Engineering

"To determine the heat flux across the plate and the actual surface temperature, we can use Fourier's Law of heat conduction:

q = -k dT/dX

q is the heat flux (W/m²)

k is the thermal conductivity of the material (W/(m·K))

dT/dX is the temperature gradient perpendicular to the direction of heat transfer (K/m)

Given that the fluids are maintained at constant bulk temperatures of 50°C and 10°C, and assuming steady-state conditions, the temperature gradient across the plate can be calculated as:

dT/dX = T hot -  T cold / L

T hot is the temperature of the hot fluid (50°C)

T cold is the temperature of the cold fluid (10°C)

L is the thickness of the plate"