Effect of viscous dissipation on forced convection heat transfer in parallel plate channels with asymmetric boundary conditions

Abstract

Effect of viscous dissipation on steady two-dimensional laminar forced convection in hydrodynamically developed and thermally developing flow between asymmetrically heated parallel plates (the plates have been kept at unequal temperatures) has been studied. The asymmetric heating is characterized by an asymmetry parameter, A, defined as the ratio of wall temperatures in excess of the fluid inlet temperature. Viscous dissipation is characterized by the Brinkman number, Br. Br <0, when the fluid is being heated and Br >0 when the fluid is being cooled. Heating and cooling have been, defined on the basis of average the wall temperatures. When the walls are subjected to equal wall temperature (i.e., A = 1), it may be recalled that the limiting value for the Nusselt number is 17.5 when viscous dissipation is included (Br ≠ 0), and is independent of the Brinkman number, Br. Similarly, when viscous dissipation is not included, for the case of unequal wall temperatures, (i.e., A ≠ 1), the Nusselt number in the conduction limit is 4, and is independent of the value of A, not equal to one. In the present investigation, it has been shown that the local Nusselt number values in the thermally developing region as well as in the limiting condition, do vary continuously with Brinkman number when the plates are kept at unequal temperatures. The axial location where the Nusselt number displays an unbounded swing depends on the Brinkman number for a given A, and vice versa. The axial position where the Nusselt number displays an unbounded swing depends on the combination of Br and A values and differs from the position for A = 1, Br < 0, or A > 0, Br = 0.