60 solved GATE ME questions on Heat Transfer, drawn from 10 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.
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Determine whether conduction, convection, or radiation dominates, then apply the corresponding rate equation with correct boundary conditions. These selected foundations cover one-dimensional conduction, convection correlations, and basic radiation exchange. They are not a complete syllabus; transient conduction, boiling, and condensation need separate study.
Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.
For a plane wall of thickness L, area A, and conductivity k: Q = kA(T₁ - T₂)/L. The thermal resistance analogy gives R_cond = L/(kA). For composite walls in series, total resistance is the sum. For a hollow cylinder, R_cond = ln(r₂/r₁)/(2πkL_cyl).
Check yourself: Are resistances in series (same heat flow) or parallel (same temperature difference)?
Q = hA(T_surface - T_fluid), where h is the convective heat transfer coefficient. The convective resistance is R_conv = 1/(hA). Nusselt number Nu = hL_c/k_fluid relates h to fluid properties and flow conditions. Correlations such as Dittus-Boelter (turbulent pipe flow) give Nu in terms of Re and Pr.
Check yourself: Is the flow laminar or turbulent, and does the chosen correlation apply?
Fins increase effective surface area for convection. Fin efficiency η = actual heat transfer / heat transfer if entire fin were at base temperature. For a long fin (insulated tip), η = tanh(mL)/(mL), where m = √(hP/(kA_c)), P is perimeter, and A_c is cross-sectional area. Adding fins helps only when Bi_fin = hA_c/(kP) is small.
Check yourself: Is the fin efficiency high enough to justify adding more fin area?
A blackbody emits E_b = σT⁴ (W/m²), with T in kelvin and σ = 5.67 x 10⁻⁸ W/m²·K⁴. For a gray diffuse surface, emissivity ε < 1 reduces emission. Net radiation exchange between two blackbody surfaces: Q₁₂ = A₁F₁₂σ(T₁⁴ - T₂⁴), where F₁₂ is the view factor from surface 1 to 2.
Check yourself: Are temperatures in kelvin, and have you used the correct view factor?
When Biot number Bi = hL_c/k_solid < 0.1, internal temperature gradients are negligible. The body cools or heats as T(t) - T_∞ = (T_i - T_∞)e^(-t/τ), where τ = ρcV/(hA) is the time constant. L_c = V/A for the Biot number check. This model assumes uniform temperature within the solid at each instant.
Check yourself: Is Bi < 0.1, confirming that internal resistance is negligible compared to surface resistance?
Original teaching example · not a PYQ
Original example: a plane wall has thickness L = 0.1 m, thermal conductivity k = 50 W/m·K, and surface area A = 2 m². The inner surface is at T₁ = 200 °C, and the outer surface is exposed to convection with h = 25 W/m²·K and fluid at T_∞ = 30 °C. Assume steady state and one-dimensional heat flow. Find the heat transfer rate and outer surface temperature T₂.
Q ≈ 8095 W; outer surface temperature T₂ ≈ 191.9 °C.
A small steel sphere (ρ = 7800 kg/m³, c = 500 J/kg·K, k = 40 W/m·K) of diameter 20 mm is initially at 500 °C. It is quenched in oil at 30 °C with h = 200 W/m²·K. Check if lumped analysis applies and find the time to reach 100 °C.
Bi ≈ 0.0167 < 0.1; lumped analysis applies. Time ≈ 124 s.
L_c = V/A = (πd³/6)/(πd²) = d/6 = 0.02/6 = 0.00333 m. Bi = hL_c/k = 200 x 0.00333/40 ≈ 0.0167 < 0.1. Time constant τ = ρcV/(hA) = ρc(d/6)/h = 7800 x 500 x 0.00333/200 = 65.0 s. (T - T_∞)/(T_i - T_∞) = e^(-t/τ). (100 - 30)/(500 - 30) = 70/470 ≈ 0.1489. t = -τ ln(0.1489) = -65.0 x (-1.905) ≈ 124 s.
Supplemental reading, not an official GATE reading list or an endorsement of these notes.
Free supplemental lecture notes covering conduction, convection, and radiation with worked examples and problem sets relevant to GATE ME heat transfer topics.
This page shows 60 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE ME papers. Questions can carry more than one subject tag; counts are not marks weightage.
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