Every time I try to evaluate the integral, it fails to converge. Anyone who can solve this problem or have encountered a similar one?
Simplifying as a 1-D problem this should be straight forward. If the heat flux path (x-direction) is along the 6 in-path, the cross-sectional area is A=(0.09+2.91*x)*2,7=a+b*x. Using Fourier's law, q=-k*A*dT/dx and reshuffling you get dx/A=-k/q*dT, where the heat flow q is constant. The integration is straight forward and you get ln(a+b*x)/b = -k/q*T between the boundaries x=0;T=T1 and x=L; T=T2. using q=(T1-T2)/R you can find the resistance R.
you may refer this link. i am not sure whether this will help you or not
https://pdfs.semanticscholar.org/a1e4/095db2db4b22c0670496be9fc66c20c92b17.pdf
Simplifying as a 1-D problem this should be straight forward. If the heat flux path (x-direction) is along the 6 in-path, the cross-sectional area is A=(0.09+2.91*x)*2,7=a+b*x. Using Fourier's law, q=-k*A*dT/dx and reshuffling you get dx/A=-k/q*dT, where the heat flow q is constant. The integration is straight forward and you get ln(a+b*x)/b = -k/q*T between the boundaries x=0;T=T1 and x=L; T=T2. using q=(T1-T2)/R you can find the resistance R.
Hello Subham:
I will attach to you this paper where they calculate the thermal conductance and Seebeck Coefficient for pyramidal prisms, Hope it can help !
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