Question

A plane wall of thickness 2L= 30 mm and thermal conductivity k= 3 W/m·K experiences uniform volumetric heat generation at a rate q˙, while convection heat transfer occurs at both of its surfaces  (x=-L, +L), each of which is exposed to a fluid of temperature ∞T∞= 20°C. Under steady-state conditions, the temperature distribution in the wall is of the form T(x)=a+b⁢x+c⁢x2 where a= 82.0°C, b= -210°C/m, c= -2 × 10⁴°C/m², and x is in meters. The origin of the x-coordinate is at the midplane of the wall.

(a) What is the volumetric rate q˙ of heat generation in the wall?

(b) Determine the surface heat fluxes, qx"(-L)and qx"(+L).

(c) What are the convection coefficients for the surfaces at x=-L and x=+L?

Answer 1

3WImk 15 mm 0mm A(b12cx)