Question
Download Solution PDFA steel rod with the thermal conductivity of 50.2 W /(m-K) has an area of cross-section 0.02 m2 and length 15 cm. If the two ends of the rod are maintained at a temperature difference of 300°C, the rate of heat flow through the rod is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Heat conduction:
The transfer of heat between two different bodies or two different locations of the same body through molecular vibrations is known as heat conduction.
The governing law for heat conduction is Fourier's law of heat conduction.
Fourier's law of heat conduction:
It states that 'The rate of heat transfer is directly proportional to the temperature gradient' and it is given as
\(q_k \propto -k\ × \frac{dT}{dx}\)
Where x = direction of heat flow, k = thermal conductivity, T = temperature
According to Fourier’s Law:
\(Q = - kA\frac{{dT}}{{dx}}\)
Calculation:
Given,
dx = 15 cm = 0.15 m, A = 0.02 m2, dT = 300°C, k = 50.2 W/mK.
\(Q = 50.2 \times 0.02 \times \frac{{300}}{{0..15}} \)
\(Q = 2008\;J/s = 2.008\;kJ/s\)
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