Converting an equation to a standard 4th order polynomial.

[Shaun Jones]

I am trying to convert this equation into a fourth order polynomial (aTtop^4 + bTtop^3 + cTtop^2 + dTtop + e = 0).
I think I multiply each section by h/k?
Any help would be appreciated!

 

[yoscar04]

I am not sure what your problem is. Multiplying by h/k will leave you T_bot-T_top on the rhs. Your equation contains already a fourth order polynomial.

 

[HallsofIvy]

With yocar04's suggestion, multiplying by h/k, we have
$$-(h/k)(1- \alpha)F_{SW}- (h/k)F_{other}+ 0.95\cdot 5.67\cdot 10^{-8}(h/k) T_{top}^4= -T_{top}+ T_{bot}$$.

That can be written
$$0.95\cdot 5.67\cdot 10^{-8}(h/k) T_{top}^4+ T_{top}+ -(h/k)(1- \alpha)F_{SW}- (h/k)F_{other}- T_{bot}= 0$$.

That is precisely the form you want with $$a= 0.95\cdot 5.67\cdot 10^{-8}(h/k)$$, b=0, c= 0, d= 1, and $$e= -(h/k)(1- \alpha)F_{SW}- (h/k)F_{other}- T_{bot}$$.