The GATE Grind

GATE 2025 MT – Question 39

Transport Phenomena and Rate Processes · Heat transfer · 2 marks · Multiple choice

Radiative heat flux $\dot q$ at a hot surface of temperature $T_s$ is expressed as $$\dot q=A f(T_s,T_\infty)(T_s-T_\infty),$$ where $A$ is a constant and $T_\infty$ is the surroundings temperature. Temperatures are in K. The function $f(T_s,T_\infty)$ is ______.

  1. $(T_s+T_\infty)^2(T_s-T_\infty)$
  2. $(T_s^2+T_\infty^2)(T_s+T_\infty)$
  3. $(T_s^2-T_\infty^2)(T_s+T_\infty)$
  4. $(T_s-T_\infty)^2(T_s+T_\infty)$

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Show answer and explanation

Correct answer: (B) $(T_s^2+T_\infty^2)(T_s+T_\infty)$

Explanation

Net radiation is proportional to Ts⁴−T∞⁴. Factor the difference of fourth powers: (Ts−T∞)(Ts+T∞)(Ts²+T∞²). After the stated Ts−T∞ factor is removed, f=(Ts²+T∞²)(Ts+T∞), giving **B**.