| Summary: | The current study investigates the 2D entropy production and the mixed convection inside a wavy-walled chamber containing a rotating cylinder and a heat source. The heat source of finite-length <i>h</i> is placed in the middle of the left vertical surface in which its temperature is fixed at <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>h</mi> </msub> </semantics> </math> </inline-formula>. The temperature of the right vertical surface, however, is maintained at lower temperature <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula>. The remaining parts of the left surface and the wavy horizontal surfaces are perfectly insulated. The governing equations and the complex boundary conditions are non-dimensionalized and solved using the weighted residual finite element method, in particular, the Galerkin method. Various active parameters are considered, i.e., Rayleigh number <inline-formula> <math display="inline"> <semantics> <mrow> <mi>R</mi> <mi>a</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics> </math> </inline-formula>, number of oscillations: <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mo>≤</mo> <mi>N</mi> <mo>≤</mo> <mn>4</mn> </mrow> </semantics> </math> </inline-formula>, angular rotational velocity: <inline-formula> <math display="inline"> <semantics> <mrow> <mo>−</mo> <mn>1000</mn> <mo>≤</mo> <mo>Ω</mo> <mo>≤</mo> <mn>1000</mn> </mrow> </semantics> </math> </inline-formula>, and heat source length: <inline-formula> <math display="inline"> <semantics> <mrow> <mn>0</mn> <mo>.</mo> <mn>2</mn> <mo>≤</mo> <mi>H</mi> <mo>≤</mo> <mn>0</mn> <mo>.</mo> <mn>8</mn> </mrow> </semantics> </math> </inline-formula>. A mesh independence test is carried out and the result is validated against the benchmark solution. Results such as stream function, isotherms and entropy lines are plotted and we found that fluid flow can be controlled by manipulating the rotating velocity of the circular cylinder. For all the considered oscillation numbers, the Bejan number is the highest for the case involving a nearly stationary inner cylinder.
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