Question Statement:
Hot water at 95°C is used in a plate heat exchanger for heating 2 kg s⁻¹ fruit juice from 45°C to 75°C. Specific heat capacity of fruit juice is 3.7 kJ kg⁻¹ K⁻¹. Final temperature of the hot water is 70°C. Overall heat transfer coefficient is 1122 W m⁻² K⁻¹. Heat transfer area is 12.75 m². The log-mean temperature correction factor is ______
Step-by-Step Solution & Explanation
Heat duty: Q = ṁ×Cp×ΔT = 2×3.7×(75−45) = 222 kW. For counter-current arrangement, the terminal temperature differences are ΔT1 = T_hot,in−T_cold,out = 95−75 = 20°C, and ΔT2 = T_hot,out−T_cold,in = 70−45 = 25°C. LMTD = (ΔT1−ΔT2)/ln(ΔT1/ΔT2) = (20−25)/ln(20/25) = (−5)/(−0.2231) = 22.41°C. Since Q = U×A×F×LMTD, the correction factor F = Q/(U×A×LMTD) = 222,000/(1122×12.75×22.41) = 222,000/320,570 = 0.693, within the accepted band 0.68–0.70. (F<1 reflects that a plate heat exchanger is not purely counter-current, unlike the idealised LMTD calculation.)
Appendix A — Consolidated Answer Table
Appendix B — Section-wise Weightage
Preparation observations
Soil and Water Conservation Engineering and Farm Power together account for the largest share of AG marks in this paper (23 questions, 37 marks combined) — hydrology, soil mechanics, and IC-engine/tractor-transmission numericals deserve proportionally heavy practice.
Agricultural Process Engineering and Dairy & Food Engineering together contribute 13 questions (20 marks) — psychrometry, drying kinetics, heat/mass transfer, and microbial-death-kinetics numericals recur every year and are highly formula-driven, making them efficient to master.
Engineering Mathematics is a comparatively small but reliable scoring area (8 questions, 11 marks) built entirely on standard techniques (eigenvalues, ODEs, vector calculus, numerical integration) — high accuracy is achievable with formula recall alone.
Two-mark NAT numericals dominate the back half of the paper (Q26–55); most require chaining two to three standard formulas (e.g., unit conversion → intermediate quantity → final answer), so speed in unit handling is as important as knowing the formula itself.
A small number of questions in every recent AG paper (e.g., Q.37, Q.39, Q.46 here) have historically had unclear or incompletely transcribed source data across multiple independent copies of the paper — candidates should treat such outlier questions as low-yield-per-effort during time-constrained revision.