$\frac{\delta}{\delta_t} \approx Pr^{1/3}$$ For $Pr > 1$ (oils) the velocity layer is thicker; for $Pr < 1$ (liquid metals) the thermal layer is thicker; for $Pr \approx 1$ (gases) they are comparable.

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