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In an experiment setup, mineral oil is filled in between the narrow gap of two horizontal smooth plates. The setup has arrangements to maintain the plates at desired uniform temperatures. At these temperatures, $ONLY$ the radiative heat flux is negligible. The thermal conductivity of the oil does not vary perceptibly in this temperature range. Consider four experiments at steady state under different experimental conditions, as shown in the figure below. The figure shows plate temperatures and the heat fluxes in the vertical direction.

What is the steady state heat flux (in $W\:m^{-2}$) with the top plate at $70^{\circ}C$ and the bottom plate at $40^{\circ}C$ ?

  1. $26$
  2. $39$
  3. $42$
  4. $63$
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