Heat Transfer Questions & Answers  




Again, all the math should be written in LATEX. Don't attach a picture with mathematics. If there's a derivation you wish to discuss, then write it all here using LATEX.




Hmm, I am not sure if I am following you correctly. Why do you say the value for $m$ is $1/4$ to satisfy assumption (1) for an average $h$? This doesn't make sense. The value for $m$ is $1/5$ if ${\rm Gr}^*_x\lessapprox 10^{12}$ and $1/4$ otherwise. If you wish to integrate $h$ over a large Grashoff number range with a lower limit less than $10^{11}$ and an upper limit greater than $10^{13}$, then you need to split the integral in 2 and use two different $m$s. 0.5 point bonus for the effort.




You have to use the differential form when the integral form can not give you the answer. For instance, you may need it when trying to find $q^"$ just near the surface for a solid with a nonconstant thermal conductivity.




Hint: you don't need the data left of the block or within the block to find (a) or (b). You only need the temperature on the right side of the block. Think about it more.



$\pi$ 