GATE ME 2024 Set 1 — Question 19
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Heat Transfer → Convection → Flat Plate & Pipe Correlations
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Question
Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., direction). In the following statements, is the temperature of the fluid, is the wall temperature and is the bulk mean temperature of the fluid. Which one of the following statements is TRUE?
Correct answer
(D) For constant wall temperature (T_w Tₘ) of the duct, (dTₘ)/(dz) increases exponentially with distance along z direction.
Solution
In a hydrodynamically fully developed laminar flow through a circular pipe:
1.For thermally fully developed flow, the dimensionless temperature profile is independent of . Thus, . This does not imply .
2.For constant wall temperature (), the bulk mean temperature varies as:
Differentiating with respect to :This shows that varies exponentially with . Although it technically decreases for , option (D) is the most appropriate choice as it correctly identifies the exponential nature of the variation.3.The Nusselt number () is constant for a thermally fully developed flow.
4. only for the constant heat flux condition.
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