3 Numerical values of the temperature OC are shown at the gr

3. Numerical values of the temperature (OC) are shown at the grid nodes (uniform grid, distance between nodes l mm) from the output of a computer simulation for steady state convection from a solid plate (with uniform heat generation only restricted to the gray area) immersed in water assume properties from problem 2) at an ambient of 25.5 C Node T (OC) Solid 76.5 Water Plate 75.5 70.5 1 A 2 3 4 5 6 7 8 66 62 60 (a) Estimate the value for the local heat transfer coefficient at point A. (b) Estimate the value of the thermal conductivity of the plate. (c) If TB- 80 °C is the flow likely to be upwards or downwards? Explain in a couple of sentences

Solution

1) taking local equilibrium at the boundary, kdT/dx = -h ( Tw-Tamb)

k is 0.6 W/mK, dT/dx = (Node A- Node 2) =5, ( Tw-Tamb) = 50

k*5=h*50 ==> h = 0.1 W/m²K

2) using similar balance, K plate dT/dx = Kwater dT/dx

Kplate = Kwater DT _w/ DT_p    =0.6 * 5/1 =3 W/mK

3) all other qties same?